Examples
Basket Losses
GLHP Expected 10-Yr Losses:
29.6265
Gaussian Binomial Expected 10-Yr Losses:
25.8297
T Binomial Expected 10-Yr Losses:
25.6508
G Inhomogeneous Expected 10-Yr Losses:
26.111
Random G Expected 10-Yr Losses:
26.1135
Random T Expected 10-Yr Losses:
28.2459
Random Loss G Expected 10-Yr Losses:
24.058
Random Loss T Expected 10-Yr Losses:
23.6476
Base Correlation GLHP Expected 10-Yr Losses:
29.6265
Run completed in 1 m 25 s
Bermudan Swaption
G2 (analytic formulae) calibration
1x5: model 10.04549 %, market 11.48000 % (-1.43451 %)
2x4: model 10.51234 %, market 11.08000 % (-0.56766 %)
3x3: model 10.70500 %, market 10.70000 % (+0.00500 %)
4x2: model 10.83817 %, market 10.21000 % (+0.62817 %)
5x1: model 10.94387 %, market 10.00000 % (+0.94387 %)
calibrated to:
a = 0.050053, sigma = 0.0094424
b = 0.05005, eta = 0.0094424
rho = -0.76301
Hull-White (analytic formulae) calibration
1x5: model 10.62037 %, market 11.48000 % (-0.85963 %)
2x4: model 10.62959 %, market 11.08000 % (-0.45041 %)
3x3: model 10.63414 %, market 10.70000 % (-0.06586 %)
4x2: model 10.64428 %, market 10.21000 % (+0.43428 %)
5x1: model 10.66132 %, market 10.00000 % (+0.66132 %)
calibrated to:
a = 0.046414, sigma = 0.0058693
Hull-White (numerical) calibration
1x5: model 10.31185 %, market 11.48000 % (-1.16815 %)
2x4: model 10.54619 %, market 11.08000 % (-0.53381 %)
3x3: model 10.66914 %, market 10.70000 % (-0.03086 %)
4x2: model 10.74020 %, market 10.21000 % (+0.53020 %)
5x1: model 10.79725 %, market 10.00000 % (+0.79725 %)
calibrated to:
a = 0.055229, sigma = 0.0061063
Black-Karasinski (numerical) calibration
1x5: model 10.32593 %, market 11.48000 % (-1.15407 %)
2x4: model 10.56575 %, market 11.08000 % (-0.51425 %)
3x3: model 10.67858 %, market 10.70000 % (-0.02142 %)
4x2: model 10.73678 %, market 10.21000 % (+0.52678 %)
5x1: model 10.77792 %, market 10.00000 % (+0.77792 %)
calibrated to:
a = 0.043389, sigma = 0.12075
Payer bermudan swaption struck at 5.00000 % (ATM)
G2 (tree): 14.11
G2 (fdm) : 14.112
HW (tree): 12.904
HW (fdm) : 12.91
HW (num, tree): 13.158
HW (num, fdm) : 13.157
BK: 13.002
Payer bermudan swaption struck at 6.00000 % (OTM)
G2 (tree): 3.194
G2 (fdm) : 3.1808
HW (tree): 2.4921
HW (fdm) : 2.4596
HW (num, tree): 2.615
HW (num, fdm): 2.5829
BK: 3.2751
Payer bermudan swaption struck at 4.00000 % (ITM)
G2 (tree): 42.609
G2 (fdm) : 42.705
HW (tree): 42.253
HW (fdm) : 42.215
HW (num, tree): 42.364
HW (num, fdm) : 42.311
BK: 41.825
Run completed in 5 m 31 s
Bonds
Today: Monday, September 15th, 2008
Settlement date: Thursday, September 18th, 2008
ZC Fixed Floating
------------------------------------------------
Net present value 100.92 107.67 102.36
Clean price 100.92 106.13 101.80
Dirty price 100.92 107.67 102.36
Accrued coupon 0.00 1.54 0.56
Previous coupon N/A 4.50 % 2.89 %
Next coupon N/A 4.50 % 3.43 %
Yield 3.00 % 3.65 % 2.20 %
Sample indirect computations (for the floating rate bond):
------------------------------------------------
Yield to Clean Price: 101.80
Clean Price to Yield: 2.20 %
Run completed in 1 s
Callable bonds
Pricing a callable fixed rate bond using
Hull White model w/ reversion parameter = 0.03
BAC4.65 09/15/12 ISIN: US06060WBJ36
roughly five year tenor, quarterly coupon and call dates
reference date is : October 16th, 2007
sigma/vol (%) = 0.00
QuantLib price/yld (%) 96.47 / 5.48
Bloomberg price/yld (%) 96.50 / 5.47
sigma/vol (%) = 1.00
QuantLib price/yld (%) 95.64 / 5.67
Bloomberg price/yld (%) 95.68 / 5.66
sigma/vol (%) = 3.00
QuantLib price/yld (%) 92.31 / 6.49
Bloomberg price/yld (%) 92.34 / 6.49
sigma/vol (%) = 6.00
QuantLib price/yld (%) 87.08 / 7.85
Bloomberg price/yld (%) 87.16 / 7.83
sigma/vol (%) = 12.00
QuantLib price/yld (%) 77.34 / 10.64
Bloomberg price/yld (%) 77.31 / 10.65
Run completed in 1. s
CDS
***** Running example #1 *****
Calibrated hazard rate values:
hazard rate on May 15th, 2007 is 0.0299689
hazard rate on September 20th, 2007 is 0.0299689
hazard rate on December 20th, 2007 is 0.0299613
hazard rate on June 20th, 2008 is 0.0299619
hazard rate on June 22nd, 2009 is 0.0299607
Some survival probability values:
1Y survival probability: 97.040061 %
expected: 97.040000 %
2Y survival probability: 94.175780 %
expected: 94.180000 %
Repricing of quoted CDSs employed for calibration:
3M fair spread: 1.500000 %
NPV: -7.18501e-11
default leg: -5218.16
coupon leg: 5218.16
6M fair spread: 1.500000 %
NPV: -1.52795e-10
default leg: -8882.83
coupon leg: 8882.83
1Y fair spread: 1.500000 %
NPV: -2.05728e-09
default leg: -16142.9
coupon leg: 16142.9
2Y fair spread: 1.500000 %
NPV: -6.25732e-10
default leg: -30195.6
coupon leg: 30195.6
Run completed in 0 s
***** Running example #2 *****
September 22nd, 2014
December 22nd, 2014
March 20th, 2015
June 22nd, 2015
September 21st, 2015
December 21st, 2015
March 21st, 2016
June 20th, 2016
September 20th, 2016
December 20th, 2016
ISDA rate curve:
November 24th, 2014 0.000061 0.999994
December 23rd, 2014 0.000444 0.999923
January 23rd, 2015 0.000805 0.999793
April 23rd, 2015 0.001845 0.999070
July 23rd, 2015 0.002575 0.998062
October 23rd, 2015 0.003393 0.996594
October 24th, 2016 0.002217 0.995551
October 23rd, 2017 0.002749 0.991764
October 23rd, 2018 0.003521 0.985986
October 23rd, 2019 0.004516 0.977637
October 23rd, 2020 0.005725 0.966173
October 25th, 2021 0.007076 0.951562
October 24th, 2022 0.008480 0.934305
October 23rd, 2023 0.009823 0.915290
October 23rd, 2024 0.011050 0.895248
October 23rd, 2026 0.013130 0.854070
October 23rd, 2029 0.015384 0.793724
October 23rd, 2034 0.017604 0.702988
October 24th, 2044 0.018849 0.567776
first period = September 22nd, 2014 to December 22nd, 2014 accrued amount = 8888
8.888889
reference trade NPV = -43769.625488
ISDA credit curve:
June 21st, 2019;0.051655;0.948345;0.011361
***** Running example #3 *****
ISDA yield curve:
date;time;zeroyield
July 15th, 2011;0.087671;0.004511
August 15th, 2011;0.172603;0.009452
September 15th, 2011;0.257534;0.012322
December 15th, 2011;0.506849;0.017781
March 15th, 2012;0.756164;0.019367
June 15th, 2012;1.008219;0.020820
June 17th, 2013;2.013699;0.016293
June 16th, 2014;3.010959;0.019975
June 15th, 2015;4.008219;0.022863
June 15th, 2016;5.010959;0.025119
June 15th, 2017;6.010959;0.026883
June 15th, 2018;7.010959;0.028224
June 17th, 2019;8.016438;0.029336
June 15th, 2020;9.013699;0.030236
June 15th, 2021;10.013699;0.031038
June 15th, 2022;11.013699;0.031776
June 15th, 2023;12.013699;0.032565
June 15th, 2026;15.016438;0.034070
June 16th, 2031;20.021918;0.034506
June 16th, 2036;25.027397;0.034206
June 17th, 2041;30.032877;0.034108
ISDA credit curve:
date;time;survivalprob
December 21st, 2011;0.523288;0.993032
June 21st, 2012;1.024658;0.986405
June 21st, 2014;3.024658;0.939078
June 21st, 2016;5.027397;0.862452
June 21st, 2018;7.027397;0.788519
June 22nd, 2021;10.032877;0.690297
Convertable bonds
option type = Put
Time to maturity = 5.00548
Underlying price = 36
Risk-free interest rate = 6.000000 %
Dividend yield = 2.000000 %
Volatility = 20.000000 %
===============================================================
Tsiveriotis-Fernandes method
===============================================================
Tree type European American
---------------------------------------------------------------
Jarrow-Rudd 105.690610 108.160895
Cox-Ross-Rubinstein 105.698303 108.154477
Additive equiprobabilities 105.626150 108.104772
Trigeorgis 105.698806 108.154914
Tian 105.712595 108.164054
Leisen-Reimer 105.668164 108.168380
Joshi 105.668165 108.168381
===============================================================
Run completed in 15 s
CVAIRS
-- Correction in the contract fix rate in bp --
5 | 3.249 % | -0.24 | -0.87 | -2.10
10 | 4.074 % | -2.15 | -5.62 | -11.65
15 | 4.463 % | -4.60 | -10.41 | -19.60
20 | 4.675 % | -6.94 | -14.57 | -25.67
25 | 4.775 % | -8.79 | -17.63 | -29.62
30 | 4.811 % | -10.16 | -19.73 | -32.00
Run completed in 2 m 34 s
Discrete hedging
Option value: 2.51207
| | P&L | P&L | Derman&Kamal | P&L | P&L
samples | trades | mean | std.dev. | formula | skewness | kurtosis
------------------------------------------------------------------------------
50000 | 21 | 0.001 | 0.43 | 0.44 | -0.29 | 1.45
50000 | 84 | 0.001 | 0.22 | 0.22 | -0.18 | 1.83
Run completed in 2 m 14 s
Equity Option
Option type = Put
Maturity = May 17th, 1999
Underlying price = 36
Strike = 40
Risk-free interest rate = 6.000000 %
Dividend yield = 0.000000 %
Volatility = 20.000000 %
Method European Bermudan American
Black-Scholes 3.844308 N/A N/A
Heston semi-analytic 3.844306 N/A N/A
Bates semi-analytic 3.844306 N/A N/A
Barone-Adesi/Whaley N/A N/A 4.459628
Bjerksund/Stensland N/A N/A 4.453064
Integral 3.844309 N/A N/A
Finite differences 3.844342 4.360807 4.486118
Binomial Jarrow-Rudd 3.844132 4.361174 4.486552
Binomial Cox-Ross-Rubinstein 3.843504 4.360861 4.486415
Additive equiprobabilities 3.836911 4.354455 4.480097
Binomial Trigeorgis 3.843557 4.360909 4.486461
Binomial Tian 3.844171 4.361176 4.486413
Binomial Leisen-Reimer 3.844308 4.360713 4.486076
Binomial Joshi 3.844308 4.360713 4.486076
MC (crude) 3.834522 N/A N/A
QMC (Sobol) 3.844613 N/A N/A
MC (Longstaff Schwartz) N/A N/A 4.456935
Run completed in 2 m 4 s
Fitted bond curve
Today's date: December 10th, 2019
Bonds' settlement date: December 10th, 2019
Calculating fit for 15 bonds.....
(a) exponential splines
reference date : December 10th, 2019
number of iterations : 7114
(b) simple polynomial
reference date : December 10th, 2019
number of iterations : 278
(c) Nelson-Siegel
reference date : December 10th, 2019
number of iterations : 1224
(d) cubic B-splines
reference date : December 10th, 2019
number of iterations : 778
(e) Svensson
reference date : December 10th, 2019
number of iterations : 2892
(f) Nelson-Siegel spreaded
reference date : December 10th, 2019
number of iterations : 1689
Output par rates for each curve. In this case,
par rates should equal coupons for these par bonds.
tenor | coupon | bstrap | (a) | (b) | (c) | (d) | (e) | (f)
2.000 | 2.000 | 2.000 | 1.995 | 2.010 | 2.060 | 1.771 | 2.008 | 2.060
4.003 | 2.250 | 2.250 | 2.252 | 2.256 | 2.266 | 2.398 | 2.225 | 2.266
6.000 | 2.500 | 2.500 | 2.504 | 2.501 | 2.484 | 2.657 | 2.511 | 2.484
8.000 | 2.750 | 2.750 | 2.754 | 2.746 | 2.716 | 2.748 | 2.771 | 2.716
10.000 | 3.000 | 3.000 | 3.002 | 2.993 | 2.959 | 2.905 | 3.012 | 2.959
12.000 | 3.250 | 3.250 | 3.250 | 3.241 | 3.214 | 3.195 | 3.247 | 3.214
14.006 | 3.500 | 3.500 | 3.498 | 3.491 | 3.477 | 3.522 | 3.486 | 3.477
16.000 | 3.750 | 3.750 | 3.747 | 3.742 | 3.745 | 3.796 | 3.731 | 3.745
18.000 | 4.000 | 4.000 | 3.996 | 3.996 | 4.016 | 4.016 | 3.984 | 4.016
20.006 | 4.250 | 4.250 | 4.248 | 4.252 | 4.286 | 4.232 | 4.246 | 4.286
22.000 | 4.500 | 4.500 | 4.500 | 4.507 | 4.548 | 4.478 | 4.510 | 4.548
24.000 | 4.750 | 4.750 | 4.752 | 4.761 | 4.797 | 4.745 | 4.772 | 4.797
26.003 | 5.000 | 5.000 | 5.004 | 5.012 | 5.029 | 5.014 | 5.025 | 5.029
28.000 | 5.250 | 5.250 | 5.252 | 5.254 | 5.236 | 5.267 | 5.258 | 5.236
30.000 | 5.500 | 5.500 | 5.496 | 5.485 | 5.416 | 5.485 | 5.464 | 5.416
Now add 23 months to today. Par rates should be
automatically recalculated because today's date
changes. Par rates will NOT equal coupons (YTM
will, with the correct compounding), but the
piecewise yield curve par rates can be used as
a benchmark for correct par rates.
(a) exponential splines
reference date : November 10th, 2021
number of iterations : 908
(b) simple polynomial
reference date : November 10th, 2021
number of iterations : 265
(c) Nelson-Siegel
reference date : November 10th, 2021
number of iterations : 898
(d) cubic B-splines
reference date : November 10th, 2021
number of iterations : 649
(e) Svensson
reference date : November 10th, 2021
number of iterations : 3254
(f) Nelson-Siegel spreaded
reference date : November 10th, 2021
number of iterations : 908
tenor | coupon | bstrap | (a) | (b) | (c) | (d) | (e) | (f)
0.083 | 2.000 | 1.964 | 1.968 | 1.983 | 2.025 | 1.310 | 1.964 | 2.025
2.086 | 2.250 | 2.248 | 2.244 | 2.249 | 2.256 | 2.334 | 2.235 | 2.256
4.083 | 2.500 | 2.499 | 2.499 | 2.496 | 2.481 | 2.908 | 2.530 | 2.481
6.083 | 2.750 | 2.749 | 2.751 | 2.743 | 2.717 | 3.013 | 2.765 | 2.717
8.083 | 3.000 | 2.999 | 3.000 | 2.991 | 2.962 | 2.949 | 2.996 | 2.962
10.083 | 3.250 | 3.249 | 3.249 | 3.239 | 3.217 | 3.053 | 3.232 | 3.217
12.089 | 3.500 | 3.499 | 3.498 | 3.491 | 3.480 | 3.404 | 3.478 | 3.480
14.083 | 3.750 | 3.749 | 3.747 | 3.742 | 3.746 | 3.804 | 3.730 | 3.746
16.083 | 4.000 | 4.000 | 3.997 | 3.997 | 4.014 | 4.089 | 3.990 | 4.014
18.089 | 4.250 | 4.249 | 4.249 | 4.253 | 4.281 | 4.268 | 4.254 | 4.281
20.083 | 4.500 | 4.500 | 4.500 | 4.507 | 4.541 | 4.454 | 4.517 | 4.541
22.083 | 4.750 | 4.750 | 4.752 | 4.761 | 4.790 | 4.718 | 4.776 | 4.790
24.086 | 5.000 | 4.999 | 5.004 | 5.011 | 5.025 | 5.014 | 5.023 | 5.025
26.083 | 5.250 | 5.249 | 5.252 | 5.254 | 5.239 | 5.277 | 5.253 | 5.239
28.083 | 5.500 | 5.499 | 5.495 | 5.484 | 5.430 | 5.485 | 5.460 | 5.430
Now add one more month, for a total of two years
from the original date. The first instrument is
now expired and par rates should again equal
coupon values, since clean prices did not change.
(a) exponential splines
reference date : December 10th, 2021
number of iterations : 1871
(b) simple polynomial
reference date : December 10th, 2021
number of iterations : 271
(c) Nelson-Siegel
reference date : December 10th, 2021
number of iterations : 1010
(d) cubic B-splines
reference date : December 10th, 2021
number of iterations : 725
(e) Svensson
reference date : December 10th, 2021
number of iterations : 3380
(f) Nelson-Siegel spreaded
reference date : December 10th, 2021
number of iterations : 1561
tenor | coupon | bstrap | (a) | (b) | (c) | (d) | (e) | (f)
2.003 | 2.250 | 2.250 | 2.251 | 2.260 | 2.294 | 2.013 | 2.254 | 2.294
4.000 | 2.500 | 2.500 | 2.499 | 2.505 | 2.508 | 2.659 | 2.483 | 2.508
6.000 | 2.750 | 2.750 | 2.749 | 2.749 | 2.734 | 2.918 | 2.760 | 2.734
8.000 | 3.000 | 3.000 | 3.000 | 2.995 | 2.971 | 2.998 | 3.014 | 2.971
10.000 | 3.250 | 3.250 | 3.250 | 3.242 | 3.219 | 3.149 | 3.256 | 3.219
12.006 | 3.500 | 3.500 | 3.501 | 3.492 | 3.476 | 3.445 | 3.495 | 3.476
14.000 | 3.750 | 3.750 | 3.750 | 3.742 | 3.738 | 3.776 | 3.738 | 3.738
16.000 | 4.000 | 4.000 | 4.000 | 3.995 | 4.005 | 4.049 | 3.987 | 4.005
18.006 | 4.250 | 4.250 | 4.250 | 4.251 | 4.272 | 4.262 | 4.244 | 4.272
20.000 | 4.500 | 4.500 | 4.499 | 4.505 | 4.533 | 4.475 | 4.503 | 4.533
22.000 | 4.750 | 4.750 | 4.750 | 4.759 | 4.786 | 4.731 | 4.763 | 4.786
24.003 | 5.000 | 5.000 | 5.000 | 5.010 | 5.025 | 5.007 | 5.017 | 5.025
26.000 | 5.250 | 5.250 | 5.250 | 5.254 | 5.244 | 5.266 | 5.258 | 5.244
28.000 | 5.500 | 5.500 | 5.500 | 5.487 | 5.441 | 5.492 | 5.477 | 5.441
Now decrease prices by a small amount, corresponding
to a theoretical five basis point parallel + shift of
the yield curve. Because bond quotes change, the new
par rates should be recalculated automatically.
tenor | coupon | bstrap | (a) | (b) | (c) | (d) | (e) | (f)
2.003 | 2.250 | 2.299 | 2.299 | 2.311 | 2.344 | 2.060 | 2.303 | 2.344
4.000 | 2.500 | 2.550 | 2.549 | 2.554 | 2.557 | 2.710 | 2.533 | 2.557
6.000 | 2.750 | 2.800 | 2.799 | 2.798 | 2.783 | 2.970 | 2.810 | 2.783
8.000 | 3.000 | 3.050 | 3.049 | 3.043 | 3.020 | 3.047 | 3.064 | 3.020
10.000 | 3.250 | 3.299 | 3.299 | 3.290 | 3.267 | 3.197 | 3.305 | 3.267
12.006 | 3.500 | 3.547 | 3.549 | 3.539 | 3.524 | 3.492 | 3.543 | 3.524
14.000 | 3.750 | 3.798 | 3.798 | 3.790 | 3.786 | 3.824 | 3.785 | 3.786
16.000 | 4.000 | 4.048 | 4.047 | 4.043 | 4.052 | 4.097 | 4.034 | 4.052
18.006 | 4.250 | 4.296 | 4.297 | 4.298 | 4.319 | 4.309 | 4.290 | 4.319
20.000 | 4.500 | 4.547 | 4.546 | 4.552 | 4.580 | 4.522 | 4.549 | 4.580
22.000 | 4.750 | 4.797 | 4.795 | 4.806 | 4.832 | 4.777 | 4.809 | 4.832
24.003 | 5.000 | 5.044 | 5.046 | 5.056 | 5.070 | 5.052 | 5.063 | 5.070
26.000 | 5.250 | 5.296 | 5.295 | 5.299 | 5.289 | 5.311 | 5.303 | 5.289
28.000 | 5.500 | 5.545 | 5.545 | 5.531 | 5.485 | 5.537 | 5.522 | 5.485
Run completed in 14 s
FRA
Today: Tuesday, May 23rd, 2006
Settlement date: Thursday, May 25th, 2006
Test FRA construction, NPV calculation, and FRA purchase
3m Term FRA, Months to Start: 1
strike FRA rate: 3.000000 %
FRA 3m forward rate: 3.000000 % Actual/360 simple compounding
FRA market quote: 3.000000 %
FRA spot value: 99.7347
FRA forward value: 100.767
FRA implied Yield: 3.003993 % Actual/360 simple compounding
market Zero Rate: 3.003993 % Actual/360 simple compounding
FRA NPV [should be zero]: 0
3m Term FRA, Months to Start: 2
strike FRA rate: 3.100000 %
FRA 3m forward rate: 3.100000 % Actual/360 simple compounding
FRA market quote: 3.100000 %
FRA spot value: 99.4949
FRA forward value: 100.792
FRA implied Yield: 3.068054 % Actual/360 simple compounding
market Zero Rate: 3.068054 % Actual/360 simple compounding
FRA NPV [should be zero]: 0
3m Term FRA, Months to Start: 3
strike FRA rate: 3.200000 %
FRA 3m forward rate: 3.200000 % Actual/360 simple compounding
FRA market quote: 3.200000 %
FRA spot value: 99.2392
FRA forward value: 100.836
FRA implied Yield: 3.113474 % Actual/360 simple compounding
market Zero Rate: 3.113474 % Actual/360 simple compounding
FRA NPV [should be zero]: 0
3m Term FRA, Months to Start: 6
strike FRA rate: 3.300000 %
FRA 3m forward rate: 3.300000 % Actual/360 simple compounding
FRA market quote: 3.300000 %
FRA spot value: 98.4168
FRA forward value: 100.843
FRA implied Yield: 3.192770 % Actual/360 simple compounding
market Zero Rate: 3.192770 % Actual/360 simple compounding
FRA NPV [should be zero]: 1.38689e-14
3m Term FRA, Months to Start: 9
strike FRA rate: 3.400000 %
FRA 3m forward rate: 3.400000 % Actual/360 simple compounding
FRA market quote: 3.400000 %
FRA spot value: 97.6027
FRA forward value: 100.859
FRA implied Yield: 3.264191 % Actual/360 simple compounding
market Zero Rate: 3.264191 % Actual/360 simple compounding
FRA NPV [should be zero]: 2.7504e-14
Now take a 100 basis-point upward shift in FRA quotes and examine NPV
3m Term FRA, 100 notional, Months to Start = 1
strike FRA rate: 3.000000 %
FRA 3m forward rate: 4.000000 % Actual/360 simple compounding
FRA market quote: 4.000000 %
FRA spot value: 99.6469
FRA forward value: 101.022
FRA implied Yield: 4.007095 % Actual/360 simple compounding
market Zero Rate: 4.007095 % Actual/360 simple compounding
FRA NPV [should be positive]: 0.252076
3m Term FRA, 100 notional, Months to Start = 2
strike FRA rate: 3.100000 %
FRA 3m forward rate: 4.100000 % Actual/360 simple compounding
FRA market quote: 4.100000 %
FRA spot value: 99.3279
FRA forward value: 101.048
FRA implied Yield: 4.074078 % Actual/360 simple compounding
market Zero Rate: 4.074078 % Actual/360 simple compounding
FRA NPV [should be positive]: 0.251206
3m Term FRA, 100 notional, Months to Start = 3
strike FRA rate: 3.200000 %
FRA 3m forward rate: 4.200000 % Actual/360 simple compounding
FRA market quote: 4.200000 %
FRA spot value: 98.9881
FRA forward value: 101.097
FRA implied Yield: 4.122773 % Actual/360 simple compounding
market Zero Rate: 4.122773 % Actual/360 simple compounding
FRA NPV [should be positive]: 0.255665
3m Term FRA, 100 notional, Months to Start = 6
strike FRA rate: 3.300000 %
FRA 3m forward rate: 4.300000 % Actual/360 simple compounding
FRA market quote: 4.300000 %
FRA spot value: 97.9143
FRA forward value: 101.099
FRA implied Yield: 4.211735 % Actual/360 simple compounding
market Zero Rate: 4.211735 % Actual/360 simple compounding
FRA NPV [should be positive]: 0.247506
3m Term FRA, 100 notional, Months to Start = 9
strike FRA rate: 3.400000 %
FRA 3m forward rate: 4.400000 % Actual/360 simple compounding
FRA market quote: 4.400000 %
FRA spot value: 96.8616
FRA forward value: 101.112
FRA implied Yield: 4.292991 % Actual/360 simple compounding
market Zero Rate: 4.292991 % Actual/360 simple compounding
FRA NPV [should be positive]: 0.242151
Run completed in 1 s
Gaussian 1D models
Gaussian1dModel Examples
This is some example code showing how to use the GSR
(Gaussian short rate) and Markov Functional model.
The evaluation date for this example is set to April 30th, 2014
We assume a multicurve setup, for simplicity with flat yield
term structures. The discounting curve is an Eonia curve at
a level of 0.02 and the forwarding curve is an Euribior 6m curve
at a level of 0.025
For the volatility we assume a flat swaption volatility at 0.2
We consider a standard 10y bermudan payer swaption
with yearly exercises at a strike of 0.04
The model is a one factor Hull White model with piecewise
volatility adapted to our exercise dates.
The reversion is just kept constant at a level of 0.01
The model's curve is set to the 6m forward curve. Note that
the model adapts automatically to other curves where appropriate
(e.g. if an index requires a different forwarding curve) or
where explicitly specified (e.g. in a swaption pricing engine).
The engine can generate a calibration basket in two modes.
The first one is called Naive and generates ATM swaptions adapted to
the exercise dates of the swaption and its maturity date
The resulting basket looks as follows:
Expiry Maturity Nominal Rate Pay/Rec Market ivol
==================================================================================================
April 30th, 2015 May 6th, 2024 1.000000 0.025307 Receiver 0.200000
May 3rd, 2016 May 6th, 2024 1.000000 0.025300 Receiver 0.200000
May 3rd, 2017 May 6th, 2024 1.000000 0.025303 Receiver 0.200000
May 3rd, 2018 May 6th, 2024 1.000000 0.025306 Receiver 0.200000
May 2nd, 2019 May 6th, 2024 1.000000 0.025311 Receiver 0.200000
April 30th, 2020 May 6th, 2024 1.000000 0.025300 Receiver 0.200000
May 3rd, 2021 May 6th, 2024 1.000000 0.025306 Receiver 0.200000
May 3rd, 2022 May 6th, 2024 1.000000 0.025318 Receiver 0.200000
May 3rd, 2023 May 6th, 2024 1.000000 0.025353 Receiver 0.200000
(this step took 0.0s)
Let's calibrate our model to this basket. We use a specialized
calibration method calibrating the sigma function one by one to
the calibrating vanilla swaptions. The result of this is as follows:
Expiry Model sigma Model price market price Model ivol Market ivol
====================================================================================================
April 30th, 2015 0.005178 0.016111 0.016111 0.199999 0.200000
May 3rd, 2016 0.005156 0.020062 0.020062 0.200000 0.200000
May 3rd, 2017 0.005149 0.021229 0.021229 0.200000 0.200000
May 3rd, 2018 0.005129 0.020738 0.020738 0.200000 0.200000
May 2nd, 2019 0.005132 0.019096 0.019096 0.200000 0.200000
April 30th, 2020 0.005074 0.016537 0.016537 0.200000 0.200000
May 3rd, 2021 0.005091 0.013253 0.013253 0.200000 0.200000
May 3rd, 2022 0.005097 0.009342 0.009342 0.200000 0.200000
May 3rd, 2023 0.005001 0.004910 0.004910 0.200000 0.200000
(this step took 1.1s)
Finally we price our bermudan swaption in the calibrated model:
Bermudan swaption NPV (ATM calibrated GSR) = 0.003808
(this step took 0.2s)
There is another mode to generate a calibration basket called
MaturityStrikeByDeltaGamma. This means that the maturity,
the strike and the nominal of the calibrating swaption are
computed such that the npv and its first and second
derivative with respect to the model's state variable) of
the exotics underlying match with the calibrating swaption's
underlying. Let's try this in our case.
Expiry Maturity Nominal Rate Pay/Rec Market ivol
==================================================================================================
April 30th, 2015 May 6th, 2024 1.000016 0.040000 Payer 0.200000
May 3rd, 2016 May 6th, 2024 1.000000 0.040000 Payer 0.200000
May 3rd, 2017 May 6th, 2024 1.000002 0.040000 Payer 0.200000
May 3rd, 2018 May 7th, 2024 0.999948 0.040000 Payer 0.200000
May 2nd, 2019 May 6th, 2024 0.999916 0.040000 Payer 0.200000
April 30th, 2020 May 6th, 2024 0.999992 0.040000 Payer 0.200000
May 3rd, 2021 May 6th, 2024 0.999997 0.040000 Payer 0.200000
May 3rd, 2022 May 6th, 2024 1.000003 0.040000 Payer 0.200000
May 3rd, 2023 May 6th, 2024 1.000002 0.040000 Payer 0.200000
(this step took 0.2s)
The calibrated nominal is close to the exotics nominal.
The expiries and maturity dates of the vanillas are the same
as in the case above. The difference is the strike which
is now equal to the exotics strike.
Let's see how this affects the exotics npv. The
recalibrated model is:
Expiry Model sigma Model price market price Model ivol Market ivol
====================================================================================================
April 30th, 2015 0.006508 0.000191 0.000191 0.200000 0.200000
May 3rd, 2016 0.006502 0.001412 0.001412 0.200000 0.200000
May 3rd, 2017 0.006480 0.002905 0.002905 0.200000 0.200000
May 3rd, 2018 0.006464 0.004091 0.004091 0.200000 0.200000
May 2nd, 2019 0.006422 0.004766 0.004766 0.200000 0.200000
April 30th, 2020 0.006445 0.004869 0.004869 0.200000 0.200000
May 3rd, 2021 0.006433 0.004433 0.004433 0.200000 0.200000
May 3rd, 2022 0.006332 0.003454 0.003454 0.200000 0.200000
May 3rd, 2023 0.006295 0.001973 0.001973 0.200000 0.200000
(this step took 1.1s)
And the bermudan's price becomes:
Bermudan swaption NPV (deal strike calibrated GSR) = 0.007627
(this step took 0.3s)
We can do more complicated things, let's e.g. modify the
nominal schedule to be linear amortizing and see what
the effect on the generated calibration basket is:
Expiry Maturity Nominal Rate Pay/Rec Market ivol
==================================================================================================
April 30th, 2015 August 5th, 2021 0.719224 0.039997 Payer 0.200000
May 3rd, 2016 December 6th, 2021 0.641976 0.040003 Payer 0.200000
May 3rd, 2017 May 5th, 2022 0.564398 0.040005 Payer 0.200000
May 3rd, 2018 September 7th, 2022 0.486535 0.040004 Payer 0.200000
May 2nd, 2019 January 6th, 2023 0.409769 0.040008 Payer 0.200000
April 30th, 2020 May 5th, 2023 0.334095 0.039994 Payer 0.200000
May 3rd, 2021 September 5th, 2023 0.255760 0.039995 Payer 0.200000
May 3rd, 2022 January 5th, 2024 0.177038 0.040031 Payer 0.200000
May 3rd, 2023 May 6th, 2024 0.100001 0.040000 Payer 0.200000
(this step took 0.2s)
The notional is weighted over the underlying exercised
into and the maturity is adjusted downwards. The rate
on the other hand is not affected.
You can also price exotic bond's features. If you have e.g. a
bermudan callable fixed bond you can set up the call right
as a swaption to enter into a one leg swap with notional
reimbursement at maturity.
The exercise should then be written as a rebated exercise
paying the notional in case of exercise.
The calibration basket looks like this:
Expiry Maturity Nominal Rate Pay/Rec Market ivol
==================================================================================================
April 30th, 2015 April 5th, 2024 0.984098 0.039952 Payer 0.200000
May 3rd, 2016 April 5th, 2024 0.985543 0.039952 Payer 0.200000
May 3rd, 2017 May 6th, 2024 0.987059 0.039952 Payer 0.200000
May 3rd, 2018 May 7th, 2024 0.988461 0.039952 Payer 0.200000
May 2nd, 2019 May 6th, 2024 0.990032 0.039952 Payer 0.200000
April 30th, 2020 May 6th, 2024 0.991642 0.039951 Payer 0.200000
May 3rd, 2021 May 6th, 2024 0.993098 0.039951 Payer 0.200000
May 3rd, 2022 May 6th, 2024 0.994219 0.039952 Payer 0.200000
May 3rd, 2023 May 6th, 2024 0.996639 0.039950 Payer 0.200000
(this step took 0.2s)
Note that nominals are not exactly 1.0 here. This is
because we do our bond discounting on 6m level while
the swaptions are still discounted on OIS level.
(You can try this by changing the OIS level to the
6m level, which will produce nominals near 1.0).
The npv of the call right is (after recalibrating the model)
Bond's bermudan call right npv = 0.115409
(this step took 1.1s)
Up to now, no credit spread is included in the pricing.
We can do so by specifying an oas in the pricing engine.
Let's set the spread level to 100bp and regenerate
the calibration basket.
Expiry Maturity Nominal Rate Pay/Rec Market ivol
==================================================================================================
April 30th, 2015 February 5th, 2024 0.961281 0.029608 Payer 0.200000
May 3rd, 2016 March 5th, 2024 0.965325 0.029605 Payer 0.200000
May 3rd, 2017 April 5th, 2024 0.969536 0.029608 Payer 0.200000
May 3rd, 2018 April 8th, 2024 0.973640 0.029610 Payer 0.200000
May 2nd, 2019 April 8th, 2024 0.978106 0.029608 Payer 0.200000
April 30th, 2020 May 6th, 2024 0.982683 0.029612 Payer 0.200000
May 3rd, 2021 May 6th, 2024 0.987289 0.029609 Payer 0.200000
May 3rd, 2022 May 6th, 2024 0.991374 0.029603 Payer 0.200000
May 3rd, 2023 May 6th, 2024 0.996570 0.029586 Payer 0.200000
(this step took 0.2s)
The adjusted basket takes the credit spread into account.
This is consistent to a hedge where you would have a
margin on the float leg around 100bp,too.
The npv becomes:
Bond's bermudan call right npv (oas = 100bp) = 0.044980
(this step took 1.2s)
The next instrument we look at is a CMS 10Y vs Euribor
6M swaption. The maturity is again 10 years and the option
is exercisable on a yearly basis
Since the underlying is quite exotic already, we start with
pricing this using the LinearTsrPricer for CMS coupon estimation
Underlying CMS Swap NPV = 0.004447
CMS Leg NPV = -0.231736
Euribor Leg NPV = 0.236183
(this step took 0.0s)
We generate a naive calibration basket and calibrate
the GSR model to it:
Expiry Maturity Nominal Rate Pay/Rec Market ivol
==================================================================================================
April 30th, 2015 May 6th, 2024 1.000000 0.025307 Receiver 0.200000
May 3rd, 2016 May 6th, 2024 1.000000 0.025300 Receiver 0.200000
May 3rd, 2017 May 6th, 2024 1.000000 0.025303 Receiver 0.200000
May 3rd, 2018 May 6th, 2024 1.000000 0.025306 Receiver 0.200000
May 2nd, 2019 May 6th, 2024 1.000000 0.025311 Receiver 0.200000
April 30th, 2020 May 6th, 2024 1.000000 0.025300 Receiver 0.200000
May 3rd, 2021 May 6th, 2024 1.000000 0.025306 Receiver 0.200000
May 3rd, 2022 May 6th, 2024 1.000000 0.025318 Receiver 0.200000
May 3rd, 2023 May 6th, 2024 1.000000 0.025353 Receiver 0.200000
Expiry Model sigma Model price market price Model ivol Market ivol
====================================================================================================
April 30th, 2015 0.005178 0.016111 0.016111 0.200000 0.200000
May 3rd, 2016 0.005156 0.020062 0.020062 0.200000 0.200000
May 3rd, 2017 0.005149 0.021229 0.021229 0.200000 0.200000
May 3rd, 2018 0.005129 0.020738 0.020738 0.200000 0.200000
May 2nd, 2019 0.005132 0.019096 0.019096 0.200000 0.200000
April 30th, 2020 0.005074 0.016537 0.016537 0.200000 0.200000
May 3rd, 2021 0.005091 0.013253 0.013253 0.200000 0.200000
May 3rd, 2022 0.005097 0.009342 0.009342 0.200000 0.200000
May 3rd, 2023 0.005001 0.004910 0.004910 0.200000 0.200000
(this step took 0.9s)
The npv of the bermudan swaption is
Float swaption NPV (GSR) = 0.004291
(this step took 1.0s)
In this case it is also interesting to look at the
underlying swap npv in the GSR model.
Float swap NPV (GSR) = 0.005250
Not surprisingly, the underlying is priced differently
compared to the LinearTsrPricer, since a different
smile is implied by the GSR model.
This is exactly where the Markov functional model
comes into play, because it can calibrate to any
given underlying smile (as long as it is arbitrage
free). We try this now. Of course the usual use case
is not to calibrate to a flat smile as in our simple
example, still it should be possible, of course...
The option npv is the markov model is:
Float swaption NPV (Markov) = 0.003549
(this step took 0.4s)
This is not too far from the GSR price.
More interesting is the question how well the Markov
model did its job to match our input smile. For this
we look at the underlying npv under the Markov model
Float swap NPV (Markov) = 0.004301
This is closer to our terminal swap rate model price.
A perfect match is not expected anyway, because the
dynamics of the underlying rate in the linear
model is different from the Markov model, of
course.
The Markov model can not only calibrate to the
underlying smile, but has at the same time a
sigma function (similar to the GSR model) which
can be used to calibrate to a second instrument
set. We do this here to calibrate to our coterminal
ATM swaptions from above.
This is a computationally demanding task, so
depending on your machine, this may take a
while now...
Expiry Model sigma Model price market price Model ivol Market ivol
====================================================================================================
April 30th, 2015 0.010000 0.016111 0.016111 0.199996 0.200000
May 3rd, 2016 0.012276 0.020062 0.020062 0.200002 0.200000
May 3rd, 2017 0.010535 0.021229 0.021229 0.200000 0.200000
May 3rd, 2018 0.010414 0.020738 0.020738 0.199999 0.200000
May 2nd, 2019 0.010360 0.019096 0.019096 0.199999 0.200000
April 30th, 2020 0.010340 0.016537 0.016537 0.200000 0.200000
May 3rd, 2021 0.010365 0.013253 0.013253 0.199999 0.200000
May 3rd, 2022 0.010382 0.009342 0.009342 0.200001 0.200000
May 3rd, 2023 0.010392 0.004910 0.004910 0.200000 0.200000
0.009959
(this step took 29.6s)
Now let's have a look again at the underlying pricing.
It shouldn't have changed much, because the underlying
smile is still matched.
Float swap NPV (Markov) = 0.004331
(this step took 0.4s)
This is close to the previous value as expected.
As a final remark we note that the calibration to
coterminal swaptions is not particularly reasonable
here, because the european call rights are not
well represented by these swaptions.
Secondly, our CMS swaption is sensitive to the
correlation between the 10y swap rate and the
Euribor 6M rate. Since the Markov model is one factor
it will most probably underestimate the market value
by construction.
That was it. Thank you for running this demo. Bye.
Global Optimizer
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Firefly Algorithm Test
----------------------------------------------------------------
Function eggholder, Agents: 150, Vola: 1.5, Intensity: 1
Starting point: f(0, 0) = -25.4603
End point: f(512, 404.232) = -959.641
Global optimium: f(512, 404.232) = -959.641
================================================================
Run completed in 5 s
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Hybrid Simulated Annealing Test
----------------------------------------------------------------
Function: ackley, Dimensions: 3, Initial temp:100, Final temp:0, Reset scheme:1, Reset steps:150
Starting point: f(2, 2, 2) = 9
End point: f(0, -0, 0) = -2
Global optimium: f(0, 0, 0) = -2
================================================================
Function: ackley, Dimensions: 10, Initial temp:100, Final temp:0, Reset scheme:1, Reset steps:150
Starting point: f(2, 2, 2, 2, 2, 2, 2, 2, 2, 2) = 12
End point: f(19, -9, 37, 26, 43, 126, 40, -39, -38, 12) = -126
Global optimium: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = -146
================================================================
Function: ackley, Dimensions: 30, Initial temp:100, Final temp:0, Reset scheme:1, Reset steps:150
Starting point: f(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2) = 16
End point: f(-14, -2, 22, 12, 13, 10, 10, 13, -12, -1, 2, 4, -24, 22, -1, 15, 18, -5, -2, 10, 12, 12, -14, -2, 13, 19, 16, 1, 22, -13) = -186184
Global optimium: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = -3269015
================================================================
Run completed in 5 s
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Particle Swarm Optimization Test
----------------------------------------------------------------
Function: rosenbrock, Dimensions: 3, Agents: 100, K-neighbors: 25, Threshold: 500
Starting point: f(0, 0, 0) = 2
End point: f(1, 1, 1) = 0
Global optimium: f(1, 1, 1) = 0
================================================================
Function: rosenbrock, Dimensions: 10, Agents: 100, K-neighbors: 25, Threshold: 500
Starting point: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = 9
End point: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
Global optimium: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
================================================================
Function: rosenbrock, Dimensions: 30, Agents: 100, K-neighbors: 25, Threshold: 500
Starting point: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = 29
End point: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
Global optimium: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
================================================================
Run completed in 16 s
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Simulated Annealing Test
----------------------------------------------------------------
Function ackley, Lambda: 0, Temperature: 350, Epsilon: 1, Iterations: 1000
Starting point: f(2, 2, 2) = 9
End point: f(-0, 0, 0) = 0
Global optimium: f(0, 0, 0) = -2
================================================================
Function ackley, Lambda: 0, Temperature: 350, Epsilon: 1, Iterations: 1000
Starting point: f(2, 2, 2, 2, 2, 2, 2, 2, 2, 2) = 12
End point: f(4, -0, 3, 1, 3, 1, -0, 2, -2, 3) = -72
Global optimium: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = -146
================================================================
Function ackley, Lambda: 0, Temperature: 350, Epsilon: 1, Iterations: 1000
Starting point: f(2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2) = 16
End point: f(2, 2, 1, 2, 2, 2, 1, 2, -0, -0, 3, 1, 2, 2, 2, -0, 1, 2, 1, 1, -0, 2, 3, 2, -0, 1, 3, 2, 1, 3) = -757934
Global optimium: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = -3269015
================================================================
Run completed in 16 s
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Differential Evolution Test
----------------------------------------------------------------
Function: rosenbrock, Dimensions: 3, Agents: 50, Probability: 0, StepsizeWeight: 1, Strategy: BestMemberWithJitter
Starting point: f(0, 0, 0) = 2
End point: f(1, 1, 1) = 0
Global optimium: f(1, 1, 1) = 0
================================================================
Function: rosenbrock, Dimensions: 10, Agents: 150, Probability: 0, StepsizeWeight: 1, Strategy: BestMemberWithJitter
Starting point: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = 9
End point: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
Global optimium: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
================================================================
Function: rosenbrock, Dimensions: 30, Agents: 450, Probability: 0, StepsizeWeight: 1, Strategy: BestMemberWithJitter
Starting point: f(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0) = 29
End point: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
Global optimium: f(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) = 0
================================================================
Run completed in 38 s
Latent Model
Gaussian versus T prob of extreme event (random and integrable)-
-Prob of 0 events... 1 ** 0.99999 ** 1 ** 1
-Prob of 1 events... 0.252189 ** 0.249196 ** 0.2524 ** 0.24917
-Prob of 2 events... 0.0328963 ** 0.0336561 ** 0.03279 ** 0.03368
-Prob of 3 events... 0.00199248 ** 0.00421316 ** 0.00201 ** 0.0041
-- Default correlations G,T,GRand,TRand--
-----------------------------------------
1 , 0.00935891 , 0.00935891 ,
0.00935891 , 1 , 0.00935891 ,
0.00935891 , 0.00935891 , 1 ,
1 , 0.031698 , 0.031698 ,
0.031698 , 1 , 0.031698 ,
0.031698 , 0.031698 , 1 ,
1.00001 , 0.00827934 , 0.00517704 ,
0.00827934 , 1.00001 , 0.0103137 ,
0.00517704 , 0.0103137 , 1.00001 ,
1.00001 , 0.0305301 , 0.0283078 ,
0.0305301 , 1.00001 , 0.0323241 ,
0.0283078 , 0.0323241 , 1.00001 ,
Run completed in 7 s
Market models
inverse floater
fixed strikes : 0.15
number rates : 20
training paths, 65536
paths, 65536
vega Paths, 16384
rate level 0.05
-0.0161955
0.0870706
time to build strategy, 12.408, seconds.
time to price, 20.514, seconds.
vega output
factorwise bumping 0
doCaps 0
price estimate, 0.0868184
Delta, 0, 1.31847, 0.00195094
Delta, 1, 1.20837, 0.00329279
Delta, 2, 1.09916, 0.00402968
Delta, 3, 0.994986, 0.00443145
Delta, 4, 0.901078, 0.00465025
Delta, 5, 0.821622, 0.00472748
Delta, 6, 0.748171, 0.00472779
Delta, 7, 0.676147, 0.00467372
Delta, 8, 0.614106, 0.0045757
Delta, 9, 0.559666, 0.00445411
Delta, 10, 0.513673, 0.00432688
Delta, 11, 0.470293, 0.00417286
Delta, 12, 0.427822, 0.00400984
Delta, 13, 0.390045, 0.00384228
Delta, 14, 0.358827, 0.00371168
Delta, 15, 0.328362, 0.00355612
Delta, 16, 0.298648, 0.00339936
Delta, 17, 0.268562, 0.00321725
Delta, 18, 0.241715, 0.00303437
Delta, 19, 0.19752, 0.00277139
vega, 0, 0.000537163 ,0
vega, 1, 0.000512241 ,0
vega, 2, 0.000531272 ,0
vega, 3, 0.00080581 ,0
vega, 4, 0.000521218 ,0
vega, 5, 0.000474379 ,0
vega, 6, 0.000321862 ,0
vega, 7, 0.000650717 ,0
vega, 8, 0.000228025 ,0
vega, 9, 0.000366575 ,0
vega, 10, 0.000109168 ,0
vega, 11, 4.29782e-005 ,0
vega, 12, 0.000167156 ,0
vega, 13, 0.000127076 ,0
vega, 14, 0.000147648 ,0
vega, 15, -2.24295e-005 ,0
vega, 16, 1.19248e-005 ,0
vega, 17, -5.85746e-005 ,0
vega, 18, -4.45364e-005 ,0
vega, 19, 2.61674e-005 ,0
total Vega, 0.00545584
vega output
factorwise bumping 1
doCaps 0
price estimate, 0.0868184
Delta, 0, 1.31847, 0.00195094
Delta, 1, 1.20837, 0.00329279
Delta, 2, 1.09916, 0.00402968
Delta, 3, 0.994986, 0.00443145
Delta, 4, 0.901078, 0.00465025
Delta, 5, 0.821622, 0.00472748
Delta, 6, 0.748171, 0.00472779
Delta, 7, 0.676147, 0.00467372
Delta, 8, 0.614106, 0.0045757
Delta, 9, 0.559666, 0.00445411
Delta, 10, 0.513673, 0.00432688
Delta, 11, 0.470293, 0.00417286
Delta, 12, 0.427822, 0.00400984
Delta, 13, 0.390045, 0.00384228
Delta, 14, 0.358827, 0.00371168
Delta, 15, 0.328362, 0.00355612
Delta, 16, 0.298648, 0.00339936
Delta, 17, 0.268562, 0.00321725
Delta, 18, 0.241715, 0.00303437
Delta, 19, 0.19752, 0.00277139
vega, 0, 0.000178754 ,0
vega, 1, 0.000697929 ,0
vega, 2, 0.000665821 ,0
vega, 3, 0.000784743 ,0
vega, 4, 0.000552831 ,0
vega, 5, 0.000512852 ,0
vega, 6, 0.000308864 ,0
vega, 7, 0.000361828 ,0
vega, 8, 0.000269135 ,0
vega, 9, 0.000141886 ,0
vega, 10, 0.000139578 ,0
vega, 11, 1.36155e-005 ,0
vega, 12, 9.69753e-005 ,0
vega, 13, 8.70213e-006 ,0
vega, 14, 0.000134429 ,0
vega, 15, 3.91366e-007 ,0
vega, 16, 3.4873e-005 ,0
vega, 17, 7.48356e-006 ,0
vega, 18, -4.19783e-006 ,0
vega, 19, 1.37192e-005 ,0
total Vega, 0.00492021
vega output
factorwise bumping 0
doCaps 1
price estimate, 0.0868184
Delta, 0, 1.31847, 0.00195094
Delta, 1, 1.20837, 0.00329279
Delta, 2, 1.09916, 0.00402968
Delta, 3, 0.994986, 0.00443145
Delta, 4, 0.901078, 0.00465025
Delta, 5, 0.821622, 0.00472748
Delta, 6, 0.748171, 0.00472779
Delta, 7, 0.676147, 0.00467372
Delta, 8, 0.614106, 0.0045757
Delta, 9, 0.559666, 0.00445411
Delta, 10, 0.513673, 0.00432688
Delta, 11, 0.470293, 0.00417286
Delta, 12, 0.427822, 0.00400984
Delta, 13, 0.390045, 0.00384228
Delta, 14, 0.358827, 0.00371168
Delta, 15, 0.328362, 0.00355612
Delta, 16, 0.298648, 0.00339936
Delta, 17, 0.268562, 0.00321725
Delta, 18, 0.241715, 0.00303437
Delta, 19, 0.19752, 0.00277139
vega, 0, 0.000205662 ,0
vega, 1, 0.000357761 ,0
vega, 2, 0.000436371 ,0
vega, 3, 0.000744637 ,0
vega, 4, 0.000350999 ,0
vega, 5, 0.000304823 ,0
vega, 6, 7.29906e-005 ,0
vega, 7, 0.000682534 ,0
vega, 8, 0.000155682 ,0
vega, 9, 0.000403977 ,0
vega, 10, 0.000157902 ,0
vega, 11, -0.000147974 ,0
vega, 12, 0.00017657 ,0
vega, 13, -9.63953e-007 ,0
vega, 14, 0.000438237 ,0
vega, 15, -5.99954e-005 ,0
vega, 16, 1.25568e-005 ,0
vega, 17, 5.63731e-005 ,0
vega, 18, 9.71559e-005 ,0
vega, 19, 0.000129229 ,0
vega, 20, 0.000181069 ,0
vega, 21, 0.000217585 ,0
vega, 22, 0.000255643 ,0
vega, 23, 0.000203047 ,0
vega, 24, 0.000182118 ,0
vega, 25, 0.000142711 ,0
vega, 26, 0.000110869 ,0
vega, 27, 0.000134469 ,0
vega, 28, 0.000116228 ,0
vega, 29, 7.04043e-005 ,0
vega, 30, 7.04779e-005 ,0
vega, 31, -7.70875e-005 ,0
vega, 32, -6.01727e-005 ,0
vega, 33, -6.67757e-005 ,0
vega, 34, -6.83066e-005 ,0
total Vega, 0.00598681
vega output
factorwise bumping 1
doCaps 1
price estimate, 0.0868184
Delta, 0, 1.31847, 0.00195094
Delta, 1, 1.20837, 0.00329279
Delta, 2, 1.09916, 0.00402968
Delta, 3, 0.994986, 0.00443145
Delta, 4, 0.901078, 0.00465025
Delta, 5, 0.821622, 0.00472748
Delta, 6, 0.748171, 0.00472779
Delta, 7, 0.676147, 0.00467372
Delta, 8, 0.614106, 0.0045757
Delta, 9, 0.559666, 0.00445411
Delta, 10, 0.513673, 0.00432688
Delta, 11, 0.470293, 0.00417286
Delta, 12, 0.427822, 0.00400984
Delta, 13, 0.390045, 0.00384228
Delta, 14, 0.358827, 0.00371168
Delta, 15, 0.328362, 0.00355612
Delta, 16, 0.298648, 0.00339936
Delta, 17, 0.268562, 0.00321725
Delta, 18, 0.241715, 0.00303437
Delta, 19, 0.19752, 0.00277139
vega, 0, 0.000132367 ,0
vega, 1, 0.000541302 ,0
vega, 2, 0.000489328 ,0
vega, 3, 0.000706567 ,0
vega, 4, 0.000491309 ,0
vega, 5, 0.000519181 ,0
vega, 6, 0.000339452 ,0
vega, 7, 0.000464215 ,0
vega, 8, 0.000386056 ,0
vega, 9, 0.000232674 ,0
vega, 10, 0.000231736 ,0
vega, 11, 6.23271e-005 ,0
vega, 12, 0.000238341 ,0
vega, 13, 4.32892e-005 ,0
vega, 14, 0.000255305 ,0
vega, 15, 1.06151e-005 ,0
vega, 16, 9.40421e-005 ,0
vega, 17, 2.23203e-005 ,0
vega, 18, -7.00994e-005 ,0
vega, 19, -2.28062e-005 ,0
vega, 20, 1.6436e-005 ,0
vega, 21, 5.699e-005 ,0
vega, 22, 8.61217e-005 ,0
vega, 23, 8.56206e-005 ,0
vega, 24, 8.37583e-005 ,0
vega, 25, 7.14288e-005 ,0
vega, 26, 5.80925e-005 ,0
vega, 27, 3.55289e-005 ,0
vega, 28, 1.35357e-005 ,0
vega, 29, -2.1889e-006 ,0
vega, 30, -1.67405e-005 ,0
vega, 31, -2.32349e-005 ,0
vega, 32, -4.42788e-005 ,0
vega, 33, -4.67575e-005 ,0
vega, 34, -6.48239e-005 ,0
vega, 35, -6.13788e-005 ,0
vega, 36, -6.87918e-005 ,0
vega, 37, -6.52544e-005 ,0
vega, 38, -3.13134e-005 ,0
total Vega, 0.00525027
Upper - lower is, 0.00545744, with standard error 0.000555712
time to compute upper bound is, 72.417, seconds.
inverse floater
fixed strikes : 0.15
number rates : 20
training paths, 65536
paths, 65536
vega Paths, 16384
rate level 0.06
0.172515
0.21654
time to build strategy, 12.546, seconds.
time to price, 18.828, seconds.
vega output
factorwise bumping 0
doCaps 0
price estimate, 0.216636
Delta, 0, 1.26009, 0.00127668
Delta, 1, 1.16988, 0.00203805
Delta, 2, 1.0823, 0.00248746
Delta, 3, 1.00324, 0.00277846
Delta, 4, 0.931872, 0.00298804
Delta, 5, 0.862935, 0.00313688
Delta, 6, 0.800813, 0.00321048
Delta, 7, 0.745136, 0.00325251
Delta, 8, 0.696549, 0.00324712
Delta, 9, 0.648988, 0.00323495
Delta, 10, 0.604435, 0.00321175
Delta, 11, 0.566592, 0.00318165
Delta, 12, 0.524962, 0.0031222
Delta, 13, 0.488412, 0.00305025
Delta, 14, 0.454208, 0.00298178
Delta, 15, 0.420954, 0.00290667
Delta, 16, 0.39006, 0.00282624
Delta, 17, 0.360374, 0.00274247
Delta, 18, 0.327711, 0.00263971
Delta, 19, 0.280065, 0.00252801
vega, 0, -0.000384857 ,0
vega, 1, -3.52271e-005 ,0
vega, 2, -7.85158e-006 ,0
vega, 3, 0.00023008 ,0
vega, 4, 0.000521306 ,0
vega, 5, -2.98669e-005 ,0
vega, 6, 0.000390151 ,0
vega, 7, 0.00037885 ,0
vega, 8, 9.31084e-005 ,0
vega, 9, 0.000183449 ,0
vega, 10, 0.000344103 ,0
vega, 11, -8.77287e-006 ,0
vega, 12, 0.000221929 ,0
vega, 13, 0.000183133 ,0
vega, 14, 0.000141979 ,0
vega, 15, 1.33615e-005 ,0
vega, 16, 1.10357e-005 ,0
vega, 17, -8.32643e-005 ,0
vega, 18, -4.86715e-005 ,0
vega, 19, 5.30522e-005 ,0
total Vega, 0.00216703
vega output
factorwise bumping 1
doCaps 0
price estimate, 0.216636
Delta, 0, 1.26009, 0.00127668
Delta, 1, 1.16988, 0.00203805
Delta, 2, 1.0823, 0.00248746
Delta, 3, 1.00324, 0.00277846
Delta, 4, 0.931872, 0.00298804
Delta, 5, 0.862935, 0.00313688
Delta, 6, 0.800813, 0.00321048
Delta, 7, 0.745136, 0.00325251
Delta, 8, 0.696549, 0.00324712
Delta, 9, 0.648988, 0.00323495
Delta, 10, 0.604435, 0.00321175
Delta, 11, 0.566592, 0.00318165
Delta, 12, 0.524962, 0.0031222
Delta, 13, 0.488412, 0.00305025
Delta, 14, 0.454208, 0.00298178
Delta, 15, 0.420954, 0.00290667
Delta, 16, 0.39006, 0.00282624
Delta, 17, 0.360374, 0.00274247
Delta, 18, 0.327711, 0.00263971
Delta, 19, 0.280065, 0.00252801
vega, 0, -9.03408e-005 ,0
vega, 1, -6.91038e-005 ,0
vega, 2, -0.000162768 ,0
vega, 3, -5.13874e-006 ,0
vega, 4, 0.00022195 ,0
vega, 5, 0.000127121 ,0
vega, 6, 0.000161824 ,0
vega, 7, 0.000160615 ,0
vega, 8, 0.00012811 ,0
vega, 9, 0.000121993 ,0
vega, 10, 0.00027437 ,0
vega, 11, 0.000150963 ,0
vega, 12, 6.0907e-005 ,0
vega, 13, 5.54798e-005 ,0
vega, 14, 0.000115215 ,0
vega, 15, 4.66343e-005 ,0
vega, 16, 7.26397e-005 ,0
vega, 17, 1.47797e-005 ,0
vega, 18, 1.92582e-005 ,0
vega, 19, 4.99696e-005 ,0
total Vega, 0.00145448
vega output
factorwise bumping 0
doCaps 1
price estimate, 0.216636
Delta, 0, 1.26009, 0.00127668
Delta, 1, 1.16988, 0.00203805
Delta, 2, 1.0823, 0.00248746
Delta, 3, 1.00324, 0.00277846
Delta, 4, 0.931872, 0.00298804
Delta, 5, 0.862935, 0.00313688
Delta, 6, 0.800813, 0.00321048
Delta, 7, 0.745136, 0.00325251
Delta, 8, 0.696549, 0.00324712
Delta, 9, 0.648988, 0.00323495
Delta, 10, 0.604435, 0.00321175
Delta, 11, 0.566592, 0.00318165
Delta, 12, 0.524962, 0.0031222
Delta, 13, 0.488412, 0.00305025
Delta, 14, 0.454208, 0.00298178
Delta, 15, 0.420954, 0.00290667
Delta, 16, 0.39006, 0.00282624
Delta, 17, 0.360374, 0.00274247
Delta, 18, 0.327711, 0.00263971
Delta, 19, 0.280065, 0.00252801
vega, 0, -7.21714e-005 ,0
vega, 1, 0.000136659 ,0
vega, 2, 5.62648e-005 ,0
vega, 3, 0.00025997 ,0
vega, 4, 0.000553457 ,0
vega, 5, -0.000175396 ,0
vega, 6, 0.000423636 ,0
vega, 7, 0.000613373 ,0
vega, 8, 0.00011268 ,0
vega, 9, 0.00021311 ,0
vega, 10, 0.000596778 ,0
vega, 11, -2.98108e-005 ,0
vega, 12, 0.000205846 ,0
vega, 13, 0.000468935 ,0
vega, 14, 0.000175547 ,0
vega, 15, -9.41773e-005 ,0
vega, 16, -1.65462e-005 ,0
vega, 17, -6.75764e-005 ,0
vega, 18, -0.000104451 ,0
vega, 19, -0.000127399 ,0
vega, 20, -0.000137515 ,0
vega, 21, -8.34189e-005 ,0
vega, 22, -7.87685e-005 ,0
vega, 23, -0.000125187 ,0
vega, 24, -0.00010618 ,0
vega, 25, -9.40511e-005 ,0
vega, 26, -0.00013306 ,0
vega, 27, -0.000110321 ,0
vega, 28, -9.3107e-005 ,0
vega, 29, -0.000187345 ,0
vega, 30, -0.000139666 ,0
vega, 31, -0.000187661 ,0
vega, 32, -0.000156292 ,0
vega, 33, -0.00014873 ,0
vega, 34, -0.00012808 ,0
total Vega, 0.00121934
vega output
factorwise bumping 1
doCaps 1
price estimate, 0.216636
Delta, 0, 1.26009, 0.00127668
Delta, 1, 1.16988, 0.00203805
Delta, 2, 1.0823, 0.00248746
Delta, 3, 1.00324, 0.00277846
Delta, 4, 0.931872, 0.00298804
Delta, 5, 0.862935, 0.00313688
Delta, 6, 0.800813, 0.00321048
Delta, 7, 0.745136, 0.00325251
Delta, 8, 0.696549, 0.00324712
Delta, 9, 0.648988, 0.00323495
Delta, 10, 0.604435, 0.00321175
Delta, 11, 0.566592, 0.00318165
Delta, 12, 0.524962, 0.0031222
Delta, 13, 0.488412, 0.00305025
Delta, 14, 0.454208, 0.00298178
Delta, 15, 0.420954, 0.00290667
Delta, 16, 0.39006, 0.00282624
Delta, 17, 0.360374, 0.00274247
Delta, 18, 0.327711, 0.00263971
Delta, 19, 0.280065, 0.00252801
vega, 0, -3.69174e-005 ,0
vega, 1, 0.000129388 ,0
vega, 2, 6.98429e-005 ,0
vega, 3, 0.000231552 ,0
vega, 4, 0.000455463 ,0
vega, 5, 0.000321583 ,0
vega, 6, 0.000366656 ,0
vega, 7, 0.000339349 ,0
vega, 8, 0.000312691 ,0
vega, 9, 0.000270936 ,0
vega, 10, 0.000492036 ,0
vega, 11, 0.000280992 ,0
vega, 12, 0.000174691 ,0
vega, 13, 0.000152782 ,0
vega, 14, 0.000255612 ,0
vega, 15, 9.36597e-005 ,0
vega, 16, 0.000204994 ,0
vega, 17, -1.45242e-006 ,0
vega, 18, -4.71563e-005 ,0
vega, 19, -9.00451e-005 ,0
vega, 20, -1.77406e-005 ,0
vega, 21, -6.91377e-005 ,0
vega, 22, -0.000107325 ,0
vega, 23, -0.000134943 ,0
vega, 24, -0.000156467 ,0
vega, 25, -0.000167919 ,0
vega, 26, -0.000180652 ,0
vega, 27, -0.000188117 ,0
vega, 28, -0.000196438 ,0
vega, 29, -0.00019889 ,0
vega, 30, -0.00021336 ,0
vega, 31, -0.000213246 ,0
vega, 32, -0.000210818 ,0
vega, 33, -0.000206102 ,0
vega, 34, -0.000211008 ,0
vega, 35, -0.000198566 ,0
vega, 36, -0.000207652 ,0
vega, 37, -0.000176331 ,0
vega, 38, -0.000123168 ,0
total Vega, 0.000798772
Upper - lower is, 0.00259873, with standard error 0.000401346
time to compute upper bound is, 85.595, seconds.
inverse floater
fixed strikes : 0.15
number rates : 20
training paths, 65536
paths, 65536
vega Paths, 16384
rate level 0.07
0.323454
0.342527
time to build strategy, 12.779, seconds.
time to price, 21.509, seconds.
vega output
factorwise bumping 0
doCaps 0
price estimate, 0.34265
Delta, 0, 0.969376, 0.00297678
Delta, 1, 0.873762, 0.00300887
Delta, 2, 0.810786, 0.00293835
Delta, 3, 0.762095, 0.00285246
Delta, 4, 0.71986, 0.00277316
Delta, 5, 0.683966, 0.00271086
Delta, 6, 0.649749, 0.00263977
Delta, 7, 0.617911, 0.00257003
Delta, 8, 0.586519, 0.00251352
Delta, 9, 0.557197, 0.00244728
Delta, 10, 0.529481, 0.00239172
Delta, 11, 0.502225, 0.00234826
Delta, 12, 0.477742, 0.00229285
Delta, 13, 0.454561, 0.00225155
Delta, 14, 0.426553, 0.00219171
Delta, 15, 0.403822, 0.00213546
Delta, 16, 0.382686, 0.00209818
Delta, 17, 0.360938, 0.00205495
Delta, 18, 0.335242, 0.00201275
Delta, 19, 0.295622, 0.0019842
vega, 0, -0.00151791 ,0
vega, 1, 0.000148919 ,0
vega, 2, 0.000132579 ,0
vega, 3, -0.000126394 ,0
vega, 4, 9.74132e-005 ,0
vega, 5, -0.000127503 ,0
vega, 6, 0.000191537 ,0
vega, 7, -9.87701e-005 ,0
vega, 8, -9.63463e-005 ,0
vega, 9, 0.000112571 ,0
vega, 10, -0.000164674 ,0
vega, 11, 0.00015804 ,0
vega, 12, 8.74819e-005 ,0
vega, 13, 5.75986e-005 ,0
vega, 14, 9.58877e-005 ,0
vega, 15, -0.000109122 ,0
vega, 16, -3.2076e-007 ,0
vega, 17, -8.38044e-005 ,0
vega, 18, -6.75425e-005 ,0
vega, 19, 5.54097e-005 ,0
total Vega, -0.00125495
vega output
factorwise bumping 1
doCaps 0
price estimate, 0.34265
Delta, 0, 0.969376, 0.00297678
Delta, 1, 0.873762, 0.00300887
Delta, 2, 0.810786, 0.00293835
Delta, 3, 0.762095, 0.00285246
Delta, 4, 0.71986, 0.00277316
Delta, 5, 0.683966, 0.00271086
Delta, 6, 0.649749, 0.00263977
Delta, 7, 0.617911, 0.00257003
Delta, 8, 0.586519, 0.00251352
Delta, 9, 0.557197, 0.00244728
Delta, 10, 0.529481, 0.00239172
Delta, 11, 0.502225, 0.00234826
Delta, 12, 0.477742, 0.00229285
Delta, 13, 0.454561, 0.00225155
Delta, 14, 0.426553, 0.00219171
Delta, 15, 0.403822, 0.00213546
Delta, 16, 0.382686, 0.00209818
Delta, 17, 0.360938, 0.00205495
Delta, 18, 0.335242, 0.00201275
Delta, 19, 0.295622, 0.0019842
vega, 0, -0.000381813 ,0
vega, 1, -0.000405229 ,0
vega, 2, -0.000444632 ,0
vega, 3, -0.000345939 ,0
vega, 4, -0.000228287 ,0
vega, 5, -0.000195561 ,0
vega, 6, -6.20786e-005 ,0
vega, 7, -0.0001063 ,0
vega, 8, -2.03691e-005 ,0
vega, 9, -3.51976e-005 ,0
vega, 10, -5.77552e-005 ,0
vega, 11, 0.000120196 ,0
vega, 12, -8.38198e-006 ,0
vega, 13, 3.45363e-005 ,0
vega, 14, 6.17824e-005 ,0
vega, 15, 1.18413e-005 ,0
vega, 16, 2.34694e-005 ,0
vega, 17, -4.50198e-006 ,0
vega, 18, 2.36878e-005 ,0
vega, 19, 6.60989e-005 ,0
total Vega, -0.00195443
vega output
factorwise bumping 0
doCaps 1
price estimate, 0.34265
Delta, 0, 0.969376, 0.00297678
Delta, 1, 0.873762, 0.00300887
Delta, 2, 0.810786, 0.00293835
Delta, 3, 0.762095, 0.00285246
Delta, 4, 0.71986, 0.00277316
Delta, 5, 0.683966, 0.00271086
Delta, 6, 0.649749, 0.00263977
Delta, 7, 0.617911, 0.00257003
Delta, 8, 0.586519, 0.00251352
Delta, 9, 0.557197, 0.00244728
Delta, 10, 0.529481, 0.00239172
Delta, 11, 0.502225, 0.00234826
Delta, 12, 0.477742, 0.00229285
Delta, 13, 0.454561, 0.00225155
Delta, 14, 0.426553, 0.00219171
Delta, 15, 0.403822, 0.00213546
Delta, 16, 0.382686, 0.00209818
Delta, 17, 0.360938, 0.00205495
Delta, 18, 0.335242, 0.00201275
Delta, 19, 0.295622, 0.0019842
vega, 0, -4.21087e-005 ,0
vega, 1, 3.00695e-005 ,0
vega, 2, 2.36447e-005 ,0
vega, 3, -0.000182882 ,0
vega, 4, 0.000226781 ,0
vega, 5, -2.36817e-006 ,0
vega, 6, 0.000457528 ,0
vega, 7, -7.13437e-006 ,0
vega, 8, 0.000334121 ,0
vega, 9, 0.000400273 ,0
vega, 10, -0.000167116 ,0
vega, 11, 0.000475872 ,0
vega, 12, 0.000196944 ,0
vega, 13, -1.37504e-005 ,0
vega, 14, 0.00021986 ,0
vega, 15, -0.000170297 ,0
vega, 16, -0.000147472 ,0
vega, 17, -0.000228598 ,0
vega, 18, -0.000272943 ,0
vega, 19, -0.000290572 ,0
vega, 20, -0.000317381 ,0
vega, 21, -0.000312586 ,0
vega, 22, -0.000331411 ,0
vega, 23, -0.000290355 ,0
vega, 24, -0.00033999 ,0
vega, 25, -0.000346077 ,0
vega, 26, -0.000292448 ,0
vega, 27, -0.000322885 ,0
vega, 28, -0.000306835 ,0
vega, 29, -0.000306982 ,0
vega, 30, -0.000257612 ,0
vega, 31, -0.000336239 ,0
vega, 32, -0.000282398 ,0
vega, 33, -0.000246067 ,0
vega, 34, -0.000206617 ,0
total Vega, -0.00365603
vega output
factorwise bumping 1
doCaps 1
price estimate, 0.34265
Delta, 0, 0.969376, 0.00297678
Delta, 1, 0.873762, 0.00300887
Delta, 2, 0.810786, 0.00293835
Delta, 3, 0.762095, 0.00285246
Delta, 4, 0.71986, 0.00277316
Delta, 5, 0.683966, 0.00271086
Delta, 6, 0.649749, 0.00263977
Delta, 7, 0.617911, 0.00257003
Delta, 8, 0.586519, 0.00251352
Delta, 9, 0.557197, 0.00244728
Delta, 10, 0.529481, 0.00239172
Delta, 11, 0.502225, 0.00234826
Delta, 12, 0.477742, 0.00229285
Delta, 13, 0.454561, 0.00225155
Delta, 14, 0.426553, 0.00219171
Delta, 15, 0.403822, 0.00213546
Delta, 16, 0.382686, 0.00209818
Delta, 17, 0.360938, 0.00205495
Delta, 18, 0.335242, 0.00201275
Delta, 19, 0.295622, 0.0019842
vega, 0, -1.08594e-005 ,0
vega, 1, 3.28259e-005 ,0
vega, 2, -1.49747e-005 ,0
vega, 3, 6.20278e-005 ,0
vega, 4, 0.000141605 ,0
vega, 5, 0.000121746 ,0
vega, 6, 0.000272705 ,0
vega, 7, 0.000161356 ,0
vega, 8, 0.000242198 ,0
vega, 9, 0.0002107 ,0
vega, 10, 0.00011854 ,0
vega, 11, 0.000360619 ,0
vega, 12, 0.00014925 ,0
vega, 13, 0.000191178 ,0
vega, 14, 0.00024885 ,0
vega, 15, 0.000145838 ,0
vega, 16, 0.00011568 ,0
vega, 17, 4.21121e-006 ,0
vega, 18, 2.18317e-005 ,0
vega, 19, -0.000188927 ,0
vega, 20, -0.000148246 ,0
vega, 21, -0.000229671 ,0
vega, 22, -0.000277894 ,0
vega, 23, -0.000309583 ,0
vega, 24, -0.000329566 ,0
vega, 25, -0.000339254 ,0
vega, 26, -0.000353644 ,0
vega, 27, -0.000356302 ,0
vega, 28, -0.000359206 ,0
vega, 29, -0.000360529 ,0
vega, 30, -0.000351546 ,0
vega, 31, -0.00035566 ,0
vega, 32, -0.000345851 ,0
vega, 33, -0.00033724 ,0
vega, 34, -0.000337278 ,0
vega, 35, -0.000329692 ,0
vega, 36, -0.000314021 ,0
vega, 37, -0.00027431 ,0
vega, 38, -0.000231487 ,0
total Vega, -0.00355458
Upper - lower is, 0.000516568, with standard error 0.000132409
time to compute upper bound is, 93.258, seconds.
inverse floater
fixed strikes : 0.15
number rates : 20
training paths, 65536
paths, 65536
vega Paths, 16384
rate level 0.08
0.43381
0.442296
time to build strategy, 12.081, seconds.
time to price, 19.335, seconds.
vega output
factorwise bumping 0
doCaps 0
price estimate, 0.442225
Delta, 0, 0.460573, 0.00283912
Delta, 1, 0.497331, 0.00282374
Delta, 2, 0.508616, 0.00272413
Delta, 3, 0.506396, 0.00259853
Delta, 4, 0.496328, 0.00247277
Delta, 5, 0.483507, 0.00235078
Delta, 6, 0.471974, 0.00224921
Delta, 7, 0.459962, 0.00215125
Delta, 8, 0.444803, 0.00206655
Delta, 9, 0.432474, 0.0019875
Delta, 10, 0.417119, 0.00190449
Delta, 11, 0.400283, 0.0018285
Delta, 12, 0.389304, 0.00177295
Delta, 13, 0.374843, 0.00171107
Delta, 14, 0.361905, 0.00165603
Delta, 15, 0.346607, 0.00159712
Delta, 16, 0.332138, 0.001552
Delta, 17, 0.318848, 0.00152276
Delta, 18, 0.304632, 0.00148693
Delta, 19, 0.279958, 0.00148421
vega, 0, -0.00159694 ,0
vega, 1, 0.000136159 ,0
vega, 2, 0.000157006 ,0
vega, 3, -3.79828e-005 ,0
vega, 4, -8.29012e-005 ,0
vega, 5, -9.53439e-005 ,0
vega, 6, -0.000226751 ,0
vega, 7, -0.000273561 ,0
vega, 8, -6.25763e-005 ,0
vega, 9, -0.000228828 ,0
vega, 10, -0.000122139 ,0
vega, 11, -3.35834e-006 ,0
vega, 12, -8.21506e-006 ,0
vega, 13, 3.76315e-005 ,0
vega, 14, -9.71785e-005 ,0
vega, 15, -4.08222e-005 ,0
vega, 16, -3.91734e-005 ,0
vega, 17, -0.000117918 ,0
vega, 18, -0.000125125 ,0
vega, 19, 4.88174e-005 ,0
total Vega, -0.0027792
vega output
factorwise bumping 1
doCaps 0
price estimate, 0.442225
Delta, 0, 0.460573, 0.00283912
Delta, 1, 0.497331, 0.00282374
Delta, 2, 0.508616, 0.00272413
Delta, 3, 0.506396, 0.00259853
Delta, 4, 0.496328, 0.00247277
Delta, 5, 0.483507, 0.00235078
Delta, 6, 0.471974, 0.00224921
Delta, 7, 0.459962, 0.00215125
Delta, 8, 0.444803, 0.00206655
Delta, 9, 0.432474, 0.0019875
Delta, 10, 0.417119, 0.00190449
Delta, 11, 0.400283, 0.0018285
Delta, 12, 0.389304, 0.00177295
Delta, 13, 0.374843, 0.00171107
Delta, 14, 0.361905, 0.00165603
Delta, 15, 0.346607, 0.00159712
Delta, 16, 0.332138, 0.001552
Delta, 17, 0.318848, 0.00152276
Delta, 18, 0.304632, 0.00148693
Delta, 19, 0.279958, 0.00148421
vega, 0, -0.000398217 ,0
vega, 1, -0.000503983 ,0
vega, 2, -0.000433718 ,0
vega, 3, -0.00041735 ,0
vega, 4, -0.000394444 ,0
vega, 5, -0.000343568 ,0
vega, 6, -0.000203087 ,0
vega, 7, -0.000253678 ,0
vega, 8, -0.000105104 ,0
vega, 9, -0.000179857 ,0
vega, 10, -0.000128656 ,0
vega, 11, -1.26837e-005 ,0
vega, 12, -8.82276e-005 ,0
vega, 13, -2.8347e-005 ,0
vega, 14, -6.22754e-005 ,0
vega, 15, 6.69944e-006 ,0
vega, 16, -4.2464e-005 ,0
vega, 17, -1.64335e-005 ,0
vega, 18, -1.94719e-005 ,0
vega, 19, 4.86087e-005 ,0
total Vega, -0.00357626
vega output
factorwise bumping 0
doCaps 1
price estimate, 0.442225
Delta, 0, 0.460573, 0.00283912
Delta, 1, 0.497331, 0.00282374
Delta, 2, 0.508616, 0.00272413
Delta, 3, 0.506396, 0.00259853
Delta, 4, 0.496328, 0.00247277
Delta, 5, 0.483507, 0.00235078
Delta, 6, 0.471974, 0.00224921
Delta, 7, 0.459962, 0.00215125
Delta, 8, 0.444803, 0.00206655
Delta, 9, 0.432474, 0.0019875
Delta, 10, 0.417119, 0.00190449
Delta, 11, 0.400283, 0.0018285
Delta, 12, 0.389304, 0.00177295
Delta, 13, 0.374843, 0.00171107
Delta, 14, 0.361905, 0.00165603
Delta, 15, 0.346607, 0.00159712
Delta, 16, 0.332138, 0.001552
Delta, 17, 0.318848, 0.00152276
Delta, 18, 0.304632, 0.00148693
Delta, 19, 0.279958, 0.00148421
vega, 0, -3.57294e-006 ,0
vega, 1, -4.20311e-005 ,0
vega, 2, 5.32395e-005 ,0
vega, 3, -3.82564e-005 ,0
vega, 4, 6.01927e-005 ,0
vega, 5, 7.88937e-005 ,0
vega, 6, 4.03392e-005 ,0
vega, 7, -6.90019e-005 ,0
vega, 8, 0.000296113 ,0
vega, 9, 6.147e-005 ,0
vega, 10, 3.59436e-005 ,0
vega, 11, 0.000211845 ,0
vega, 12, 0.000233816 ,0
vega, 13, 0.000270493 ,0
vega, 14, 9.93468e-005 ,0
vega, 15, -0.000224188 ,0
vega, 16, -0.000161354 ,0
vega, 17, -0.00024208 ,0
vega, 18, -0.000293824 ,0
vega, 19, -0.000330228 ,0
vega, 20, -0.000362651 ,0
vega, 21, -0.00036908 ,0
vega, 22, -0.000381055 ,0
vega, 23, -0.000361797 ,0
vega, 24, -0.000381614 ,0
vega, 25, -0.000381987 ,0
vega, 26, -0.000358666 ,0
vega, 27, -0.0003594 ,0
vega, 28, -0.000373214 ,0
vega, 29, -0.000372637 ,0
vega, 30, -0.000339783 ,0
vega, 31, -0.000358079 ,0
vega, 32, -0.000316225 ,0
vega, 33, -0.000279363 ,0
vega, 34, -0.000257126 ,0
total Vega, -0.00521552
vega output
factorwise bumping 1
doCaps 1
price estimate, 0.442225
Delta, 0, 0.460573, 0.00283912
Delta, 1, 0.497331, 0.00282374
Delta, 2, 0.508616, 0.00272413
Delta, 3, 0.506396, 0.00259853
Delta, 4, 0.496328, 0.00247277
Delta, 5, 0.483507, 0.00235078
Delta, 6, 0.471974, 0.00224921
Delta, 7, 0.459962, 0.00215125
Delta, 8, 0.444803, 0.00206655
Delta, 9, 0.432474, 0.0019875
Delta, 10, 0.417119, 0.00190449
Delta, 11, 0.400283, 0.0018285
Delta, 12, 0.389304, 0.00177295
Delta, 13, 0.374843, 0.00171107
Delta, 14, 0.361905, 0.00165603
Delta, 15, 0.346607, 0.00159712
Delta, 16, 0.332138, 0.001552
Delta, 17, 0.318848, 0.00152276
Delta, 18, 0.304632, 0.00148693
Delta, 19, 0.279958, 0.00148421
vega, 0, 1.07662e-005 ,0
vega, 1, -4.76854e-005 ,0
vega, 2, 4.45414e-005 ,0
vega, 3, 3.83918e-005 ,0
vega, 4, 1.5429e-005 ,0
vega, 5, 1.42451e-005 ,0
vega, 6, 0.00016313 ,0
vega, 7, 5.55873e-005 ,0
vega, 8, 0.000188954 ,0
vega, 9, 7.5709e-005 ,0
vega, 10, 9.97703e-005 ,0
vega, 11, 0.000235537 ,0
vega, 12, 9.99334e-005 ,0
vega, 13, 0.000194768 ,0
vega, 14, 8.93619e-005 ,0
vega, 15, 0.000203512 ,0
vega, 16, 1.81428e-005 ,0
vega, 17, 5.97403e-005 ,0
vega, 18, 3.41968e-006 ,0
vega, 19, -0.000256639 ,0
vega, 20, -0.000162996 ,0
vega, 21, -0.000245118 ,0
vega, 22, -0.000302819 ,0
vega, 23, -0.000341443 ,0
vega, 24, -0.000365459 ,0
vega, 25, -0.000378764 ,0
vega, 26, -0.000394877 ,0
vega, 27, -0.000400764 ,0
vega, 28, -0.000404833 ,0
vega, 29, -0.000403374 ,0
vega, 30, -0.00039906 ,0
vega, 31, -0.000400152 ,0
vega, 32, -0.000391187 ,0
vega, 33, -0.000390598 ,0
vega, 34, -0.000378079 ,0
vega, 35, -0.000380115 ,0
vega, 36, -0.000350165 ,0
vega, 37, -0.000325744 ,0
vega, 38, -0.000285695 ,0
total Vega, -0.00539463
Upper - lower is, 0.000252942, with standard error 8.50214e-005
time to compute upper bound is, 97.575, seconds.
inverse floater
fixed strikes : 0.15
number rates : 20
training paths, 65536
paths, 65536
vega Paths, 16384
rate level 0.09
0.510945
0.514723
time to build strategy, 12.071, seconds.
time to price, 19.094, seconds.
vega output
factorwise bumping 0
doCaps 0
price estimate, 0.514711
Delta, 0, 0.229676, 0.001063
Delta, 1, 0.274306, 0.00162927
Delta, 2, 0.30378, 0.00183364
Delta, 3, 0.322475, 0.00189356
Delta, 4, 0.331584, 0.00187659
Delta, 5, 0.335404, 0.00182654
Delta, 6, 0.336513, 0.00177115
Delta, 7, 0.333858, 0.00169962
Delta, 8, 0.331342, 0.00164102
Delta, 9, 0.326109, 0.00157015
Delta, 10, 0.321658, 0.00150764
Delta, 11, 0.314438, 0.00144099
Delta, 12, 0.306646, 0.00138098
Delta, 13, 0.299191, 0.00131957
Delta, 14, 0.293588, 0.00127327
Delta, 15, 0.287061, 0.00122609
Delta, 16, 0.279314, 0.00118218
Delta, 17, 0.268988, 0.00114027
Delta, 18, 0.263255, 0.00109395
Delta, 19, 0.253101, 0.00107555
vega, 0, -0.000553764 ,0
vega, 1, -0.000313659 ,0
vega, 2, -7.74467e-005 ,0
vega, 3, -7.31924e-005 ,0
vega, 4, -0.000183027 ,0
vega, 5, -7.11524e-005 ,0
vega, 6, -0.000320414 ,0
vega, 7, -0.000191643 ,0
vega, 8, -0.000179688 ,0
vega, 9, -0.000188523 ,0
vega, 10, -0.000262632 ,0
vega, 11, -0.000104735 ,0
vega, 12, -3.67112e-005 ,0
vega, 13, 5.0801e-005 ,0
vega, 14, -7.67124e-005 ,0
vega, 15, -7.93589e-005 ,0
vega, 16, -8.17007e-005 ,0
vega, 17, -0.000139193 ,0
vega, 18, -0.000148013 ,0
vega, 19, -5.69882e-006 ,0
total Vega, -0.00303646
vega output
factorwise bumping 1
doCaps 0
price estimate, 0.514711
Delta, 0, 0.229676, 0.001063
Delta, 1, 0.274306, 0.00162927
Delta, 2, 0.30378, 0.00183364
Delta, 3, 0.322475, 0.00189356
Delta, 4, 0.331584, 0.00187659
Delta, 5, 0.335404, 0.00182654
Delta, 6, 0.336513, 0.00177115
Delta, 7, 0.333858, 0.00169962
Delta, 8, 0.331342, 0.00164102
Delta, 9, 0.326109, 0.00157015
Delta, 10, 0.321658, 0.00150764
Delta, 11, 0.314438, 0.00144099
Delta, 12, 0.306646, 0.00138098
Delta, 13, 0.299191, 0.00131957
Delta, 14, 0.293588, 0.00127327
Delta, 15, 0.287061, 0.00122609
Delta, 16, 0.279314, 0.00118218
Delta, 17, 0.268988, 0.00114027
Delta, 18, 0.263255, 0.00109395
Delta, 19, 0.253101, 0.00107555
vega, 0, -9.56784e-005 ,0
vega, 1, -0.000349316 ,0
vega, 2, -0.000368785 ,0
vega, 3, -0.000392395 ,0
vega, 4, -0.000416583 ,0
vega, 5, -0.00038777 ,0
vega, 6, -0.000283443 ,0
vega, 7, -0.000292427 ,0
vega, 8, -0.000225062 ,0
vega, 9, -0.000172927 ,0
vega, 10, -0.000200831 ,0
vega, 11, -9.84221e-005 ,0
vega, 12, -8.84595e-005 ,0
vega, 13, -6.60413e-005 ,0
vega, 14, -0.000103 ,0
vega, 15, -6.94627e-005 ,0
vega, 16, -5.59954e-005 ,0
vega, 17, -2.0873e-005 ,0
vega, 18, -6.98918e-005 ,0
vega, 19, -1.7545e-006 ,0
total Vega, -0.00375912
vega output
factorwise bumping 0
doCaps 1
price estimate, 0.514711
Delta, 0, 0.229676, 0.001063
Delta, 1, 0.274306, 0.00162927
Delta, 2, 0.30378, 0.00183364
Delta, 3, 0.322475, 0.00189356
Delta, 4, 0.331584, 0.00187659
Delta, 5, 0.335404, 0.00182654
Delta, 6, 0.336513, 0.00177115
Delta, 7, 0.333858, 0.00169962
Delta, 8, 0.331342, 0.00164102
Delta, 9, 0.326109, 0.00157015
Delta, 10, 0.321658, 0.00150764
Delta, 11, 0.314438, 0.00144099
Delta, 12, 0.306646, 0.00138098
Delta, 13, 0.299191, 0.00131957
Delta, 14, 0.293588, 0.00127327
Delta, 15, 0.287061, 0.00122609
Delta, 16, 0.279314, 0.00118218
Delta, 17, 0.268988, 0.00114027
Delta, 18, 0.263255, 0.00109395
Delta, 19, 0.253101, 0.00107555
vega, 0, 2.94452e-005 ,0
vega, 1, -7.00698e-005 ,0
vega, 2, 5.31718e-005 ,0
vega, 3, 2.2747e-005 ,0
vega, 4, -1.53564e-005 ,0
vega, 5, 8.88767e-005 ,0
vega, 6, -0.000126364 ,0
vega, 7, 2.06188e-005 ,0
vega, 8, 0.000160274 ,0
vega, 9, 0.000167783 ,0
vega, 10, -0.000177057 ,0
vega, 11, 1.47564e-005 ,0
vega, 12, 0.000243835 ,0
vega, 13, 0.000153604 ,0
vega, 14, 0.000211906 ,0
vega, 15, -0.000305443 ,0
vega, 16, -3.49366e-005 ,0
vega, 17, -0.000112531 ,0
vega, 18, -0.000180932 ,0
vega, 19, -0.000236119 ,0
vega, 20, -0.000291275 ,0
vega, 21, -0.000318101 ,0
vega, 22, -0.000331099 ,0
vega, 23, -0.000332397 ,0
vega, 24, -0.000358864 ,0
vega, 25, -0.000382323 ,0
vega, 26, -0.000343456 ,0
vega, 27, -0.000325816 ,0
vega, 28, -0.000356584 ,0
vega, 29, -0.000354673 ,0
vega, 30, -0.000333586 ,0
vega, 31, -0.000377143 ,0
vega, 32, -0.000344616 ,0
vega, 33, -0.000308718 ,0
vega, 34, -0.00028993 ,0
total Vega, -0.00514037
vega output
factorwise bumping 1
doCaps 1
price estimate, 0.514711
Delta, 0, 0.229676, 0.001063
Delta, 1, 0.274306, 0.00162927
Delta, 2, 0.30378, 0.00183364
Delta, 3, 0.322475, 0.00189356
Delta, 4, 0.331584, 0.00187659
Delta, 5, 0.335404, 0.00182654
Delta, 6, 0.336513, 0.00177115
Delta, 7, 0.333858, 0.00169962
Delta, 8, 0.331342, 0.00164102
Delta, 9, 0.326109, 0.00157015
Delta, 10, 0.321658, 0.00150764
Delta, 11, 0.314438, 0.00144099
Delta, 12, 0.306646, 0.00138098
Delta, 13, 0.299191, 0.00131957
Delta, 14, 0.293588, 0.00127327
Delta, 15, 0.287061, 0.00122609
Delta, 16, 0.279314, 0.00118218
Delta, 17, 0.268988, 0.00114027
Delta, 18, 0.263255, 0.00109395
Delta, 19, 0.253101, 0.00107555
vega, 0, 7.98415e-006 ,0
vega, 1, -2.4354e-005 ,0
vega, 2, 3.70234e-005 ,0
vega, 3, 3.92433e-005 ,0
vega, 4, -1.83597e-005 ,0
vega, 5, -2.70327e-005 ,0
vega, 6, 7.08649e-005 ,0
vega, 7, -7.11253e-006 ,0
vega, 8, 6.39676e-005 ,0
vega, 9, 9.43271e-005 ,0
vega, 10, 2.82271e-005 ,0
vega, 11, 0.000131976 ,0
vega, 12, 9.74938e-005 ,0
vega, 13, 0.000161235 ,0
vega, 14, 6.30819e-005 ,0
vega, 15, 0.000104268 ,0
vega, 16, 5.25182e-005 ,0
vega, 17, 0.00010306 ,0
vega, 18, 1.90082e-005 ,0
vega, 19, -0.000340687 ,0
vega, 20, -3.52881e-005 ,0
vega, 21, -0.000117964 ,0
vega, 22, -0.000188503 ,0
vega, 23, -0.000245255 ,0
vega, 24, -0.000284163 ,0
vega, 25, -0.000311209 ,0
vega, 26, -0.000335292 ,0
vega, 27, -0.000345112 ,0
vega, 28, -0.000355703 ,0
vega, 29, -0.000362711 ,0
vega, 30, -0.000363717 ,0
vega, 31, -0.000366123 ,0
vega, 32, -0.00036084 ,0
vega, 33, -0.000365133 ,0
vega, 34, -0.000358883 ,0
vega, 35, -0.000358315 ,0
vega, 36, -0.000343427 ,0
vega, 37, -0.00033602 ,0
vega, 38, -0.000324417 ,0
total Vega, -0.00510134
Upper - lower is, 0.000176731, with standard error 6.68822e-005
time to compute upper bound is, 100.103, seconds.
Multi-dim Integral
--------------
Exact: 2.6303
Quad: 2.6303
Grid: 2.6303
Seconds for Quad: 0.0020
Seconds for Grid: 0.1270
Replication
===========================================================================
Initial market conditions
===========================================================================
Option NPV Error
---------------------------------------------------------------------------
Original barrier option 4.260726 N/A
Replicating portfolio (12 dates) 4.322358 0.061632
Replicating portfolio (26 dates) 4.295464 0.034738
Replicating portfolio (52 dates) 4.280909 0.020183
===========================================================================
Modified market conditions: out of the money
===========================================================================
Option NPV Error
---------------------------------------------------------------------------
Original barrier option 2.513058 N/A
Replicating portfolio (12 dates) 2.539365 0.026307
Replicating portfolio (26 dates) 2.528362 0.015304
Replicating portfolio (52 dates) 2.522105 0.009047
===========================================================================
Modified market conditions: in the money
===========================================================================
Option NPV Error
---------------------------------------------------------------------------
Original barrier option 5.739125 N/A
Replicating portfolio (12 dates) 5.851239 0.112114
Replicating portfolio (26 dates) 5.799867 0.060742
Replicating portfolio (52 dates) 5.773678 0.034553
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The replication seems to be less robust when volatility and
risk-free rate are changed. Feel free to experiment with
the example and contribute a patch if you spot any errors.
Run completed in 0 s
Repo
Underlying bond clean price: 89.9769
Underlying bond dirty price: 93.288
Underlying bond accrued at settlement: 3.31111
Underlying bond accrued at delivery: 3.33333
Underlying bond spot income: 3.9834
Underlying bond fwd income: 4.08465
Repo strike: 91.5745
Repo NPV: -2.8066e-005
Repo clean forward price: 88.2411
Repo dirty forward price: 91.5745
Repo implied yield: 5.000063 % Actual/360 simple compounding
Market repo rate: 5.000000 % Actual/360 simple compounding
Compare with example given at
http://www.fincad.com/support/developerFunc/mathref/BFWD.htm
Clean forward price = 88.2408
In that example, it is unknown what bond calendar they are
using, as well as settlement Days. For that reason, I have
made the simplest possible assumptions here: NullCalendar
and 0 settlement days.
Run completed in 0 s
Swap valuation
Today: Monday, September 20th, 2004
Settlement date: Wednesday, September 22nd, 2004
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5-year market swap-rate = 4.43 %
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5-years swap paying 4.00 %
term structure | net present value | fair spread | fair fixed rate |
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depo-swap | 19065.88 | -0.42 % | 4.43 % |
depo-fut-swap | 19076.14 | -0.42 % | 4.43 % |
depo-FRA-swap | 19056.02 | -0.42 % | 4.43 % |
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5-years, 1-year forward swap paying 4.00 %
term structure | net present value | fair spread | fair fixed rate |
--------------------------------------------------------------------
depo-swap | 40049.46 | -0.92 % | 4.95 % |
depo-fut-swap | 40092.79 | -0.92 % | 4.95 % |
depo-FRA-swap | 37238.92 | -0.86 % | 4.88 % |
====================================================================
5-year market swap-rate = 4.60 %
====================================================================
5-years swap paying 4.00 %
term structure | net present value | fair spread | fair fixed rate |
--------------------------------------------------------------------
depo-swap | 26539.06 | -0.58 % | 4.60 % |
depo-fut-swap | 26553.34 | -0.58 % | 4.60 % |
depo-FRA-swap | 26525.34 | -0.58 % | 4.60 % |
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5-years, 1-year forward swap paying 4.00 %
term structure | net present value | fair spread | fair fixed rate |
--------------------------------------------------------------------
depo-swap | 45736.04 | -1.06 % | 5.09 % |
depo-fut-swap | 45782.40 | -1.06 % | 5.09 % |
depo-FRA-swap | 42922.60 | -0.99 % | 5.02 % |
Run completed in 2 s