analytic Heston-model engine based on Fourier transform
Integration detail:
Two algebraically equivalent formulations of the complex
logarithm of the Heston model exist. Gatherals [2005]
(also Duffie, Pan and Singleton [2000], and Schoutens,
Simons and Tistaert[2004]) version does not cause
discoutinuities whereas the original version (e.g. Heston [1993])
needs some sort of "branch correction" to work properly.
Gatheral's version does also work with adaptive integration
routines and should be preferred over the original Heston version.
References:
Heston, Steven L., 1993. A Closed-Form Solution for Options
with Stochastic Volatility with Applications to Bond and
Currency Options. The review of Financial Studies, Volume 6,
Issue 2, 327-343.
analytic Heston-model engine based on Fourier transform
Integration detail:
Two algebraically equivalent formulations of the complex logarithm of the Heston model exist. Gatherals [2005] (also Duffie, Pan and Singleton [2000], and Schoutens, Simons and Tistaert[2004]) version does not cause discoutinuities whereas the original version (e.g. Heston [1993]) needs some sort of "branch correction" to work properly. Gatheral's version does also work with adaptive integration routines and should be preferred over the original Heston version.
References:
Heston, Steven L., 1993. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. The review of Financial Studies, Volume 6, Issue 2, 327-343.
A. Sepp, Pricing European-Style Options under Jump Diffusion Processes with Stochastic Volatility: Applications of Fourier Transform (http://math.ut.ee/~spartak/papers/stochjumpvols.pdf)
R. Lord and C. Kahl, Why the rotation count algorithm works, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=921335
H. Albrecher, P. Mayer, W.Schoutens and J. Tistaert, The Little Heston Trap, http://www.schoutens.be/HestonTrap.pdf
J. Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley Finance
F. Le Floc'h, Fourier Integration and Stochastic Volatility Calibration, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2362968
L. Andersen, and V. Piterbarg, 2010, Interest Rate Modeling, Volume I: Foundations and Vanilla Models, Atlantic Financial Press London.
test the correctness of the returned value is tested by reproducing results available in web/literature and comparison with Black pricing.