Prices a cms coupon using a linear terminal swap rate model
The slope parameter is linked to a gaussian short rate model.
Reference: Andersen, Piterbarg, Interest Rate Modeling, 16.3.2
The cut off point for integration can be set
by explicitly specifying the lower and upper bound
by defining the lower and upper bound to be the strike where
a vanilla swaption has 1% or less vega of the atm swaption
by defining the lower and upper bound to be the strike where
undeflated (!) payer resp. receiver prices are below a given
threshold
by specificying a number of standard deviations to cover
using a Black Scholes process with an atm volatility as
a benchmark
In every case the lower and upper bound are applied though.
In case the smile section is shifted lognormal, the specified
lower and upper bound are applied to strike + shift so that
e.g. a zero lower bound always refers to the lower bound of
the rates in the shifted lognormal model.
Note that for normal volatility input the lower rate bound
is adjusted to min(-upperBound, lowerBound), except the bounds
are set explicitly.
CMS-coupon pricer
Prices a cms coupon using a linear terminal swap rate model The slope parameter is linked to a gaussian short rate model. Reference: Andersen, Piterbarg, Interest Rate Modeling, 16.3.2
The cut off point for integration can be set
In every case the lower and upper bound are applied though. In case the smile section is shifted lognormal, the specified lower and upper bound are applied to strike + shift so that e.g. a zero lower bound always refers to the lower bound of the rates in the shifted lognormal model. Note that for normal volatility input the lower rate bound is adjusted to min(-upperBound, lowerBound), except the bounds are set explicitly.