Pricing Bermudan Swaptions in a Stochastic Volatility Model

Abstract

In this thesis we consider the one-factor Quassi-Gaussian model with stochastic volatility which is a stochastic volatility model within the Cheytte model framework. We describe how the model can be used to price European swaptions in closed-form and Bermudan swaptions using least squares Monte Carlo simulation. We analyze how well the model calibrates to the implied volatility surfaces of European swaptions on five yearly spaced dates in September from 2019 to 2023. We test the model in three variations based on the number of parameters that we allow to be functions of time. We find that time-dependency in the parameters is necessary for the model to produce an acceptable fit across most of the observations and that allowing for the level of volatility to be a function of time is the most impactful. By calibrating the model to a coterminal swaption strip, we show in detail how the calibrated model can be used to price a selection of Bermudan payer swaptions of varying maturity through simulation techniques. We show how the mean reversion parameter in the model affects the prices of Bermudan payer swaptions, and how it can be used as a free parameter to control the price of Bermudan swaptions.