Pricing American/Bermudan-style Options under Stochastic Volatility

Jankelow, Adam

Pricing American/Bermudan-style Options under Stochastic Volatility

Master Thesis

2020

Abstract

A method to price American options under a stochastic volatility framework is introduced which is based on Rambharat and Brockwell (2010). We price American options under the Heston and Bates stochastic volatility models where volatility is assumed to be a latent process. The pricing algorithm is based on the least-squares Monte Carlo approach made popular by Longstaff and Schwartz (2001). Information about the volatility of the underlying asset is used to assist in solving the pricing problem. Since volatility is assumed to be a latent, a particle filter is used to estimate the filtering distribution of volatility. A summary vector is constructed which captures the essential features of the filtering distribution. At each time step before maturity, the elements of the summary vector and the current share price are used as explanatory variables in a regression function which estimates the continuation value of the option. Estimating the continuation value assists in finding the optimal time to exercise the option. This pricing approach is benchmarked against a method which assumes volatility is observable. Furthermore, our pricing approach is compared to simpler methods which do not use particle filtering. Results from our numerical experiments suggest the proposed approach produces accurate option prices.

Keywords

Mathematical Finance

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