Pricing American options under partial observation of stochastic volatility

Abstract

Stochastic volatility models capture the impact of time-varying volatility on the financial markets, and hence are heavily used in financial engineering. However, stochastic volatility is not directly observable in reality, but is only “partially” observable through the inference from the observed asset price. Most of the past research studied American option pricing in stochastic volatility models under the assumption that the volatility is fully observable, which often leads to overpricing of the option. In this paper, we treat the problem under the more realistic assumption of partially observable stochastic volatility, and propose a numerical solution method by extending the regression method and the martingale duality approach to the partially observable case. More specifically, we develop a filtering-based martingale duality approach that complements a lower bound on the option price with an approximate upper bound. Numerical experiments show that our method reduces overpricing of the option with a moderate computational cost.