Power Series Representations for European Option Prices under Stochastic Volatility Models

TL;DR

This paper develops power series representations for European call option prices under stochastic volatility models, utilizing expectation formulas, Malliavin calculus, and Monte Carlo methods to improve pricing accuracy and computational efficiency.

Contribution

It introduces novel power series coefficient formulas based on the generalized Hull-White approach and extends sensitivity analysis using Malliavin calculus for various options.

Findings

Effective Monte Carlo estimators demonstrated for multiple models

Power series approach improves option pricing accuracy

Sensitivity analysis extended beyond vanilla options

Abstract

In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset price process and the volatility process. We first obtain expressions for the power series' coefficients from the generalized Hull and White formula obtained by Elisa Al\`os. Afterwards, we provide representations turning out from the approach for the sensitivity problem tackled by Malliavin calculus techniques, and these allow to handle not only vanilla options. Finally, we show the numerical performance of the associated Monte Carlo estimators for several stochastic volatility models.