Pricing Forward Skew Dependent Derivatives. Multifactor Versus Single‐Factor Stochastic Volatility Models

Abstract

AbstractEmpirical evidence shows that, in equity options markets, the slope of the skew is largely independent of the volatility level. Single‐factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew. On the other hand, multifactor stochastic volatility models are able to account for the existence of stochastic skew. This study studies the effects of introducing stochastic skew in the valuation of forward skew dependent exotic options. In particular, I consider cliquet, as well as reverse cliquet structures. The study also derives a semi‐closed‐form solution for the price of forward‐start options under the multifactor stochastic specification. The empirical results indicate that the consideration of additional volatility factors in the context of stochastic volatility models allows us to generate more flexible smile patterns. This additional flexibility has a relevant impact on the valuation of forward skew dependent derivatives. In this sense, this study shows that similar calibrations of single factor and multifactor stochastic volatility models to the current market prices of plain vanilla options can lead to important discrepancies in the pricing of exotic forward skew dependent derivatives such as regular cliquet structures and reverse cliquet options. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:124–144, 2014