Quanto Derivatives in Local Volatility Models

Abstract

The valuation of quanto options is dependent on the dynamic of the underlying equity and FX processes, and valuing them under models capturing both implied volatility skews is an active topic of research. In this article, we present a new method to calculate quanto options under a local volatility assumption. Our approach is based on applying stochastic expansion techniques pioneered by Emmanuel Gobet to a time-dependent quadratic local variance model. In passing we also derive accurate time averaging formulas for such models enabling an efficient and robust calibration to implied volatility.