The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model

Abstract

The author considers SABR model which is a two factor stochastic volatility model and gives an asymptotic expansion formula of implied volatilities for this model. His approach is based on infinite dimensional analysis on the Malliavin calculus and large deviation.

Furthermore, he applies the approach to a foreign exchange model where interest rates and the FX volatilities are stochastic and gives an asymptotic expansion formula of implied volatilities of foreign exchange options.

Keywords: stochastic volatility models, volatility smile, Malliavin calculus, asymptotic approximation, Foreign Exchange Options

JEL Classification: G12, G13