Exotic Geometric Average Options Pricing under Stochastic Volatility

Abstract

This article derives semi-analytical pricing formulae for geometric average options (GAOs) within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, the cross-moment generating function is derived and the cumulative probabilities are recovered using the Gauss–Laguerre quadrature rule. Fixed and floating strikes as well as other exotic GAO on different assets such as stocks, currency exchange rates and interest rates are derived. The approach is found to be very accurate and efficient.