Geometric Asian options: valuation and calibration with stochastic volatility

This paper studies continuously sampled geometric Asian options (GAO) in a stochastic volatility economy. The underlying asset price is assumed to follow a geometric Brownian motion with stochastic volatility driven by a mean-reverting process. Semi-analytical pricing formulae for GAO are derived in a fast mean-reverting stochastic volatility economy by the means of a perturbation method. The effects of stochastic volatility on averaging type options are examined. A unified regression approach is proposed to capture smiles of some geometric Asian options and European options in one shot.