Calibration of the Multiscale Stochastic Volatility Model via an Asymptotic Expansion Approach

Abstract: We study a model of multiscale stochastic volatility for European option pricing. In this model there are two volatility factors. The rst volatility factor is of fast scale of mean-reverting and the second one is of slow scale of mean-reverting. We review the useful calibration formula derived by Fouque et al.[2] via an asymptotic expansion method. Our purpose of this study is two-fold. The rst task is to implement this calibration formula to Swedish market data, more specically to call option data of ABB stock during the time span of 4th Mar 2016 to 6th May 2016. We investigate how well the data tting is assuming only the fast volatility factor and the full model with both fast and slow volatility factors. We study also the time stability of the tted parameters over a time period of 10 weeks. The second task is to study the eect of the parameters included in the calibration formula on the volatility surface and smile.