Testing robustness in calibration of stochastic volatility models

Many numerical aspects are involved in parameter estimation of stochastic volatility models. We investigate a model for stochastic volatility suggested by Hobson and Rogers and we focus on its calibration performance with respect to numerical methodology. In recent financial literature there are many papers dealing with stochastic volatility models and their capability in capturing European option prices; in Figà-Talamanca and Guerra a comparison between some of the most significant models is done. The model proposed by Hobson and Rogers seems to describe quite well the dynamics of volatility. In Figà-Talamanca and Guerra a deep investigation of the Hobson and Rogers model was put forward, introducing different ways of parameters' estimation. In this paper we test the robustness of the numerical procedures involved in calibration: the quadrature formula to compute the integral in the definition of some state variables, called offsets, that represent the weight of the historical log-returns, the discretization schemes adopted to solve the stochastic differential equation for volatility and the number of simulations in the Monte Carlo procedure introduced to obtain the option price. The main results can be summarized as follows. The choice of a high order of convergence scheme is not fully justified because the option prices computed via calibration method are not sensitive to the use of a scheme with 2.0 order of convergence or greater. The refining of the approximation rule for the integral, on the contrary, allows to compute option prices that are often closer to market prices. In conclusion, a number of 10 000 simulations seems to be sufficient to compute the option price and a higher number can only slow down the numerical procedure.