On the calibration of stochastic volatility models: A comparison study

We studied the application of gradient based optimization methods for calibrating stochastic volatility models. In this study, the algorithmic differentiation is proposed as a novel approach for Greeks computation. The “payoff function independent” feature of algorithmic differentiation offers a unique solution cross distinct models. To this end, we derived, analysed and compared Monte Carlo estimators for computing the gradient of a certain payoff function using four different methods: algorithmic differentiation, Pathwise delta, likelihood ratio and finite differencing. We assessed the accuracy and efficiency of the four methods and their impacts into the optimisation algorithm. Numerical results are presented and discussed.