Calibration of GARCH models using concurrent accelerated random search

This paper investigates a global optimization algorithm for the calibration of stochastic volatility models. Two GARCH models are considered, namely the Leverage and the Heston-Nandi model. Empirical information on option prices is used to minimize a loss function that reflects the option pricing error. It is shown that commonly used gradient based optimization procedures may not lead to a good solution and often converge to a local optimum. A concurrent approach where several optimizers (“particles”) execute an accelerated random search (ARS) procedure has been introduced to thoroughly explore the whole parameter domain. The number of particles influences the solution quality and computation time, leading to a trade-off between these two factors. In order to speed up the computation, distributed computing and variance reduction techniques are employed. Tests show that the concurrent ARS approach clearly outperforms the standard gradient based method.