The double Heston model via filtering methods

[摘要] ENGLISH ABSTRACT : Stochastic volatility models are well-known for their ability to generate avolatility smile for financial securities. The development of the stochasticvolatility models followed shortly after the crash of 1987 which violates theBlack-Scholes model which has constant volatility. In this study we introducenon-linear filtering methods to estimate the implied volatilities of the DoubleHeston model. We compare our results to the Standard Heston model. Thenon-linear filtering methods used are the extended Kalman filter, the unscentedKalman filter and the particle filter. We combine thefiltering methods togetherwith the maximum likelihood estimation method to estimate the model's hiddenparameters. Our numerical results show that the Double Heston model ts the market implied volatilities better than the Standard Heston model.The particlelter also performs better than the other twofilters.

[发布机构] Stellenbosch University