Calibration Of Option Pricing Models And Empirical Comparison Of Hedging Effectiveness On Exotic Options

This thesis selects Hang Seng Chinese Enterprise Index (HSCEI) as underlyingasset of exotic options to test the empirical hedging effectiveness of five popular optionpricing models, i.e. Black-Scholes model, Merton’s jump-diffusion model, Heston’sstochastic volatility model, Bates model and local volatility model.To estimate the model parameters, three calibration algorithms are studied and theircalibration performances are examined by a series of simulation experiments. Theresults of simulation experiments show that Levenberg-Marquardt algorithm convergesto the true parameters fastest and is able to function stably given poor initial guess ofparameters. By using Levenberg-Marquardt algorithm, the four parametric optionpricing models are calibrated to the market prices of HSCEI call options. Thenon-parametric local volatility model is calibrated by Dupire’s formula.With the calibrated option pricing models, the hedging effectiveness of the fiveoption pricing models is tested to find out which one yields the best hedgingperformance on exotic options (barrier and Asian options) with different characteristicsunder minimum variance and delta-vega neutral hedging strategies. The test results showthat the hedging effectiveness is closely related to the path-dependency of exotic optionsand that increased path-dependency would lead to worse hedging effectiveness. Throughthe comparison of relative hedging performances of the five models, Bates model isfound to be the overall best performer under minimum variance hedging strategy whileHeston’s stochastic volatility model shows the best hedging effectiveness underdelta-vega neutral hedging strategy.