| An alternative option pricing model is proposed, in which the underlying asset follows a stochastic-volatility jump-diffusion model with log-uniform jump amplitude (SVJD-Uniform) and mean-reverting square-root stochastic volatility process under "risk-neutral" probability measure. Fourier transforms are applied to solve the problem for risk-neutral European option prices under this compound process. Closed form European option pricing formulas are obtained. The numerical implementation of pricing formulas is accomplished by both FFTs and highly accurate Gaussian quadrature.; Based on the accurate and fast European option pricing formulas, we calibrate the models to S&P 500 Index option quotes by least squares method. Spot variance and structural parameters for different models including Black-Scholes, Stochastic-Volatility. SVJD-Uniform, SVJD-Normal, SVJD-DbExp are estimated. Fitting performance of different models are compared and our proposed SVJD-Uniform model is found to fit the market data the best.; For American option pricing on SVJD-Uniform model we derive an analytical quadratic approximation and give the finite difference scheme on Linear Complementarity Problem (LCP) formulation. The results of these two approaches are compared. American option values from two approaches are close and each method has its advantage. The American option pricing approximation formula is checked with real market S&P 100 Index option quotes and gives satisfying results. |
