关键词: 混合指数跳扩散模型, FST 方法, 欧式期权定价, 偏积分-微分方程, 模型校正

Abstract: The mixed exponential jump-diffusion model that can approximate any distribution is widely used to describe the actual trend of stock price. Based on the Fourier Space Time-stepping (FST) method, this paper considers European option pricing under the mixed exponential jump-diffusion model. By the Fourier transform and the characteristic exponent, the partial integral-differential equation for pricing European options is transformed into an ordinary differential equations and solved to obtain European option prices. Numerical results indicate that the FST method is accurate and fast. Moreover, by collecting real market data and the nonlinear least squares method, we apply the obtained option price to model calibration to obtain the model parameters which match the real market. By examining the impact of jump parameters on the implied volatility, we find that the mixed exponential jump-diffusion model can well reflect the volatility ``smile" of asset returns.

Key words: mixed-exponential jump diffusion model, FST method, European option pricing, partial-integro differential equation, model calibration