Topics on option valuation and model calibration

option pricing;model calibration;analytic class;characteristic function;simulation;inverse transform

Chen, Zisheng

关键词: option pricing;    model calibration;    analytic class;    characteristic function;    simulation;    inverse transform;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/44400/Zisheng_Chen.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

This dissertation is devoted to high performance numerical methods for option valuation and modelcalibration in L´evy process and stochastic volatility models. In the first part, a numerical schemefor simulating from an analytic characteristic function is developed. Theoretically, error boundsfor bias are explicitly given. Practically, different types of options in commonly used L´evy processmodels could be priced through this method fast and accurately. Also, sensitivity analysis could beconducted through this approach effectively. Numerical results show that the schemes are effectivefor both options valuation and sensitivity analysis in L´evy process models. In the second part, anumerical scheme for Asian option pricing in jump-diffusion models is analyzed. Approximationerrors are shown to decay exponentially. Numerical results show the speed and accuracy of thescheme. In the third part, for calibration purpose, certain numerical schemes are studied to priceEuropean and American options. For European options, error bounds are explicitly given. ForAmerican contracts, multiple options with different strikes and maturities could be priced simultaneously.Numerical results show that the combination of the above schemes with state-of-the-artoptimization schemes makes efficient calibration of option pricing models possible.