A Fast Fourier Transform Technique for Pricing European Options with Stochastic Volatility and Jump Risk. (27th February 2012)

• Record Type: Journal Article
• Authors: Zhang, Su-mei; Wang, Li-he
• Other Names: Aliyu M. D. S. Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-02-27
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/761637
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility (SVDEJD). We developed fast and accurate numerical solutions by using fast Fourier transform (FFT) technique. We compared the density of our model with those of other models, including the Black-Scholes model and the double exponential jump-diffusion model. At last, we analyzed several effects on option prices under the proposed model. Simulations show that the SVDEJD model is suitable for modelling the long-time real-market changes and stock returns are negatively correlated with volatility. The model and the proposed option pricing method are useful for empirical analysis of asset returns and managing the corporate credit risks.