Study On Jump-Diffusion Model For China’s Financial Market

In early1970s, Black and Scholes set up stock price model based on ge-ometric Brownian motion, and obtained the famous option pricing formula. In1979. Merton modified the Black-Scholes Model by adding jumps to the diffusion process, which could better describe the rare events in the finan-cial market. Later, different, forms of jump-diffusion model were proposed, among which the most representative model is Kou’s double exponential jump-diffusion model. Compared to the more general Levy process-driven model, jump-diffusion model is easier to understand and easier to process simulation. Concerned with daily limit to stock price in China’s financial market, this pa-per proposes a new class of jump-diffusion model. Different with Merton and Kou model. in this model the jump amplitude is limited to a finite interval. rather than the entire real axis. In this paper, the jump magnitude which meets the log uniform distribution is further modified to meet the so-called " triangular distribution". And this paper also takes advantage of the Fourier transform method for the European option pricing formula, and uses the FFT algorithm and Monte Carlo methods for numerical solution.