European Option Pricing Under The Mean-reverting Bivariate Exponential Jump-diffusion Model With Stochastic Interest Rate And Stochastic Volatility

Option was the successful innovation example of the financial derivative market in the 20 th century. And options market is an important part of the global financial market. In early 2015 the first national branch 50 ETF advent options open a new chapter in the domestic options market, option pricing theory research presented more diversified.Based on the traditional Black-Scholes model, the probability for a classic double exponential jump process considers generated after its jump process occurs attenuation affect the probability of continuing in the same direction jump occurred is changing, that jump process is self-dependent, but bounded autocorrelation relative performance in the probability of occurrence, thereby projecting in the same direction may be limited successive jumping and jumping state results, construct a mean-reverting bivariate exponential jump-diffusion model, which makes its more reality of simulation the market emergencies. The probability of occurrence of the jump process constraints such models become more complex. Through detailed analysis of the cumulative process jumps state change, state transition probability matrix is solved by means of a characteristic function accumulation process and complementary characteristics often no arbitrage interest rate volatility model based on martingale condition. Reintroduction Stochastic Interest stochastic volatility model based on CIR process in this no-arbitrage model. Followed by change of measure, the introduction of zero-coupon bonds under a long-term measure as the standard unit of account, calculated on the number of actual price measure and equivalent martingale measure under the characteristic function, using the fast fourier transform to solve a Continental characteristic function expression call and put option pricing formula.