支付红利的跳-扩散过程的股票期权定价

Option pricing from the price of stock dividends-payment and a jump-diffusion process

目的研究股票支付红利。方法在市场无套利条件下建立随机微分方程,运用鞅论、随机分析的方法分析并求解方程。结果得到了支付红利的跳-扩散过程的欧式看涨期权的定价公式及欧式看涨看跌期权之间的平价公式。结论在实际中股票价格的跳过程不一定是Poisson跳,红利率也未必是常数,其价格服从跳-扩散过程的期权定价还有待于进一步研究更为复杂情形下的期权定价。

Aim To study the option pricing from the price of stock dividends-payment and a Jump-diffusion process. Methods Build up differential equation under the circumstance of the market no arbitrage. Analyze and work out the solution of equation. Results European call option pricing formula and put-call parity were obtained considering the price of stock dividends-payment and a jump-diffusion process. Conclusion Getting option pricing formula, but in practice the price of stock is not always Poisson jump and dividend is not constant. Therefore, we should study further.