连续红利支付的跳-扩散模型下幂期权的定价

Power option pricing of the continuous dividend payment model with jump-diffusion

在假设股票价格服从带非齐次Poisson跳-扩散过程且在连续时间支付红利的情况下,建立了股票价格行为模型,同时应用保险精算法给出一类奇异期权——欧式幂期权——看涨和看跌两种情形的定价公式,以推广Merton关于期权定价的结果.得到的结果优于无红利支付的情况,使该定价公式更接近市场实际情况.

Assuming that the stock company pays dividend continuously and the dividend was related with the price of the stock in the time that the stock company pays dividend,and the pricing process was jump-diffu-sion process,the jump process was Poisson process,the stock pricing model was established.And it gave the European call power option and the European put power option pricing model using insurance actuary pri-cing.The result of Merton on European option pricing was generalized.It was superior to no-dividend payment and it was more closed to the actual market situation.