一类混合跳-扩散分数布朗运动的欧式回望期权定价

利用混合分数布朗运动的Itó公式和复合泊松过程驱动的随机微分方程, 建立了一类混合跳-扩散分数布朗运动环境下的价格模型,在Merton假设条件下对其随机微分方程的Cauchy初值问题采用迭代法作了估计,得到了混合跳-扩散模型下的欧式看跌期权定价的Merton公式, 从而给出了混合跳-扩散分数布朗运动欧式浮动履约价的看涨回望期权和看跌回望期权定价公式。

A kind of European lookback option pricing model under fractional jump-diffusion mixed fractional Brownian motion

The mixed jump-diffusion fractional Brownian motion model under the Itó formula and fractional diffusion process with non-homogeneous Poisson process was proposed. By using the iterative method, the Cauchy initial problem of stochastic differential equations were estimated under the conditions of Merton assumptions. Then the pricing Merton formula of European option that meets the pricing model for the European floating strike price of the lookback option was obtained. Finally the pricing formulas of floating strike lookback call option and lookback put option were proofed.