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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。
Using the Itó formula of mixed fractional Brownian motion and the stochastic differential equation driven by complex Poisson process, a class of mixed jump - diffusion fractional Brownian motion environment price model is established. The Cauchy initial value of stochastic differential equations under the Merton assumption The problem is estimated by an iterative method, and the Merton formula for the European put option pricing under the mixed jump-diffusion model is given. The put-call lookback option and putback look-back option are given for the European floating strike price of the hybrid jump-diffusion fractional Brownian move Pricing formula.