一类特殊混合跳-扩散模型的欧式回望期权定价

Pricing European lookback option by a special kind of mixed jump-diffusion model

利用分数Girsanov公式和分数Wick-It-Skorohod积分,建立了一个基于标准布朗运动、分数布朗运动、Poisson过程的线性组合的金融市场模型,结合Merton假设条件以及风险资产所满足的随机微分方程的Cauchy初值问题,给出了混合跳-扩散模型下的欧式看跌期权定价的Merton公式,给出了混合跳-扩散分数布朗运动下连续支付红利的欧式固定履约价和浮动履约价的看涨回望期权及看跌回望期权定价公式.数值模拟与仿真结果验证了模型的有效性和准确性.

By using fractional Girsanov formula and fractional Wick-Ito-Skorohod integral, based on a linear combination of Brownian motion, fractional Brownian motion and Poisson process, a new market pricing model is built. Under the conditions of Merton assumptions, we analyze the Cauchy initial problem of stochastic parabolic partial differential equations. Then the pricing Merton-formula of European option meets the pricing model for the European fixed strike and floating strike price of the lookback option. Finally the pricing formulas of fixed strike and floating strike lookback call option and lookback put option are proved. Numerical simulations illustrate that our model are valid and accurate.