混合次分数跳扩散模型下回望期权的定价及模拟  

Pricing and simulation of lookback options under the mixed sub-fractional jump-diffusion model

作　　者：安翔 郭精军 AN Xiang;GUO Jing-jun(School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020,Gansu,China)

机构地区：[1]兰州财经大学统计学院,甘肃兰州730020

出　　处：《山东大学学报（理学版）》2022年第4期100-110,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(71961013);甘肃省教育厅“双一流”科研重点项目(GSSYLXM-06);甘肃省飞天学者计划。

摘　　要：基于混合次分数布朗运动和Poisson过程,建立了具有交易费用的欧式回望期权定价模型。首先,利用Δ-对冲原理得到了该期权价格所满足的非线性偏微分方程,并通过构造Crank-Nicolson格式求得其数值解。然后,验证了该数值解的有效性,并讨论了交易费用、波动率与无风险利率等对期权价值的影响。最后,选取浦东发展银行的日收盘价进行模拟分析,结果表明:基于混合次分数跳扩散模型的模拟价格更加接近股票的真实值,能够更好地反映股票的整体走势。The pricing model of European lookback options with transaction costs is established based on the mixed sub-fractional Brownian motion and Poisson process. Firstly, the nonlinear partial differential equation satisfied by the price of the option is obtained using the Delta hedging principle, and its numerical solution is obtained by constructing a Crank-Nicolson format. Secondly, the validity of the numerical method is verified, and the effects of transaction costs, volatility and risk-free interest rate on the value of the option are respectively discussed. Finally, the daily closing price of Shanghai Pudong Development Bank is selected for the simulation, and the results show that the simulated price based on the mixed sub-fractional jump-diffusion model is closer to the real value of the stock, and can better reflect the overall stock trend.

关 键 词：混合次分数布朗运动 跳扩散模型 欧式回望期权 交易费 CRANK-NICOLSON格式 

分 类 号：O211.6[理学—概率论与数理统计] F224.7[理学—数学]