混合次分数布朗运动机制下带有随机利率的欧式期权定价模型  

Option Pricing Under the Merton Short Rate Model in the Mixed Sub-fractional Brownian Motion Regime

作　　者：王欣怡 郭志东 WANG Xinyi;GUO Zhidong(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2022年第1期92-98,共7页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省自然科学基金(1908085QA29)。

摘　　要：期权定价是金融数学中的重要研究问题,而长程相关性是标的资产价格变化的一个重要特征。标的资产价格变化的随机驱动源通常为几何布朗运动,已有的期权定价模型无法刻画标的资产价格变化的这一特征,而混合次分数布朗运动可以较好地描述。此外,利率的非常值性也是金融市场的重要特征之一,Merton利率模型是一个经典的随机利率模型。基于此,将混合次分数布朗运动和随机利率同时纳入到期权定价模型中,建立混合次分数布朗运动机制下的Merton随机利率模型,运用偏微分方程方法得到欧式期权的定价公式,给出了相关的数值计算并讨论模型下的隐含波动率问题。Option pricing is an important research problem in financial mathematics.Long-range correlation is an important characteristic of the price changes of the underlying assets.In the existing option pricing models,the random driving source of the price changes of the underlying assets is usually geometric Brownian motion,which cannot describe the characteristic of the price changes of the underlying assets,while the mixed sub-fractional Brownian motion can better describe this feature.Moreover,non-constant value of interest rate is also one of the important characteristics of financial market,and Merton model of the short rate is a relatively classical stochastic interest rate model.Based on this,the mixed sub-fractional Brownian motion and stochastic short rate are incorporated into the option pricing model at the same time in this paper.Option pricing under the Merton model of the short rate in the mixed sub-fractional Brownian motion regime is established.We derive the pricing formula for European option by using partial differential equation method and give the related numerical calculation.In addition,we also discuss implied volatility of this model.

关 键 词：期权定价 混合次分数布朗运动 Merton随机利率模型 隐含波动率 

分 类 号：O29[理学—应用数学]