基于跳跃-扩散过程的股票期权定价分析  

Analysis of Stock Option Pricing Based on the Jump-Diffusion Process

作　　者：杨德林 马梓钧 唐之祺 张余萍 YANG Delin;MA Zijun;TANG Zhiqi;ZHANG Yuping(College of Mathematics and Computer Science,Northwest Minzu Uiversity,Lanzhou,Gansu Province,730030 China)

机构地区：[1]西北民族大学数学与计算机科学学院,甘肃兰州730030

出　　处：《科技资讯》2023年第5期127-131,共5页Science & Technology Information

基　　金：西北民族大学大学生创新创业训练计划资助项目(项目编号:X202210742179)。

摘　　要：该文研究股票价格服从跳跃-扩散过程时的股票期权定价问题。金融市场的不断发展涌现出众多的金融理财产品,传统股票期权定价模型难以合理描述突发性的股票价格变动,而在实际情况中股票价格因受国际局势、地区政策以及突发问题等影响会急剧性上涨或下跌,因此传统股票期权定价模型对于实际金融市场缺乏一定的适用性。基于此,该文通过股票价格的跳跃-扩散过程,利用鞅方法将股票定价问题转化为期望求解问题,推导出股票价格行为服从跳跃-扩散过程的期权定价公式。This paper studies stock option pricing when the stock price is subject to the jump-diffusion process.With the continuous development of the financial market,a large number of financial products have emerged,the traditional stock option pricing model is difficult to reasonably describe the sudden changes in stock prices,and in the actual situation,the stock price will rise or fall sharply due to the influences of international situation,regional policies and unexpected problems,so the traditional stock option pricing model lacks certain applicability to the actual financial market.Based on this,through the jump-diffusion process of stock prices,this paper uses the martingale method to transform the stock pricing problem into the expectation solution problem,and derives the option pricing formula that the stock price behavior is subject to the jump-diffusion process.

关 键 词：股票期权定价 跳跃-扩散过程 随机微分方程 计数过程 

分 类 号：F830[经济管理—金融学] F224