基于快速分数阶Fourier变换的期权定价——以上证50ETF期权为例  

The Option Pricing Based on Fast Fractional Fourier Transform——Take 50ETF Options in Shanghai Stock Exchange as An Example

作　　者：姚艾嘉 张艳慧[1] 李明阳 康蕊 YAO Aijia;ZHANG Yanhui;LI Mingyang;KANG Rui(School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China;Department of Statistics,School of Mathematics Science,University of Nottingham,Nottingham,NG8 1AF,The United Kingdom)

机构地区：[1]北京工商大学数学与统计学院,北京100048 [2]英国诺丁汉大学数学科学学院统计系,诺丁汉NG81AF

出　　处：《江西师范大学学报（自然科学版）》2020年第6期614-620,共7页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11971042);北京市自然科学基金(1182008)资助项目.

摘　　要：受美国股市熔断影响,近期中国欧式期权波动剧烈,从而对其定价问题产生一定挑战.基于VG过程刻画上证50ETF期权标的资产对数价格变化情况,对美国股市熔断前后各9支期权数据,采用快速分数阶Fourier变换进行期权定价研究,并与实际价格进行对比.实证分析表明:在美国股市熔断期间标的资产价格波动相对剧烈时VG过程依然拟合较好,用快速分数阶Fourier变换数值方法具有一定优势.European option pricing under fast fractional Fourier transform is affected by the circuit breakers in the US stock market,and European option pricing in China fluctuates dramatically recently,which poses a certain challenge to its pricing problem.Based on the VG process,the logarithm price changes of the underlying assets of the 50ETF options in Shanghai Stock Exchange are described.The option pricing is studied by using fast fractional Fourier transform on the data of nine options before and after the circuit breaker in the US stock market,and compared with the actual prices.The empirical analysis shows that the VG process still fits well when the underlying asset price fluctuations are relatively severe during the US stock circuit breaker,and the numerical method using fast fractional Fourier transform has certain advantages.

关 键 词：方差伽玛过程 期权定价 快速分数阶Fourier变换 

分 类 号：F224.0[经济管理—国民经济]