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

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.