Option Statistical Arbitrage Strategy Based On Stationary Process And Stochastic Volatility

Option is one of the most popular financial derivatives in today’s financial field.This paper constructs a trading strategy based on option,and proves its effectiveness under different models and firm offer data.Firstly,this paper introduces the stationary selling put option strategy based on con-stant volatility,and proves the theoretical validity of the strategy based on the assumption that μ>r>0 and the logarithmic return of assets satisfies the stationary process.Then,this paper focuses on two stochastic forms of volatility in the stationary selling put option strategy,the first is based on the B-S model,the stochastic transformation of volatility.In order to describe the performance of volatility more accurately,the second is based on Heston model,and it is proved that the stochastic process of volatility under the model satisfies the stationary process.Based on two models,this paper give the strategy single return series{r_{i T}}is a stationary process and the theoretical validity of the strategy is proved.In the empirical part,based on QQQ,DIA and SPY,this paper makes an empirical study under the two models,and finds that the strategic return is stable,which proves the effectiveness of the theory.The risk and return are significantly better than the underlying asset itself.Finally,this paper conducts a strategic empirical study on the option market data of the above index funds,and obtains that the strategic return is stable and significantly better than the underlying assets,which indicates that the strategy is still effective when applied to the firm offer trading.The strategy results under Heston model are closer to those under the option firm offer data,which indicates that the model is suitable for option pricing.