Forecasting semi-stationary processes and statistical arbitrage

ABSTRACT

If a financial derivative can be traded consecutively and its terminal payoffs can be adjusted as the sum of a bounded process and a stationary process, then we can use the moving average of the historical payoffs to forecast and the corresponding errors form a generalised mean reversion process. Thus we can price the financial derivatives by its moving average. One can even possibly get statistical arbitrage from certain derivative pricing. We particularly discuss the example of European call options. We show that there is a possibility to get statistical arbitrage from Black–Scholes's option price.

Keywords:

• Stationary process
• statistical arbitrage
• Black–Scholes model
• mean reversion

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Si Bao

Si Bao is now working in Xiangcai security Co., LTD. She studied for her Ph.D. in School of Statistics from ECNU.

Shi Chen

Shi Chen is a data scientist of PayPal Holding Inc. He received his Ph.D in statistics from ECNU in 2017.

Wei An Zheng

Wei An Zheng is Professor of ECNU and Professor Emeritus of University of California, Irvine, USA.

Yu Zhou

Yu Zhou works in Guotai Junan Securities. He received his Ph.D in statistics from ECNU in 2016.