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.

When a financial derivative can be traded consecutively and its terminal payoffs can be adjusted into a stationary time series, there might be a statistical arbitrage opportunity even under the efficient market hypothesis. In particular, we show the examples of selling put options of the three major ETFs (Exchange Traded Funds) in the U.S. market.