In the financial world, time series analysis is frequently used to predict stock prices, interest rates, and currency exchange rates. Econometric models are a type of time series analysis that uses historical data to forecast future asset prices and volatilities.
Reference  applied the autoregressive integrated moving average (ARIMA) model to the SP500 index. Specifically, it utilized the ARIMA(1,1,1) model for trading the index options. The authors used the ARIMA (1, 1, 1) model to forecast the SP 500 index. If the forecasted index price is greater (lower) than the option strike price at option maturity and the option premium is underpriced ( overpriced) at time zero, an option is bought (sold) and held until expiration. They found out,
The paper demonstrates the valuable contribution of this option trading strategy when trading index options. More specifically, the latter generates more profit with call than put options, as the period tested in our paper is set in a bull market, the intrinsic value of calls increasing with the index value while the intrinsic value of puts decreases. In addition, the ARIMA(1, 1, 1) forecasting model with calls offers a higher discounted net profit than the one based on GARCH (1, 1) forecasting model. In this situation, the percentage of times (out of 34,990) that the call option is correctly identified as undervalued or overvalued is 64% with ARIMA (1, 1, 1) vs 59% with GARCH (1, 1). Finally, the GARCH (1, 1) forecasting model with puts offers a higher discounted net profit than the one based on ARIMA (1, 1, 1) forecasting model. Thus, we observe that peaks of net profits with puts correspond to peaks of volatility of the S&P 500 Composite index represented by the VIX index. As the GARCH (1, 1) model incorporates a volatility component, this model is expected to provide a better forecasting accuracy than the ARIMA (1, 1, 1) model in period of high volatility when the strategy generates higher profit.
In short, the paper demonstrated that the ARIMA forecasting model is a valid method for forecasting the S&P 500 composite index and is superior to the GARCH model in the context of an application to index options trading.
The conclusion came as a surprise to us. We used to believe that the ARIMA model is better suited for modeling the implied volatility index (VIX) than the index itself. Let us know what you think in the comments below.
 Pierre Rostan, Alexandra Rostan, and Mohammad Nurunnabi, Options trading strategy based on ARIMA forecasting, 2020, PSU Research Review, Vol. 4 No. 2, pp. 111-127.
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