Implementing option pricing models when asset returns follow an autoregressive moving average process

Motivated by the empirical findings that asset returns or volatilities are predictable, this paper studies the pricing of European options on stock or volatility, the instantaneous changes of which depend upon an autoregressive moving average (ARMA) process. The pricing formula of an ARMA-type option is similar to that of Black and Scholes, except that the total volatility input depends upon the AR and MA parameters. From numerical analyses, the option values are increasing functions of the levels of AR or MA parameters across all moneyness levels. Specifically, the AR effect is more significant than the MA effect. Finally, based on the daily closing prices of TAIEX options from 2004 to 2008, the ad hoc ARMA(1,1) model provides the best in-sample fit and the second best out-of-sample fit, whereas the variance gamma model provides the second best in-sample fit and the best out-of-sample fit. Therefore, both variance gamma model and ad hoc ARMA model are superior models for pricing TAIEX options.