Modeling SPX Volatility to Improve Options Pricing
Aiman, Jared; Iglesias, Vicente; Sarkar, Sumit
In this project, we develop a model to predict future stock market volatility and facilitate more accurate options pricing. The Black Scholes model gives an expected premium for an options contract; however, it uses an unknown fixed parameter referred to as volatility. We advance this by using a modified Glosten-Jagannathan-Runkle Generalized Autoregressive Conditional Heteroskedasticity (GJR-GARCH) model that uses previous returns, as well as the market’s expectation of future volatility, to better predict future volatility. Additionally, we apply an Autoregressive Moving Average (ARMA) model to predict the value of future stock prices. We find that our model is able to model volatility better than using either the market volatility or a traditional GJR-GARCH model alone. This is particularly true due to our model’s ability to capture the dependence between the S&P 500 returns and the changes in the market’s expectation of volatility.