Modeling the Implied Volatility Surface: An Empirical Study for S&P 500 Index Option

Volatilities play a critical role in financial industry as it is considered a common method to measure the risk. In order to minimize the risk or at least to be certain about how much risk is to be taken, investors seek various ways to estimate volatilities. The implied volatility surface is one of those methodologies and it displays the structure of volatilities as it varies with strike price (or moneyness) and time to maturity. The method can also be used to forecast the future volatilities. This paper aims, to present a simple framework to capture the common characteristics of this structure based on the S&P 500 options in real time, to address the issue of the thin volume of option trading and missing data, and to present some possible applications of the methodology. The parametric model of Dumas, Fleming and Whaley (1998) is used in this paper to estimate the implied volatility surfaces for given option moneyness and time to expiration.