Modeling the Dynamics of Implied Volatility Surfaces

Abstract

The objective of this study is to model implied volatility surfaces and identify risk factors that account for most of the randomness in the volatility surface. The approach is similar to the Dumas, Fleming and Whaley (DFW) (1998) study; we use moneyness (e.g., in forward price) and out-of-the-money (OTM) put-call options on FTSE100 index. After these adjustments, the nonlinear parametric optimization technique is employed to estimate different models of DFW in order to characterize the implied volatility surfaces and produce smooth implied volatility surfaces. Next, principal component analysis (PCA) is applied to the implied volatility surfaces to extract principal components that account for most of the dynamics in the shape of the surface. Hence, we estimate and obtain smooth implied volatility surfaces with the parametric models that account for both smile and time to maturity, and, therefore, the constant volatility model fails to explain the variations in the surfaces. Finally, we find that the first three principal components can explain about 69-82% of the variances in the implied volatility surfaces. The applications of our study are hedging of derivatives positions, trading, risk management, and policy making.