Modeling the Dynamics of Implied Volatility Surfaces

31 Pages Posted: 26 Feb 2009 Last revised: 4 Apr 2010

See all articles by Ihsan Badshah

Ihsan Badshah

Auckland University of Technology

Date Written: February 23, 2009


The purpose of this study is to model implied volatility surfaces and identify risk factors that account for most of the randomness in the volatility surfaces. The approach is similar to that of the Dumas, Fleming and Whaley (DFW) (1998) study. We use moneyness in implied forward price and out-of-the-money put-call options on the FTSE 100 stock index. After adjustments, a nonlinear parametric optimization technique is used to estimate different DFW models to characterize and produce smooth implied volatility surfaces. Next, principal component analysis is applied to the implied volatility surfaces to extract principal components that account for most of the dynamics in the shape of the surfaces. We then estimate and obtain smooth implied volatility surfaces with the parametric models that account for both smirk(skew) and time to maturity. We find the constant volatility model fails to explain the variations in the surfaces. However, the first three principal components (or factors) can explain about 69-88% of the variances in the implied volatility surfaces: in which on average 56% explains by the level factor, 15% by the term structure factor, and additional 7% by the jump-fear factor. The applications of our study can be in options trading, hedging of derivatives positions, risk management of options, and policy making.

Keywords: implied volatility, implied volatility surface, options, principal component analysis, smirk

JEL Classification: G13

Suggested Citation

Badshah, Ihsan, Modeling the Dynamics of Implied Volatility Surfaces (February 23, 2009). Available at SSRN: or

Ihsan Badshah (Contact Author)

Auckland University of Technology ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
+64 9 9219999 Extn: 5394 (Phone)
+64 9 219940 (Fax)

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