Assessing the Performance of Symmetric and Asymmetric Implied Volatility Functions
Posted: 9 Jul 2008 Last revised: 16 Jan 2011
Date Written: December 17, 2010
We seek to identify the best approach to model the daily implied volatility functions for pricing S&P 500 index options for the period 1996-2009. We compare the linear versus the nonlinear estimation approach, symmetric versus asymmetric model shapes with respect to the moneyness ratio, transformations of the underlying asset, and model estimation using joint datasets of calls and puts versus separating calls from puts. In-sample, we find models that are asymmetric functions of moneyness ratio work better, but out-of-sample the symmetric functions of the logarithmic transformation of the strike price are the best models. It is optimal to estimate the models nonlinearly and with the use of the joint dataset of out-of-money options instead of separating calls from puts. In contrast with other approaches that have been adopted in empirical research, the one we identify is consistent with the put-call-parity; hence, we avoid issues relating to model misspecification problems.
Keywords: Option pricing, implied volatilities, deterministic volatility functions, implied volatility functions
JEL Classification: G13, G14
Suggested Citation: Suggested Citation