Mandelbrot and the Smile
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Mandelbrot and the Smile
Credit and Capital Markets – Kredit und Kapital, Vol. 42 (2009), Iss. 1 : pp. 125–144
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Dr. Thorsten Lehnert, Associate Professor of Finance, Universiteit Maastricht, Limburg Institute of Financial Economics, P.O.Box 616, NL-6200 MD Maastricht/Niederlande.
Abstract
Mandelbrot and the Smile
It is a well-documented empirical fact that index option prices systematically differ from Black-Scholes prices. However, previous research provides inconclusive results whether the observed volatility smile could be explained by a discretetime dynamic model of stock returns with skewed, leptokurtic innovations. The improvements in pricing errors are particularly pronounced for out-of-the money put options, while the models partly underperform a Gaussian alternative for near-the-money options. Motivated by theses empirical evidence, I develop a new GARCH option-pricing model with a more flexible innovation structure. In an application of the model to DAX index options, I test the relative performance of the approach against a standard nested GARCH specification and the well-known practitioners Black-Scholes model. I show that the performance of the truncated Lévy GARCH option pricing model is superior to existing approaches. (JEL G12)