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Lehnert, T. Mandelbrot and the Smile. Credit and Capital Markets – Kredit und Kapital, 42(1), 125-144.
Lehnert, Thorsten "Mandelbrot and the Smile" Credit and Capital Markets – Kredit und Kapital 42.1, 2009, 125-144.
Lehnert, Thorsten (2009): Mandelbrot and the Smile, in: Credit and Capital Markets – Kredit und Kapital, vol. 42, iss. 1, 125-144, [online]


Mandelbrot and the Smile

Lehnert, Thorsten

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.


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)