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Mandelbrot and the Smile

Listed author(s):
  • Thorsten Lehnert

    (Assistant Professor of Finance, Universiteit Maastricht, Limburg Institute of Financial Economics, P.O.Box 616, NL-6200 MD Maastricht/Niederlande)

Registered author(s):

    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.

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    Article provided by Credit and Capital Markets in its journal Kredit und Kapital.

    Volume (Year): 42 (2009)
    Issue (Month): 1 ()
    Pages: 125-144

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    Handle: RePEc:kuk:journl:v:42:y:2009:i:1:p:125-144
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