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Mandelbrot and the Smile


  • Thorsten Lehnert

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


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.

Suggested Citation

  • Thorsten Lehnert, 2009. "Mandelbrot and the Smile," Credit and Capital Markets, Credit and Capital Markets, vol. 42(1), pages 125-144.
  • Handle: RePEc:kuk:journl:v:42:y:2009:i:1:p:125-144

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    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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