Original Article

Mathematical Methods of Operations Research

, 69:411

First online:

Smoothly truncated stable distributions, GARCH-models, and option pricing

  • Christian MennAffiliated withSal. Oppenheim jr. & Cie KGaA Email author 
  • , Svetlozar T. RachevAffiliated withInstitut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe and Karlsruhe Institute of Technology (KIT)

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Abstract

Although asset return distributions are known to be conditionally leptokurtic, this fact has rarely been addressed in the recent GARCH model literature. For this reason, we introduce the class of smoothly truncated stable distributions (STS distributions) and derive a generalized GARCH option pricing framework based on non-Gaussian innovations. Our empirical results show that (1) the model’s performance in the objective as well as the risk-neutral world is substantially improved by allowing for non-Gaussian innovations and (2) the model’s best option pricing performance is achieved with a new estimation approach where all model parameters are obtained from time-series information whereas the market price of risk and the spot variance are inverted from market prices of options.

Keywords

Incomplete financial markets Discrete-time models Non-Gaussian GARCH models Option pricing