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

Christian Menn, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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.

Original languageEnglish
Pages (from-to)411-438
Number of pages28
JournalMathematical Methods of Operations Research
Volume69
Issue number3
DOIs
StatePublished - Jul 2009

Keywords

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

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