A GARCH option pricing model with α-stable innovations

Christian Menn, Svetlozar T. Rachev

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We develop an option pricing model which is based on a GARCH asset return process with α-stable innovations with truncated tails. The approach utilizes a canonic martingale measure as pricing measure which provides the possibility of a model calibration to market prices. The GARCH-stable option pricing model allows the explanation of some well-known anomalies in empirical data as volatility clustering and heavy tailedness of the return distribution. Finally, the results of Monte Carlo simulations concerning the option price and the implied volatility with respect to different strike and maturity levels are presented.

Original languageEnglish
Pages (from-to)201-209
Number of pages9
JournalEuropean Journal of Operational Research
Volume163
Issue number1
DOIs
StatePublished - May 16 2005

Keywords

  • GARCH processes
  • Option pricing
  • Stable distributions
  • Tail truncation
  • Volatility smile

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