On Option Pricing Models in the Presence of Heavy Tails

M.H. Vellekoop, J.W. Nieuwenhuis

    Research output: Contribution to journalArticleAcademicpeer-review

    15 Citations (Scopus)

    Abstract

    We propose a modification of the option pricing framework derived by Borland which removes the possibilities for arbitrage within this framework. It turns out that such arbitrage possibilities arise due to an incorrect derivation of the martingale transformation in the non-Gaussian option models which are used in that paper. We show how a similar model can be built for the asset price processes which excludes arbitrage. However, the correction causes the pricing formulas to be less explicit than the ones in the original formulation, since the stock price itself is no longer a Markov process. Practical option pricing algorithms will therefore have to resort to Monte Carlo methods or partial differential equations and we show how these can be implemented. An extra parameter, which needs to be specified before the model can be used, will give market makers some extra freedom when fitting their model to market data.
    Original languageUndefined
    Article number10.1080/14697680601077967
    Pages (from-to)563-573
    Number of pages11
    JournalQuantitative finance
    Volume7
    Issue number5
    DOIs
    Publication statusPublished - Oct 2007

    Keywords

    • EWI-11678
    • IR-62096
    • METIS-247091

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