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On Option Pricing Models in the Presence of Heavy Tails

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Vellekoop, Michel; Nieuwenhuis, Hans

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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.
Classification Basic Research, General Concepts and History of Economics; Economic Statistics, Econometrics, Business Informatics
Method theory application
Free Keywords Arbitrage Relationship; Financial Modelling; Pricing of Derivatives Securities; Stochastic Volatility
Document language English
Publication Year 2007
Page/Pages p. 563-573
Journal Quantitative Finance, 7 (2007) 5
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)