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May 1999 Pricing contingent claims on stocks driven by Lévy processes
Terence Chan
Ann. Appl. Probab. 9(2): 504-528 (May 1999). DOI: 10.1214/aoap/1029962753

Abstract

We consider the problem of pricing contingent claims on a stock whose price process is modelled by a geometric Lévy process, in exact analogy with the ubiquitous geometric Brownian motion model. Because the noise process has jumps of random sizes, such a market is incomplete and there is not a unique equivalent martingale measure. We study several approaches to pricing options which all make use of an equivalent martingale measure that is in different respects "closest" to the underlying canonical measure, the main ones being the Föllmer-Schweizer minimal measure and the martingale measure which has minimum relative entropy with respect to the canonical measure. It is shown that the minimum relative entropy measure is that constructed via the Esscher transform, while the Föllmer-Schweizer measure corresponds to another natural analogue of the classical Black-Scholes measure.

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Terence Chan. "Pricing contingent claims on stocks driven by Lévy processes." Ann. Appl. Probab. 9 (2) 504 - 528, May 1999. https://doi.org/10.1214/aoap/1029962753

Information

Published: May 1999
First available in Project Euclid: 21 August 2002

zbMATH: 1054.91033
MathSciNet: MR1687394
Digital Object Identifier: 10.1214/aoap/1029962753

Subjects:
Primary: 60G35 , 90A09
Secondary: 60J30 , 60J75

Keywords: equivalent martingale measures , incomplete market , option pricing

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.9 • No. 2 • May 1999
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