The Annals of Applied Probability

Pricing contingent claims on stocks driven by Lévy processes

Terence Chan

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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.

Article information

Ann. Appl. Probab. Volume 9, Number 2 (1999), 504-528.

First available in Project Euclid: 21 August 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90A09 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
Secondary: 60J30 60J75: Jump processes

Option pricing incomplete market equivalent martingale measures


Chan, Terence. Pricing contingent claims on stocks driven by Lévy processes. Ann. Appl. Probab. 9 (1999), no. 2, 504--528. doi:10.1214/aoap/1029962753.

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