Pricing contingent claims on stocks driven by Levy processes
成果类型：
Article
署名作者：
Chan, T
署名单位：
Heriot Watt University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1999
页码：
504-528
关键词：
摘要：
We consider the problem of pricing contingent claims on a stock whose price process is modelled by a geometric Levy 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 Follmer-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 Follmer-Schweizer measure corresponds to another natural analogue of the classical Black-Scholes measure.