Comparison of option prices under different martingale measures
Date Issued
2006
Date
2006
Author(s)
Chiu, Yi-Tai
DOI
en-US
Abstract
In this paper, we consider the problem of pricing a contingent claim on a stock whose price process is modelled by a geometric Lévy process, a generalization of geometric Brownian motion model. The market is incomplete and there is no unique equivalent martingale measure due to the random jumps of the stock process. We study three approaches to pricing European option:the Föllmer-Schweizer[1990] minimal measure, the Black-Scholes [1973] measure and Esscher transform. They make use of equivalent martingale measures, in different senses closest to the
martingale measure of classical Black-Scholes equation. We will compare the European option prices under different martingale measures and discuss the influence of the volatility on the price.
Subjects
Lé
vy過程
平賭測度
最小測度
Black-Scholes測度
Esscher
波動率
vy process
martingale measure
minimal measure
Black-Scholes measure
volatility
Type
thesis
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