Three Essays on Contingent Claim Valuation in Incomplete Markets
Date Issued
2007
Date
2007
Author(s)
Tsai, Hung-Chou
DOI
en-US
Abstract
The main purpose of this dissertation is to investigate the problems of contingent claim valuation in incomplete markets, especially focused on the pricing measures for Levy processes. This dissertation is constituted by three essays and each essay is self-contained.
Essay 1 reviews some known results in an incomplete market in the case of exponential utility function. We also discuss the notion of utility indifference price for a contingent claim and investigate the asymptotic behavior of utility indifference price.
Essay 2 uses the Esscher transform to construct a martingale measure in the framework of geometric Levy process. By means of a relation between exponential Levy process and stochastic exponential of Levy process, we have shown that a Levy process is a martingale if and only if its stochastic exponential is a martingale. Using this result, we also define a necessary condition for the Esscher measure to be the minimal entropy martingale measure.
Essay 3 formulates an approach to computing the density process of the minimal entropy martingale measure for a jump-diffusion model and the stochastic volatility model by Barndorff-Nielsen and Shepherd. In addition, we also calculate the explicit forms of the minimal entropy martingale measure for those two models.
Subjects
效用無差異價格
跳躍-擴散模型
平賭
Esscher measure
jump-diffusion model
Levy process
minimal entropy martingale measure
utility indifference price
Type
thesis