Valuing risky income streams in incomplete markets

Empirical evidence suggesting that world financial markets are incomplete leads to the question of how best to price and hedge contingent claims and derivative securities in incomplete markets. The focus of this dissertation is on a model proposed by Carr, Geman and Madam [7], which combines elements of arbitrage pricing theory with expected utility maximisation to decide whether a risky investment opportunity is worth undertaking or not. An account of the state of the art of pricing and hedging in incomplete markets is followed by a detailed exposition of the new model. A chapter which details the issues which arise when the model is extended treats multiple time periods, continuous time, and an infinite state space. It is not entirely obvious in each case how the model may be extended, and current work is considered along with some new suggestions to address these issues. A small battery of computer simulations based on the proposed multiple period model is performed using a trinomial tree structure. A justification for using the new model rather than finite difference or classical multinomial tree methods is provided in the form of an argument which establishes the validity of a new approach in cases when the Black-Scholes formulation cannot be applied, chiefly when the market is incomplete.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2001

Author dc:creator

• Johnson, Clare

Advisor dc:contributor.advisor

• Ouwehand, Peter

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/4892

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/4892