Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Applied Mathematics

Supervisor

Dr. Mark Reesor

Abstract

Multiple exercise options may be considered as generalizations of American-style options as they provide the holder more than one exercise right. Examples of financial derivatives and real options with these properties have become more prevalent over the past decade and appear in sectors ranging from insurance to energy industries. Throughout the thesis particular attention is paid to swing options although we note that the methods described are equally applicable to other types of multiple exercise options. This thesis presents two novel methods for pricing multiple exercise option by simulation; the forest of stochastic trees and the forest of stochastic meshes. The proposed methods are of particular use in cases where there are potentially a large number (3 or more) of assets underlying the contract and/or if a number of risk factors are desirable for modelling the underlying price process.

These valuation methods result in positively- and negatively-biased estimators for the true option value. We prove the sign of the estimator bias and show that these estimators are consistent for the true option value. A confidence interval for the true option value is easily constructed. Examples confirm that the implementation of these methods is correct and consistent with the theoretical properties of the estimators.

This thesis also explores in detail a number of methods meant to enhance the effectiveness of the proposed simulation methods. These include using high performance computing techniques which include both parallel computing techniques on CPU-clusters and General purpose Graphics Processing Units (GPGPU) that take advantage of relatively inexpensive processors. Additionally we explore bias-corrected estimators for the option values which attempt to estimate the bias introduced at each time step by the estimator and then subtract this result. These improvements are desirable due to the computationally intensive nature of both methods.

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