Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
In this dissertation, we evaluate existing Monte Carlo estimators and develop new Monte Carlo estimators for pricing financial options with the goal of improving precision. In Chapter 2, we discuss the conditional expectation Monte Carlo estimator for pricing barrier options, and show that the formulas for this estimator that are used in the literature are incorrect. We provide a correct version of the formula. In Chapter 3, we focus on importance sampling methods in estimating the price of barrier options. We show how a simulated annealing procedure can be used to estimate the parameters required in the importance sampling method. We end this chapter by evaluating the performance of the combined importance sampling and conditional expectation method. In Chapter 4, we analyze the estimators introduced by Ross and Shanthikumar in pricing barrier options and present a numerical example to test their performance.
Truncated Distribution, Tilted Density, Black-Scholes-Merton, Glasserman and Staum Estimators, Option Price Estimation, Asian Options, Markov Chain, Stochastic Optimization, Heuristics, Likelihood Ratio
Date of Defense
September 25, 2008.
A Dissertation Submitted to the Department of Mathematics in Partial FulﬁLlment of the Requirements for the Degree of Doctor of Philosophy.
Includes bibliographical references.
Giray Okten, Professor Directing Dissertation; Ashok Srinivasan, Outside Committee Member; Bettye Anne Case, Committee Member; Brian Ewald, Committee Member; Craig Nolder, Committee Member; John R. Quine, Committee Member.
Florida State University
Use and Reproduction
This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them.