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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.
Submitted Note
A Dissertation Submitted to the Department of Mathematics in Partial FulfiLlment of the Requirements for the Degree of Doctor of Philosophy.
Bibliography Note
Includes bibliographical references.
Advisory Committee
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.
Publisher
Florida State University
Identifier
FSU_migr_etd-2102
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