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Probabilistic Methods in Estimation and Prediction of Financial Models

Title: Probabilistic Methods in Estimation and Prediction of Financial Models.
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Name(s): Nguyen, Nguyet Thi, author
Okten, Giray, professor directing dissertation
Hawkes, Lois, university representative
Case, Bettye Anne, committee member
Kim, Kyounghee, committee member
Nichols, Warren, committee member
Zhang, Jinfeng, committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2014
Publisher: Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: Many computational finance problems can be classified into two categories: estimation and prediction. In estimation, one starts with a probability model and expresses the quantity of interest as an expected value or a probability of an event. These quantities are then computed either exactly, or numerically using methods such as numerical PDEs or Monte Carlo simulation. Many problems in derivative pricing and risk management are in this category. In prediction, the main objective is to use methods such as machine learning, neural networks, or Markov chain models, to build a model, train it using historical data, and predict future behavior of some financial indicators. In this dissertation, we consider an estimation method known as the (randomized) quasi-Monte Carlo method. We introduce an acceptance-rejection algorithm for the quasi-Monte Carlo method, which substantially increases the scope of applications where the method can be used efficiently. We prove a convergence result, and discuss examples from applied statistics and derivative pricing. In the second part of the dissertation, we present a novel prediction algorithm based on hidden Markov models. We use the algorithm to predict economic regimes, and stock prices, based on historical data.
Identifier: FSU_migr_etd-9059 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2014.
Date of Defense: July 10, 2014.
Keywords: Acceptance-Rejection, Beta, Gamma, hidden Markov model, Quasi-Monte Carlo, Variance Gamma
Bibliography Note: Includes bibliographical references.
Advisory Committee: Giray Okten, Professor Directing Dissertation; Lois Hawkes, University Representative; Bettye Anne Case, Committee Member; Kyounghee Kim, Committee Member; Warren Nichols, Committee Member; Jinfeng Zhang, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-9059
Owner Institution: FSU

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Nguyen, N. T. (2014). Probabilistic Methods in Estimation and Prediction of Financial Models. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-9059