Statistical Modeling of Diffusion Processes with Financial Applications
(2004) Abstract
 This thesis consists of five papers (Paper AE) on statistical modeling of diffusion processes.
Two papers (Paper A & D) consider Maximum Likelihood estimators for nonlinear diffusion processes. An offline Maximum Likelihood estimator is derived in Paper A, and it is shown that this estimator is computationally more efficient than other Maximum Likelihood estimators. The offline algorithm is modified into an online algortihm in Paper D, where it is shown that the statistical properites are preserved while the computational cost is reduced.
Model validation is discussed in Paper B and C. A general and numerically robust definition of Gaussian residuals for diffusion processes is presented in Paper... (More)  This thesis consists of five papers (Paper AE) on statistical modeling of diffusion processes.
Two papers (Paper A & D) consider Maximum Likelihood estimators for nonlinear diffusion processes. An offline Maximum Likelihood estimator is derived in Paper A, and it is shown that this estimator is computationally more efficient than other Maximum Likelihood estimators. The offline algorithm is modified into an online algortihm in Paper D, where it is shown that the statistical properites are preserved while the computational cost is reduced.
Model validation is discussed in Paper B and C. A general and numerically robust definition of Gaussian residuals for diffusion processes is presented in Paper B, where it is shown that these residuals are independent and identically distributed under the null hypothesis. Paper C adds suggestions on how these residuals can be tested to detect nonlinear dependence.
Finally, paper E introduces a simple bias correction framework to the Black & Scholes option pricing formula by correcting for parameter uncertainty. This correction improves the predictive performance of the Black & Scholes formula significantly. Furthermore, it is argued that the bias correction in paper E can be extended to more advanced option pricing models. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/544061
 author
 Lindström, Erik ^{LU}
 supervisor

 Jan Holst ^{LU}
 opponent

 Professor Hans Rudolf, Kunsch, Seminar fur Statistik, ETHZ
 organization
 publishing date
 2004
 type
 Thesis
 publication status
 published
 subject
 keywords
 actuarial mathematics, Statistik, operations research, programming, Option pricing, Model validation, Recursive estimation, Diffusion processes, Maximum Likelihood Estimation, operationsanalys, programmering, aktuariematematik, Statistics
 pages
 170 pages
 publisher
 Mathematical Statistics, Centre for Mathematical Sciences, Lund University
 defense location
 MH:C
 defense date
 20041220 10:15
 ISSN
 14040034
 ISBN
 9162863126
 language
 English
 LU publication?
 yes
 id
 d67e3c8d71a74f4489a7e15e54ff90da (old id 544061)
 date added to LUP
 20070927 15:49:53
 date last changed
 20190308 03:24:09
@phdthesis{d67e3c8d71a74f4489a7e15e54ff90da, abstract = {This thesis consists of five papers (Paper AE) on statistical modeling of diffusion processes.<br/><br> <br/><br> Two papers (Paper A & D) consider Maximum Likelihood estimators for nonlinear diffusion processes. An offline Maximum Likelihood estimator is derived in Paper A, and it is shown that this estimator is computationally more efficient than other Maximum Likelihood estimators. The offline algorithm is modified into an online algortihm in Paper D, where it is shown that the statistical properites are preserved while the computational cost is reduced.<br/><br> <br/><br> Model validation is discussed in Paper B and C. A general and numerically robust definition of Gaussian residuals for diffusion processes is presented in Paper B, where it is shown that these residuals are independent and identically distributed under the null hypothesis. Paper C adds suggestions on how these residuals can be tested to detect nonlinear dependence.<br/><br> <br/><br> Finally, paper E introduces a simple bias correction framework to the Black & Scholes option pricing formula by correcting for parameter uncertainty. This correction improves the predictive performance of the Black & Scholes formula significantly. Furthermore, it is argued that the bias correction in paper E can be extended to more advanced option pricing models.}, author = {Lindström, Erik}, isbn = {9162863126}, issn = {14040034}, keyword = {actuarial mathematics,Statistik,operations research,programming,Option pricing,Model validation,Recursive estimation,Diffusion processes,Maximum Likelihood Estimation,operationsanalys,programmering,aktuariematematik,Statistics}, language = {eng}, pages = {170}, publisher = {Mathematical Statistics, Centre for Mathematical Sciences, Lund University}, school = {Lund University}, title = {Statistical Modeling of Diffusion Processes with Financial Applications}, year = {2004}, }