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Statistical Modeling of Diffusion Processes with Financial Applications

Lindström, Erik LU (2004)
Abstract
This thesis consists of five papers (Paper A-E) on statistical modeling of diffusion processes.



Two papers (Paper A & D) consider Maximum Likelihood estimators for non-linear 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 A-E) on statistical modeling of diffusion processes.



Two papers (Paper A & D) consider Maximum Likelihood estimators for non-linear 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 non-linear 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:
author
supervisor
opponent
  • Professor Hans Rudolf, Kunsch, Seminar fur Statistik, ETHZ
organization
publishing date
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
2004-12-20 10:15
ISSN
1404-0034
ISBN
91-628-6312-6
language
English
LU publication?
yes
id
d67e3c8d-71a7-4f44-89a7-e15e54ff90da (old id 544061)
date added to LUP
2007-09-27 15:49:53
date last changed
2017-02-08 13:39:15
@phdthesis{d67e3c8d-71a7-4f44-89a7-e15e54ff90da,
  abstract     = {This thesis consists of five papers (Paper A-E) on statistical modeling of diffusion processes.<br/><br>
<br/><br>
Two papers (Paper A &amp; D) consider Maximum Likelihood estimators for non-linear 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 non-linear dependence.<br/><br>
<br/><br>
Finally, paper E introduces a simple bias correction framework to the Black &amp; Scholes option pricing formula by correcting for parameter uncertainty. This correction improves the predictive performance of the Black &amp; 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         = {91-628-6312-6},
  issn         = {1404-0034},
  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},
}