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 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.
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.
Original language  English 

Qualification  Doctor 
Awarding Institution 

Supervisors/Advisors 

Award date  2004 Dec 20 
Publisher  
ISBN (Print)  9162863126 
Publication status  Published  2004 
Bibliographical note
Defence detailsDate: 20041220
Time: 10:15
Place: MH:C
External reviewer(s)
Name: Hans Rudolf, Kunsch
Title: Professor
Affiliation: Seminar fur Statistik, ETHZ

Subject classification (UKÄ)
 Probability Theory and Statistics
Free keywords
 actuarial mathematics
 Statistik
 operations research
 programming
 Option pricing
 Model validation
 Recursive estimation
 Diffusion processes
 Maximum Likelihood Estimation
 operationsanalys
 programmering
 aktuariematematik
 Statistics