Statistical Modeling of Diffusion Processes with Financial Applications
Erik Lindström
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology
2004
ISBN 9162863126
LUTFMS10252004

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.



Keywords:

Diffusion processes; Maximum Likelihood Estimation; Recursive estimation;
Model validation; Option pricing.



