文档介绍：The Generalized Hyperbolic Model:
Estimation, Financial Derivatives, and Risk Measures
Dissertation zur Erlangung des rades
der Mathematischen Fakult¨at
der Albert-Ludwigs-Universit¨at Freiburg i. Br.
vorgelegt von
Karsten Prause
Oktober 1999
Dekan: Prof. Dr. Wolfgang Soergel
Referenten: Prof. Dr. Ernst Eberlein
Prof. . Bent Jesper Christensen
Datum der Promotion: 15. Dezember 1999
Institut f¨ur Mathematische Stochastik
Albert-Ludwigs-Universit¨at Freiburg
Eckerstraße 1
D–79104 Freiburg im Breisgau
To Ulrike
Preface
The aim of this dissertation is to describe more realistic models for financial assets based on
generalized hyperbolic (GH) distributions and their subclasses.
Generalized hyperbolic distributions were introduced by Barndorff-Nielsen (1977), and
stochastic processes based on these distributions were first applied by Eberlein and Keller
(1995) in Finance. Being a normal variance-mean mixture, GH distributions possess semi-
heavy tails and allow for a natural definiton of volatility models by replacing the mixing
generalized inverse Gaussian (GIG) distribution by appropriate volatility processes.
In the first Chapter we introduce univariate GH distributions, construct an estimation
algorithm and examine statistically the fit of generalized hyperbolic distributions to log-
return distributions of financial assets. We extend the hyperbolic model for the pricing of
derivatives to generalized hyperbolic L´evy motions and discuss the calculation of prices by
fast Fourier methods and saddle-point approximations.
Chapter 2 contains on the one hand a general recipe for the evaluation of option pricing
models; on the other hand the derivative pricing based on GH L´evy motions is studied from
various points of view: The accordance with observed asset price processes is investigated
statistically, and by simulation studies the sensitivity to relevant variables; finally, theoretical
prices pared with quoted option prices. Fu