Financial models based on Lévy processes (John von Neumann Lecture)

Lecture Announcement (PDF)
  

John von Neumann Visiting Professorship

This lecture is held by Prof. Dr. Ernst Eberlein as part of the TUM John von Neumann Visiting Professorship.
  

Abstract

In the first half of this course an introduction to the theory of Lévy processes will be given. Topics are: explicit construction of Lévy processes based on infinitely divisible distributions, Brownian motion, Poisson process and jump diffusions as standard examples, Lévy-Ito decomposition, analytic as well as path properties, more advanced processes via subordination (generalized hyerbolic, normal inverse Gaussian and variance gamma processes). In the second half of the course dynamic financial models which are driven by Lévy processes will be investigated. Efficient pricing of a broad spectrum of derivative financial products will be discussed. Finally the Lévy interest rate theory (forward rate (HJM), Libor and forward process models) will be developed and pricing formulas for standard interest rate options will be derived.