統計数学セミナー
Seminar on Probability and Statistics 
Home : Archive [ 2003 to 04 ] [ 2004 to 05 ] [ 2005 to 06 ] [ 2006 to 07 ] [ 2007 to 08 ] [ 2008 to 09 ] [ 2009 to 10 ] [ 2010 to 11 ] [ 2011 to 12 ] [ 2012 to 13 ] [ 2013 to 14 ] [ 2014 to 15 ] 
Previous Seminar : Next Seminar 
Seminar on Probability and Statistics Monday January 28 2013 Tokyo 006 1:002:10 pm
Laplace and Fourier based valuation methods in exponential Levy models
Ernst August Frhr. v. Hammerstein AlbertLudwigsUniversität Freiburg Abstract A fundamental problem in mathematical finance is the explicit
computation of expectations which arise as prices of derivatives. Closed
formulas that can easily be evaluated are typically only available in
models driven by a Brownian motion. If one considers more sophisticated
jumptype Levy processes as drivers, the problem quickly becomes rather
nontrivial and complicated. Starting with the paper of Carr and Madan
(1999) and the PhD thesis of Raible (2000), Laplace and Fourier based
methods have been used to derive option pricing formulas that can be
evaluated very efficiently numerically. In this talk we review the
initial idea of Raible (2000), show how it can be generalized and
discuss under which precise mathematical assumptions the Laplace and
Fourier approach work. We then give several examples of specific options
and Levy models to which the general framework can be applied to. In the
last part, we present some formulas for pricing options on the supremum
and infimum of the asset price process that use the WienerHopf
factorization.

Previous Seminar : Next Seminar 
Seminar on Probability and Statistics 