Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Wavelet finite element method for option pricing in highdimensional diffusion market models

by N. Hilber and S. Kehtari and Ch. Schwab and C. Winter

(Report number 2010-01)

Abstract
We consider the numerical solution of high-dimensional partial differential equations arising in option pricing problems in computational finance. To reduce the complexity in the number of degrees of freedom sparse tensor product spaces are applied for Galerkin discretization in log-price space. Using this technique we are able to price multi-asset options with up to eight underlying assets for the Black-Scholes framework and stochastic volatility models. Dimensionality reduction by principal component analysis and asymptotic expansion is investigated in order to price options on indices by considering the whole vector process of all of their constituents.

Keywords:

@Techreport{HKSW10_423,
  author = {N. Hilber and S. Kehtari and Ch. Schwab and C. Winter},
  title = {Wavelet finite element method for option pricing in highdimensional diffusion market models},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2010-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-01.pdf },
  year = {2010}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).