Monte Carlo Euler approximations of HJM term structure financial models

Tomas Björk, Anders Szepessy, Raul Tempone, Georgios E. Zouraris

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We present Monte Carlo-Euler methods for a weak approximation problem related to the Heath-Jarrow-Morton (HJM) term structure model, based on Itô stochastic differential equations in infinite dimensional spaces, and prove strong and weak error convergence estimates. The weak error estimates are based on stochastic flows and discrete dual backward problems, and they can be used to identify different error contributions arising from time and maturity discretization as well as the classical statistical error due to finite sampling. Explicit formulas for efficient computation of sharp error approximation are included. Due to the structure of the HJM models considered here, the computational effort devoted to the error estimates is low compared to the work to compute Monte Carlo solutions to the HJM model. Numerical examples with known exact solution are included in order to show the behavior of the estimates. © 2012 Springer Science+Business Media Dordrecht.
Original languageEnglish (US)
Pages (from-to)341-383
Number of pages43
JournalBIT Numerical Mathematics
Volume53
Issue number2
DOIs
StatePublished - Nov 22 2012

ASJC Scopus subject areas

  • Computational Mathematics
  • Software
  • Applied Mathematics
  • Computer Networks and Communications

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