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Monte Carlo Euler approximations of HJM term structure financial models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2013 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 53, no 2, 341-383 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. Vol. 53, no 2, 341-383 p.
Keyword [en]
A posteriori error estimates, A priori error estimates, Bond market, HJM model, Monte Carlo methods, Option price, Stochastic differential equations
National Category
URN: urn:nbn:se:kth:diva-134446DOI: 10.1007/s10543-012-0410-4ISI: 000319992600004ScopusID: 2-s2.0-84878807291OAI: diva2:676325

QC 20131205

Available from: 2013-12-05 Created: 2013-11-25 Last updated: 2013-12-09Bibliographically approved

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Szepessy, A.
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