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Monte Carlo Euler approximations of HJM term structure financial models
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- Björk, T. (author)
- Stockholm School of Economics,Handelshögskolan i Stockholm
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- Szepessy, A. (author)
- KTH,Numerisk analys, NA,Royal Institute of Technology (SE)
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- Tempone, R. (author)
- King Abdullah University of Science and Technology (SA)
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- (creator_code:org_t)
- 2012-11-22
- 2013
- English.
- In: BIT Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 53:2, s. 341-383
- Journal article (peer-reviewed)
Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- A posteriori error estimates
- A priori error estimates
- Bond market
- HJM model
- Monte Carlo methods
- Option price
- Stochastic differential equations
Publication and Content Type
- ref (subject category)
- art (subject category)
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- Björk, T.
- Szepessy, A.
- Tempone, R.
- Zouraris, G. E.
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- NATURAL SCIENCES
- NATURAL SCIENCES
- and Mathematics
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- Royal Institute of Technology
- Stockholm School of Economics
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