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Efficient simulation and calibration of general HJM models by splitting schemes

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  • Philipp Doersek
  • Josef Teichmann

Abstract

We introduce efficient numerical methods for generic HJM equations of interest rate theory by means of high-order weak approximation schemes. These schemes allow for QMC implementations due to the relatively low dimensional integration space. The complexity of the resulting algorithm is considerably lower than the complexity of multi-level MC algorithms as long as the optimal order of QMC-convergence is guaranteed. In order to make the methods applicable to real world problems, we introduce and use the setting of weighted function spaces, such that unbounded payoffs and unbounded characteristics of the equations in question are still allowed. We also provide an implementation, where we efficiently calibrate an HJM equation to caplet data.

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  • Philipp Doersek & Josef Teichmann, 2011. "Efficient simulation and calibration of general HJM models by splitting schemes," Papers 1112.5330, arXiv.org.
    • Handle: RePEc:arx:papers:1112.5330
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    References listed on IDEAS

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    1. Philipp Doersek & Josef Teichmann, 2010. "A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial) Differential Equations," Papers 1011.2651, arXiv.org.
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