Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations

Emmanuel Coffie

Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations

Emmanuel Coffie

Mathematics And Statistics

Research output: Working paper

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Abstract

In this paper, we study analytical properties of the solutions to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jump. Since this model does not have explicit solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate finite time strong convergence theory of the numerical solutions under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.

Original language	English
Place of Publication	Ithaca, N.Y.
Number of pages	27
Publication status	Published - 13 Mar 2021

Keywords

stochastic interest rate model
delay volatility
Poisson jump
truncated EM scheme
strong convergence
Monte Carlo scheme

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Coffie-arXiv-2021-Delay-stochastic-interest-rate-model-with-jump-and-strong-convergenceFinal published version, 255 KBLicence: CC BY 4.0

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title = "Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations",

abstract = "In this paper, we study analytical properties of the solutions to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jump. Since this model does not have explicit solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate finite time strong convergence theory of the numerical solutions under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.",

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T1 - Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations

AU - Coffie, Emmanuel

PY - 2021/3/13

Y1 - 2021/3/13

N2 - In this paper, we study analytical properties of the solutions to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jump. Since this model does not have explicit solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate finite time strong convergence theory of the numerical solutions under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.

AB - In this paper, we study analytical properties of the solutions to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jump. Since this model does not have explicit solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate finite time strong convergence theory of the numerical solutions under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.

KW - stochastic interest rate model

KW - delay volatility

KW - Poisson jump

KW - truncated EM scheme

KW - strong convergence

KW - Monte Carlo scheme

UR - https://arxiv.org/abs/2103.07651

M3 - Working paper

BT - Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations

CY - Ithaca, N.Y.

ER -

Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations

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Keywords

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