An unbiased Monte Carlo estimator for derivatives. Application to CIR

Victor Reutenauer 1 Etienne Tanré 2
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : In this paper, we present extensions of the exact simulation algorithm introduced by Beskos et al. (2006). First, a modification in the order in which the simulation is done accelerates the algorithm. In addition, we propose a truncated version of the modified algorithm. We obtain a control of the bias of this last version, exponentially small in function of the truncation parameter. Then, we extend it to more general drift functions. Our main result is an unbiased algorithm to approximate the two first derivatives with respect to the initial condition x of quantities with the form EΨ(X^x_T). We describe it in details in dimension 1 and also discuss its multi-dimensional extensions for the evaluation of EΨ(X^x_T). Finally, we apply the algorithm to the CIR process and perform numerical tests to compare it with classical approximation procedures.
Type de document :
Pré-publication, Document de travail
2017
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Dernière modification le : mardi 17 avril 2018 - 09:04:39
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  • HAL Id : hal-01371448, version 3
  • ARXIV : 1609.07431

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Victor Reutenauer, Etienne Tanré. An unbiased Monte Carlo estimator for derivatives. Application to CIR. 2017. 〈hal-01371448v3〉

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