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Implicit American Monte Carlo methods for nonlinear functional of future portfolio value

Abstract

We introduce a new approximation algorithm for nonlinear functional of future portfolio value. We call it as “Implicit method” in contrast with calling existing method as “Explicit method”. In this paper, we show both “Implicit” and “Explicit” algorithms converge to true value using Stochastic mesh which is an typical example of American Monte Carlo methods. And we show the efficiency of “Implicit method” through the theoretical convergence order and numerical simulation.

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Correspondence to Yusuke Morimoto.

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Morimoto, Y. Implicit American Monte Carlo methods for nonlinear functional of future portfolio value. Japan J. Indust. Appl. Math. 34, 635–674 (2017). https://doi.org/10.1007/s13160-017-0271-y

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Keywords

  • Computational finance
  • Option pricing
  • Malliavin calculus
  • Stochastic mesh method
  • XVA

Mathematics Subject Classification

  • 65C05
  • 60G40

JEL Classification

  • C63
  • G12