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Comonotonic Monte Carlo and its applications in option pricing and quantification of risk

Alain Chateauneuf (), Mina Mostoufi and David Vyncke ()
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David Vyncke: Universiteit Gent - Vakgroep Toegepaste Wiskunde en Informatica

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting, such as estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, by using the comonotonic approximation as a control variate. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options when the logreturns follow a Black-Scholes model or a variance gamma model.

Keywords: control variate Monte Carlo; comonotonicity; option pricing; tarification d'option; méthode de Monte-Carlo; comonotonicité; variable de contrôle (search for similar items in EconPapers)
Date: 2015-06
New Economics Papers: this item is included in nep-cmp, nep-ore and nep-rmg
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Published in 2015

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Working Paper: Comonotonic Monte Carlo and its applications in option pricing and quantification of risk (2015) Downloads
Working Paper: Comonotonic Monte Carlo and its applications in option pricing and quantification of risk (2015) Downloads
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