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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, https://www.ugent.be/

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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) similation, 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 (search for similar items in EconPapers)
JEL-codes: G17 C02 C13 C15 C63 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2015-02, Revised 2015-06
New Economics Papers: this item is included in nep-cmp, nep-ore and nep-rmg
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ftp://mse.univ-paris1.fr/pub/mse/CES2015/15015R.pdf (application/pdf)

Related works:
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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