A Forward Solution for Computing Risk-Neutral Derivatives Exposure

Marouan Iben Taarit and Bernard Lapeyre ()
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Marouan Iben Taarit: Natixis, CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique
Bernard Lapeyre: CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - ENPC - École nationale des ponts et chaussées, MATHRISK - Mathematical Risk Handling - UPEM - Université Paris-Est Marne-la-Vallée - ENPC - École nationale des ponts et chaussées - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique

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Abstract: In this paper, we derive a forward analytical formula for computing the expected exposure of financial derivatives. Under general assumptions about the underlying diffusion process, we give a convenient decomposition of the exposure into two terms: The first term is an intrinsic value part which is directly deduced from the term structure of the forward mark-to-market. The second term expresses the variability of the future mark-to-market and represents the time value part. Abstract In the spirit of Dupire's equation for local volatility, our representation establishes a differential equation for the evolution of the expected exposure with respect to the observation dates. Our results are twofold: First, we derive analytically an integral formula for the exposure's expectation and we highlight straightforward links with local times and the co-area formula. Second, we show that from a numerical perspective, our solution can be significantly efficient when compared to standard numerical methods. The accuracy and time-efficiency of the forward representation are of special interest in benchmarking XVA valuation adjustments at the trade level.

Keywords: Expected exposure; co-area formula; local times; Dupire's equation (search for similar items in EconPapers)
Date: 2017-12-19
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-01667100

DOI: 10.2139/ssrn.2353308

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