Avoiding Zero Probability Events When Computing Value at Risk Contributions: A Malliavin Calculus Approach

14 Pages Posted: 28 May 2020

See all articles by Yuri Saporito

Yuri Saporito

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics

Rodrigo Targino

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics

Date Written: April 27, 2020

Abstract

This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). Making use of Malliavin calculus, we recast the traditional Euler contributions from an expectation conditional to an event of zero probability to a ratio of conditional expectations, where both the numerator and the denominator's conditioning events have positive probability. For several different models we show empirically that the estimator using this novel representation has no perceivable bias and variance smaller than a standard estimator used in practice.

Keywords: Risk Management, Capital Allocation, Malliavin Calculus

JEL Classification: G32, C15

Suggested Citation

Saporito, Yuri and Targino, Rodrigo, Avoiding Zero Probability Events When Computing Value at Risk Contributions: A Malliavin Calculus Approach (April 27, 2020). Available at SSRN: https://ssrn.com/abstract=3588083 or http://dx.doi.org/10.2139/ssrn.3588083

Yuri Saporito

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics ( email )

Praia de Botafogo
Rio de Janeiro, 22250-900
Brazil

Rodrigo Targino (Contact Author)

Getulio Vargas Foundation (FGV) - EMAp - School of Applied Mathematics ( email )

Praia de Botafogo
Rio de Janeiro, 22250-900
Brazil

HOME PAGE: http://rtargino.netlify.app/

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