Estimation of risk contributions with MCMC

Takaaki Koike, Mihoko Minami

Research output: Contribution to journalArticle

Abstract

Determining risk contributions of unit exposures to portfolio-wide economic capital is an important task in financial risk management. Computing risk contributions involves difficulties caused by rare-event simulations. In this study, we address the problem of estimating risk contributions when the total risk is measured by value-at-risk (VaR). Our proposed estimator of VaR contributions is based on the Metropolis-Hasting (MH) algorithm, which is one of the most prevalent Markov chain Monte Carlo (MCMC) methods. Unlike existing estimators, our MH-based estimator consists of samples from the conditional loss distribution given a rare event of interest. This feature enhances sample efficiency compared with the crude Monte Carlo method. Moreover, our method has consistency and asymptotic normality, and is widely applicable to various risk models having a joint loss density. Our numerical experiments based on simulation and real-world data demonstrate that in various risk models, even those having high-dimensional (≈500) inhomogeneous margins, our MH estimator has smaller bias and mean squared error when compared with existing estimators.

Original languageEnglish
JournalQuantitative Finance
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Markov chain Monte Carlo
Estimator
Simulation
Value at risk
Rare events
Risk model
Markov chain Monte Carlo methods
Monte Carlo method
Metropolis-Hastings algorithm
Mean squared error
Numerical experiment
Financial risk management
Economic capital
Total risk
Asymptotic normality
Margin
Loss distribution

Keywords

  • Copulas
  • Markov chain Monte Carlo
  • Metropolis-Hastings algorithm
  • Risk allocation
  • Risk contributions
  • Value-at-risk
  • VaR contributions

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

Cite this

Estimation of risk contributions with MCMC. / Koike, Takaaki; Minami, Mihoko.

In: Quantitative Finance, 01.01.2019.

Research output: Contribution to journalArticle

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