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 language | English |
|---|---|
| Journal | Quantitative Finance |
| DOIs | |
| Publication status | Published - 2019 Jan 1 |
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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 journal › Article
}
TY - JOUR
T1 - Estimation of risk contributions with MCMC
AU - Koike, Takaaki
AU - Minami, Mihoko
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Copulas
KW - Markov chain Monte Carlo
KW - Metropolis-Hastings algorithm
KW - Risk allocation
KW - Risk contributions
KW - Value-at-risk
KW - VaR contributions
UR - http://www.scopus.com/inward/record.url?scp=85064638789&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85064638789&partnerID=8YFLogxK
U2 - 10.1080/14697688.2019.1588469
DO - 10.1080/14697688.2019.1588469
M3 - Article
JO - Quantitative Finance
JF - Quantitative Finance
SN - 1469-7688
ER -