The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Value at Risk calculation using sparse vine copula models

성근 바인 코풀라 모형을 이용한 고차원 금융 자료의 VaR 추정

  • 안광준 (성균관대학교 통계학과) ;
  • 백창룡 (성균관대학교 통계학과)
  • Received : 2021.07.26
  • Accepted : 2021.09.15
  • Published : 2021.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Value at Risk (VaR) is the most popular measure for market risk. In this paper, we consider the VaR estimation of portfolio consisting of a variety of assets based on multivariate copula model known as vine copula. In particular, sparse vine copula which penalizes too many parameters is considered. We show in the simulation study that sparsity indeed improves out-of-sample forecasting of VaR. Empirical analysis on 60 KOSPI stocks during the last 5 years also demonstrates that sparse vine copula outperforms regular copula model.

최대예상손실액(VaR)은 위험관리수단으로 금융에서 시장위험을 측정하는 대표적인 값이다. 본 논문에서는 다양한 자산으로 이루어진 고차원 금융자료에서 자산들 간의 의존성 구조를 잘 설명할 수 있는 성근 바인 코풀라를 이용한 VaR 추정에 대해서 논의한다. 성근 바인 코풀라는 정규 바인 코풀라 모형에 벌점화를 적용한 방법으로 추정하는 모수의 개수를 벌점화를 통해 축소하는 방법이다. 모의 실험 결과 성근 바인 코풀라를 이용한 VaR 추정이 더 작은 표본 외 예측오차를 줌을 살펴볼수 있었다. 또한 최근 5년간의 코스피 60개 종목을 바탕으로 실시한 실증 자료 분석에서도 성근 바인 코풀라 모형이 더 좋은 예측 성능을 보임을 확인할 수 있었다.

Keywords

Acknowledgement

이 논문은 한국연구재단의 지원을 받아 수행된 기초연구 사업임 (NRF-2019R1F1A1057104).

References

  1. Bedford T and Cooke RM (2001). Probability density decomposition for conditionally dependent random variables modeled by vines, Annals of Mathematics and Artificial intelligence, 32, 245-268. https://doi.org/10.1023/A:1016725902970
  2. Bedford T and Cooke RM (2002). Vines: A new graphical model for dependent random variables, Annals of Statistics, 30, 1031-1068.
  3. Brechmann EC and Czado C (2013). Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50, Statistics & Risk Modeling, 30, 307-342. https://doi.org/10.1524/strm.2013.2002
  4. Dissmann J, Brechmann EC, Czado C, and Kurowicka D (2013). Selecting and estimating regular vine copulae and application to financial returns, Computational Statistics and Data Analysis, 59, 52-69, https://doi.org/10.1016/j.csda.2012.08.010
  5. Embrechts P, McNeil A, and Straumann D (2002). Correlation and dependence in risk management: properties and pitfalls, Risk Management: Value at Risk and Beyond, 1, 176-223. https://doi.org/10.1017/CBO9780511615337.008
  6. Fan J, Qi L, and Xiu D (2014). Quasi-maximum likelihood estimation of GARCH models with heavy-tailed likelihoods, Journal of Business & Economic Statistics, 32, 178-191. https://doi.org/10.1080/07350015.2013.840239
  7. Friedman J, Hastie T, and Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent, Journal of Statistical Software, 33, 1-22.
  8. Joe H (1996). Families of m-variate distributions with given margins and m(m - 1)/2 bivariate dependence parameters, Lecture Notes-Monograph Series, 120-141.
  9. Jorion P (2002). Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill.
  10. Kupiec P (1995). Techniques for verifying the accuracy of risk measurement models, The Journal of Derivatives, 3, 73-84. https://doi.org/10.3905/jod.1995.407942
  11. MacKenzie D and Spears T (2014). 'A device for being able to book P&L': The organizational embedding of the Gaussian copula, Social Studies of Science, 44, 418-440. https://doi.org/10.1177/0306312713517158
  12. Muller D and Czado C (2019). Selection of sparse vine copulas in high dimensions with the lasso, Statistics and Computing, 29, 269-287. https://doi.org/10.1007/s11222-018-9807-5
  13. Nagler T, Schepsmeier U, Stoeber J, Brechmann EC, Graeler B, and Erhardt T (2021). VineCopula: Statistical Inference of Vine Copulas, R package version 2.4.2.
  14. Park S and Baek C (2014). On multivariate GARCH model selection based on risk management, Journal of the Korean Data and Information Science Society, 25, 1333-1343. https://doi.org/10.7465/jkdi.2014.25.6.1333
  15. Ryan JA and Ulrich JM (2020). quantmod: Quantitative Financial Modelling Framework, R package version 0.4-16.
  16. Sklar M (1959). Fonctions de repartition an dimensions et leurs marges, Publications de l'Institut Statistique de l'Universite de Paris, 8, 229-231.