Reducing Variation of Risk Estimation by Using Importance Sampling

Abstract

In today's world, risk measurement and risk management are of great importance for various economic reasons. Especially in the crisis periods, the tail risk becomes very important in risk estimation. Many methods have been developed for accurate measurement of risk. The easiest of these methods is the Value at Risk (VaR) method. However, standard VaR methods are not very effective in tail risks. This study aims to demonstrate the usage of delta normal method, historical simulation method, Monte Carlo simulation, and importance sampling to calculate the value at risk and to show which method is more effective by applying them to the S&P index between 1993 and 2003.

Keywords

• Importance Sampling,Value at Risk,Monte Carlo Simulation,Delta Normal Method,Tail Risk

References

1. Bassamboo, A., Juneja, S. & Zeevi, A. (2005). Portfolio Credit Risk with Extremal Dependence. Ssrn, 56(3), 593–606.
2. Brereton, T., Kroese, D. & Chan, J. (2012). Monte Carlo methods for portfolio credit risk, ANU Working Papers in Economics and Econometrics. Access Domain: https://ideas.repec.org/p/acb/cbeeco/2012-579.html
3. Danielsson, J. (2011). Financial Risk Forecasting: The Theory and Practice of Forecasting Market Risk, with Implementation in R and Matlab, Wiley&Sons Inc:UK
4. De Vooys, F. (2012). Importance Sampling for Credit Risk Monte Carlo simulations using the Cross Entropy Approach, Nederland Open University Computer Science, Master Thesis. Access Domain: https://dspace.ou.nl/bitstream/1820/4285/1/INF_20120417_Vooys.pdf
5. Glasserman, P. (2003). Monte Carlo Methods in Financial Engineering. Springer-Verlag New York.
6. Glasserman, P. & Li, J. (2005). Importance Sampling for Portfolio Credit Risk. Management Science, 51(11), 1643–1656.
7. Glasserman, P., Heidelberger, P. & Shahabuddin. P. (1999a). Asymptotically optimal importance sampling and stratification for pricing path-dependent options. Mathematical Finance, 9,117–152.
8. Glasserman, P., Heidelberger, P. & Shahabuddin. P. (1999b). Importance sampling in the HeathJarrow-Morton framework. Technical report, IBM Research Report RC 21367, Yorktown Heights,NY.

9. Gupta, J. & Chaudhry, S. (2019). Mind the Tail, or Risk to Fail, Journal of Business Research, 99, 167-185.
10. Jorion, P. (2003). Financial Risk Manager Handbook. John Wiley&Sons Inc: New Jersey
11. Kahn, H. (1950a). Random sampling (Monte Carlo) techniques in neutron attenuation problems, I. Nucleonics, 6(5), 27–37.
12. Kahn, H. (1950b). Random sampling (Monte Carlo) techniques in neutron attenuation problems, II. Nucleonics, 6(6), 60–65.
13. Kahn, H. & Marshall, A. (1953). Methods of reducing sample size in Monte Carlo computations. Journal of the Operations Research Society of America, 1(5), 263–278.
14. Kalkbrener, M., Lotter, H. & Overbeck, L. (2004) Sensible and efficient allocation for credit portfolios, Risk, 17, S19-S24
15. Keasler, T.R. (2001). The Underwriter's Early Lock-Up Release: Empirical Evidence. Journal of Economics and Finance, 25(2), 214-228.
16. Keçeci, N.F. & Demirtaş, Y.E. (2018). Risk-Based DEA Efficiency and SSD Efficiency of OECD Members Stock Indices. Alphanumeric Journal, 6 (1), 25-36. DOI: 10.17093/alphanumeric. 345483
17. Liu, G. (2010). Importance sampling for risk contributions of credit portfolios. Proceedings - Winter Simulation Conference, 2771–2781.
18. Morokoff, W. J. (2004). Proceedings of the 2004 Winter Simulation Conference R .G. Ingalls, M. D. Rossetti, J. S. Smith, and B. A. Peters, eds.
19. Müller, A. (2016). Improved Variance Reduced Monte-Carlo Simulation of in-the-Money Options. Journal of Mathematical Finance, 6(3), 361–367.
20. Neftci, S. N. (2000). Value at Risk Calculations, Extreme Events, and Tail Estimation, Journal of Derivatives, 7, 23-38.
21. Rubinstein, M.(2002). Markowitz's "Portfolio Selection": A Fifty-Year Retrospective . The Journal of Finance, 57(3), 1041-1045.
22. Van den Goorbergh, R.W.J. & Vlaar P.J.G. (1999). Value-at-Risk Analysis of Stock Returns:Historical Simulation, Variance Techniques or Tail Index Estimation?. Research Memorandum WO&E nr 579, 1-38.