The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Performance Analysis of Economic VaR Estimation using Risk Neutral Probability Distributions

  • Heo, Se-Jeong (Department of Applied Statistics, Konkuk University) ;
  • Yeo, Sung-Chil (Department of Applied Statistics, Konkuk University) ;
  • Kang, Tae-Hun (School of Business Administration, Kyungsung University)
  • Received : 2012.07.31
  • Accepted : 2012.09.12
  • Published : 2012.10.31
Download PDF
⟨ Previous Next ⟩

Abstract

Traditional value at risk(S-VaR) has a difficulity in predicting the future risk of financial asset prices since S-VaR is a backward looking measure based on the historical data of the underlying asset prices. In order to resolve the deficiency of S-VaR, an economic value at risk(E-VaR) using the risk neutral probability distributions is suggested since E-VaR is a forward looking measure based on the option price data. In this study E-VaR is estimated by assuming the generalized gamma distribution(GGD) as risk neutral density function which is implied in the option. The estimated E-VaR with GGD was compared with E-VaR estimates under the Black-Scholes model, two-lognormal mixture distribution, generalized extreme value distribution and S-VaR estimates under the normal distribution and GARCH(1, 1) model, respectively. The option market data of the KOSPI 200 index are used in order to compare the performances of the above VaR estimates. The results of the empirical analysis show that GGD seems to have a tendency to estimate VaR conservatively; however, GGD is superior to other models in the overall sense.

Keywords

References

  1. Ait-Sahalia, Y. and Lo, A. W. (2000). Nonparametric risk management and implied risk aversion, Journal of Econometrics, 94, 9-51. https://doi.org/10.1016/S0304-4076(99)00016-0
  2. Bahra, B. (1997). Implied riskneutral probability density functions from option prices: Theory and application, Working paper, Bank of England.
  3. Bali, T. G. (2007). An extreme value approach to estimating interest-rate volatility: Pricing implications for interest-rate options, Management Science, 53, 323-339. https://doi.org/10.1287/mnsc.1060.0628
  4. Berkowitz, J. (2001). Testing density forecasts, with applications to risk management, Journal of Business and Economic Statistics, 19, 465-474. https://doi.org/10.1198/07350010152596718
  5. Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637-659. https://doi.org/10.1086/260062
  6. Christoffersen, P. (1998). Evaluating interval forecasts, International Economic Review, 39, 841-862. https://doi.org/10.2307/2527341
  7. Fabozzi, F. J., Tunaru, R. and Albota, G. (2009). Estimating risk-neutral density with parametric models in interest rate markets, Quantitative Finance, 9, 55-70. https://doi.org/10.1080/14697680802272045
  8. Glosten, L. R., Jagannathan, R. and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks, Journal of Finance, 48, 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
  9. Grith, M. and Kratschmer, V. (2010). Parametric estimation of risk neutral density functions, SFB 649, Discussion Paper
  10. Harrison, J. M. and Pliska, S. R. (1981). Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes Applications, 11, 215-260. https://doi.org/10.1016/0304-4149(81)90026-0
  11. Kim, M. S. and Kang, T. H. (2010). Value at risk using generalized extreme value distribution implied in the KOSPI 200 index options, Asian Review of Financial Research, 23, 367-404.
  12. Markose, S. and Alentorn, A. (2010). The Generalized extreme value(GEV) distribution, implied tail index and option pricing, Forthcoming Spring 2011 in The Journal of Derivatives.
  13. Ritchey, R. J. (1990). Call option valuation for discrete normal mixtures, Journal of Financial Research, 13, 285-296. https://doi.org/10.1111/j.1475-6803.1990.tb00633.x
  14. Rosenblatt, M. (1952). Remarks on a multivariate transformation, The Annals of Mathematical Statistics, 23, 470-472. https://doi.org/10.1214/aoms/1177729394
  15. Savickas, R. (2002). A simple option-pricing formula, The Financial Review, 37, 207-226. https://doi.org/10.1111/1540-6288.00012

Cited by

  1. Vector at Risk and alternative Value at Risk vol.29, pp.4, 2016, https://doi.org/10.5351/KJAS.2016.29.4.689
  2. Properties of alternative VaR for multivariate normal distributions vol.27, pp.6, 2016, https://doi.org/10.7465/jkdi.2016.27.6.1453