The original Risk-Metrics method is underpinned by the assumption that daily asset returns are conditional Gaussian independently identically distributed (iid) random variables with a mean of zero. In this paper, a new method to calculate Value at Risk (VaR) was suggested to overcome the shortcoming of Risk-Metrics by employing binary response models to compute probability forecasts of the portfolio return by exceeding a grid of candidate quantile values. From those values, the VaR quantile value was selected. The proposed model was called BRV (Binary Response VaR method). Consistent application of BRV to the Dow Jones Industrial Average (INDEXDJX: DJI) and Dow Jones U.S. Marine Transportation Index (DJUSMT) time series proved that it was more accurate than the Risk-Metric system. This method not only worked similar to quantile regression but had the advantage that conventional maximum likelihood methods could be used for parameter estimation and inference. The BRV method was the best performing method for computing the daily VaR at both the 95% and 99% confidence levels over the period 02/01/06–31/12/08. The BRV and the QR (quantile regression) methods performed similarly, but the BRV method had the practical advantage that conventional maximum likelihood (ML) technique could be used for parameter estimation and robust inference.
Citation: Kasra Pourkermani. VaR calculation by binary response models[J]. Data Science in Finance and Economics, 2024, 4(3): 350-361. doi: 10.3934/DSFE.2024015
The original Risk-Metrics method is underpinned by the assumption that daily asset returns are conditional Gaussian independently identically distributed (iid) random variables with a mean of zero. In this paper, a new method to calculate Value at Risk (VaR) was suggested to overcome the shortcoming of Risk-Metrics by employing binary response models to compute probability forecasts of the portfolio return by exceeding a grid of candidate quantile values. From those values, the VaR quantile value was selected. The proposed model was called BRV (Binary Response VaR method). Consistent application of BRV to the Dow Jones Industrial Average (INDEXDJX: DJI) and Dow Jones U.S. Marine Transportation Index (DJUSMT) time series proved that it was more accurate than the Risk-Metric system. This method not only worked similar to quantile regression but had the advantage that conventional maximum likelihood methods could be used for parameter estimation and inference. The BRV method was the best performing method for computing the daily VaR at both the 95% and 99% confidence levels over the period 02/01/06–31/12/08. The BRV and the QR (quantile regression) methods performed similarly, but the BRV method had the practical advantage that conventional maximum likelihood (ML) technique could be used for parameter estimation and robust inference.
| [1] |
Altun M (2020) A new approach to Value-at-Risk: GARCH-TSLx model with inference. Comm Stat Simu Comput 49: 3134–3151. https://doi.org/10.1080/03610918.2018.1535069 doi: 10.1080/03610918.2018.1535069
|
| [2] |
Christoffersen PF (1998) Evaluating Interval Forecasts. Int Econ Review 39: 841–862. https://doi.org/10.2307/2527341 doi: 10.2307/2527341
|
| [3] |
Christoffersen PF, Diebold FX (2006) Financial Asset Returns, Direction-of-Change Forecasting and Volatility Dynamics. Manag Sci 52: 1273–1287. https://doi.org/10.1287/mnsc.1060.0520 doi: 10.1287/mnsc.1060.0520
|
| [4] | Dumitrescu EI, Hurlin C, Pham V (2012) Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests. Halshs. https://shs.hal.science/halshs-00671658 |
| [5] |
Emenogu NG, Adenomon MO, Nweze NO (2020) On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting. Financ Innov 6: 18. https://doi.org/10.1186/s40854-020-00178-1 doi: 10.1186/s40854-020-00178-1
|
| [6] | Engle RF, Manganelli S (2004) CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles. J Bus Econ Stat 22: 367–381. http://www.jstor.org/stable/1392044 |
| [7] |
Foresi S, Peracchi F (1995) The Conditional Distribution of Excess Returns: An Empirical Analysis. J Amer Statist Assoc 90: 451–466. https://doi.org/10.1080/01621459.1995.10476537 doi: 10.1080/01621459.1995.10476537
|
| [8] | Huber PJ (1967) The Behavior of Maximum Likelihood Estimates Under Nonstandard Conditions. Proceedings of the fifth Berkeley symposium on mathematical statistics and probability 1: 221–233. |
| [9] |
Jelito D, Pitera M (2021) New fat-tail normality test based on conditional second moments with applications to finance. Stat Pap 62: 2083–2108. https://doi.org/10.1007/s00362-020-01176-2 doi: 10.1007/s00362-020-01176-2
|
| [10] | Jorge M, Jerry X (2001) Return to Risk Metrics: The Evolution of a Standard. Risk Metrics Group Inc. |
| [11] | Jorion P (2007) Value at Risk: The New Benchmark for Managing Financial Risk. 3. McGraw-Hill, New York. |
| [12] |
Koenker R, Bassett G (1978) Regression Quantiles. Econometrica 46: 33–50. http://dx.doi.org/10.2307/1913643 doi: 10.2307/1913643
|
| [13] |
Koenker R, Park BJ (1966) An interior point algorithm for nonlinear quantile regression. J Econometrics 71: 265–283. https://doi.org/10.1016/0304-4076(96)84507-6 doi: 10.1016/0304-4076(96)84507-6
|
| [14] |
Kupiec P (1995) Techniques for Verifying the Accuracy of Risk Measurement Models. J Deriv 3: 73–84. http://dx.doi.org/10.3905/jod.1995.407942 doi: 10.3905/jod.1995.407942
|
| [15] |
Mudhokar GS, George O (1978) A remark on the shape of the logistic distribution. Biometrika 65: 667–668. https://doi.org/10.1093/biomet/65.3.667 doi: 10.1093/biomet/65.3.667
|
| [16] |
Nieto MR, Ruiz E (2016) Frontiers in VaR forecasting and backtesting. Intl J Forecasting 32: 475–501. https://doi.org/10.1016/j.ijforecast.2015.08.003 doi: 10.1016/j.ijforecast.2015.08.003
|
| [17] |
Peracchi F (2002) On estimating conditional quantiles and distribution functions. Comput Statis Data Anal 38: 433–447. https://doi.org/10.1016/S0167-9473(01)00070-6 doi: 10.1016/S0167-9473(01)00070-6
|
| [18] |
Slim S, Koubaa Y, BenSaida A (2017) Value-at-Risk under Lévy GARCH models: Evidence from global stock markets. J Int Financ Mark I 46: 30–53 https://doi.org/10.1016/j.intfin.2016.08.008 doi: 10.1016/j.intfin.2016.08.008
|
| [19] |
Tabasi H, Yousefi V, Tamošaitienė J, et al. (2019) Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models. Adm Sci 9: 40. https://doi.org/10.3390/admsci9020040 doi: 10.3390/admsci9020040
|
| [20] |
Taylor JW (1999) A quantile regression method to estimating the distribution of multi period returns. J Deriv 7: 64–78. https://doi.org/10.3905/jod.1999.319106 doi: 10.3905/jod.1999.319106
|
| [21] |
Taylor JW (2008) Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall. J Financ Economet 6: 382–406. https://doi.org/10.1093/jjfinec/nbn007 doi: 10.1093/jjfinec/nbn007
|
| [22] |
Thavaneswaran A, Paseka A, Frank J (2020) Generalized value at risk forecasting. Commun Stat-Theor M 49: 4988–4995. https://doi.org/10.1080/03610926.2019.1610443 doi: 10.1080/03610926.2019.1610443
|
| [23] |
Ugurlu K (2023) A new coherent multivariate average-value-at-risk. Optimization 72: 493–519. https://doi.org/10.1080/02331934.2021.1970755 doi: 10.1080/02331934.2021.1970755
|
| [24] |
White H (1980) A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica 48: 817–838. https://doi.org/10.2307/1912934 doi: 10.2307/1912934
|
| [25] | Zumbach G (2006) The Risk Metrics 2006 Methodology. Available at SSRN. http://dx.doi.org/10.2139/ssrn.1420185 |
Kasra Pourkermani. VaR calculation by binary response models[J]. Data Science in Finance and Economics, 2024, 4(3): 350-361. doi: 10.3934/DSFE.2024015
DownLoad: