Risk Estimation in Exchange Rate Markets Based on Stochastic Copula Approach

Table 5

Backtesting of VaR forecasts at 99% confidence level.

Estimation method	Exceeds of VaR	Exceeds of CoVaR	(P-value)	(P-value)
Portfolio 1: USD/TRY–EUR/TRY
Static t copula	9	7	0.20352 (0.65188)	3.10763 (0.21143)	0.00525
Stochastic-normal	9	6	0.20352 (0.64188)	3.10763 (0.21143)	0.00414
Stochastic-gumbel	10	7	0.62222 (0.43022)	3.12586 (0.20952)	0.00494
Stochastic-frank	10	7	0.62222 (0.43022)	3.12586 (0.20952)	0.00548
Stochastic-rotGumbel	8	5	0.01013 (0.91980)	3.37601 (0.18488)	0.00390
Historical simulation	19	8	11.83104 (0.00058)	18.64638 (<0.001)	0.01370
Variance-covariance	25	10	24.58674 (<0.001)	28.47479 (<0.001)	0.01686
Portfolio 2: USD/TRY–JPY/TRY
Static t copula	8	6	0.01013 (0.91980)	3.37601 (0.18488)	0.00288
Stochastic-normal	8	7	0.01013 (0.91980)	3.37601 (0.18488)	0.02439
Stochastic-gumbel	8	7	0.01013 (0.91980)	3.37601 (0.18488)	0.00293
Stochastic-clayton	7	4	0.07001 (0.79130)	3.97508 (0.13703)	0.00223
Stochastic-frank	10	7	0.62222 (0.43022)	3.12586 (0.20952)	0.00343
Stochastic-rotgumbel	7	4	0.07001 (0.79130)	3.97508 (0.13703)	0.00225
Stochastic-rotclayton	11	6	2.19791 (0.13819)	2.23963 (0.32633)	0.00475
Historical simulation	14	8	4.15854 (0.04142)	14.46645 (<0.001)	0.01031
Variance-covariance	15	9	5.43664 (0.01971)	15.07623 (<0.001)	0.01066
Portfolio 3: EUR/TRY–JPY/TRY
Static t copula	8	6	0.01013 (0.91980)	3.37601 (0.18488)	0.00355
Stochastic-normal	8	6	0.01013 (0.91980)	3.37601 (0.18488)	0.00273
Stochastic-gumbel	8	7	0.01013 (0.91980)	3.37601 (0.18488)	0.00349
Stochastic-frank	8	7	0.01013 (0.91980)	3.37601 (0.18488)	0.00373
Stochastic-rotgumbel	8	5	0.01013 (0.91980)	3.37601 (0.18488)	0.00250
Historical simulation	13	8	3.02607 (0.08193)	14.48208 (<0.001)	0.01086
Variance-covariance	18	10	10.05496 (<0.001)	17.49497 (<0.001)	0.01305