Risk Estimation in Exchange Rate Markets Based on Stochastic Copula Approach

Table 4

Backtesting of VaR forecasts at 95% confidence level.

Estimation method	Exceeds of VaR	Exceeds of CoVaR
			P value	P value
Portfolio 1: USD/TRY–EUR/TRY
Static t copula	44	17	0.76234 (0.38259)	4.85892 (0.08808)	0.02470
Stochastic-normal	38	16	0.00986 (0.92087)	0.65313 (0.72061)	0.01934
Stochastic-Gumbel	39	15	0.00434 (0.94741)	0.52398 (0.76951)	0.02160
Stochastic-Frank	37	15	0.07074 (0.79025)	0.85703 (0.65147)	0.01934
Stochastic-rotGumbel	34	12	0.60015 (0.43851)	0.76717 (0.68141)	0.01859
Historical simulation	61	23	11.72106 (<0.001)	16.96855 (<0.001)	0.07096
Variance-covariance	42	19	0.30684 (0.57962)	3.09041 (0.21326)	0.04274
Portfolio 2: USD/TRY–JPY/TRY
Static t copula	37	14	0.07074 (0.79025)	2.41326 (0.29920)	0.01748
Stochastic-normal	32	14	1.25816 (0.26199)	2.99303 (0.22390)	0.01522
Stochastic-Gumbel	33	13	0.89750 (0.34345)	2.40800 (0.29999)	0.01617
Stochastic-Clayton	32	11	1.25816 (0.26199)	2.99303 (0.22390)	0.01444
Stochastic-Frank	32	13	1.25816 (0.26199)	2.99303 (0.22390)	0.01501
Stochastic-rotGumbel	32	10	1.25816 (0.26199)	2.99303 (0.22390)	0.01462
Stochastic-rotClayton	39	15	2.73964 (0.09788)	3.40725 (0.18202)	0.01933
Historical simulation	52	21	4.43744 (0.03515)	6.16530 (0.04583)	0.04879
Variance-covariance	38	18	0.00986 (0.92087)	4.14689 (0.12575)	0.02890
Portfolio 3: EUR/TRY–JPY/TRY
Static t copula	41	15	0.15408 (0.69466)	0.46543 (0.79237)	0.02012
Stochastic-normal	29	13	2.73964 (0.09788)	5.26395 (0.07193)	0.01550
Stochastic-Gumbel	38	15	0.00986 (0.92087)	0.65531 (0.07206)	0.01751
Stochastic-Frank	29	11	2.73964 (0.09788)	5.26395 (0.07193)	0.01546
Stochastic-rotGumbel	29	9	2.73964 (0.09788)	5.26395 (0.07193)	0.01503
Historical simulation	51	22	3.82532 (0.05048)	4.62346 (0.09908)	0.05065
Variance-covariance	39	18	0.00434 (0.94741)	3.77213 (0.15166)	0.03483