Forecasting USD-BRL Currency Rate Volatility using Realized and Implied Volatilities Data

Campani, Carlos Heitor; Durães, Assis Gustavo da Silva

doi:10.1590/0101-41614845cca

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Artigo de Pesquisa • Estud. Econ. 48 (4) • Oct-Dec 2018 • https://doi.org/10.1590/0101-41614845cca copy

Forecasting USD-BRL Currency Rate Volatility using Realized and Implied Volatilities Data^♦ Universidade Federal do Rio de Janeiro Rio de Janeiro RJ Brazil carlos.heitor@coppead.ufrj.br Professor of Finance - Universidade Federal do Rio de Janeiro (UFRJ) Endereço: Rua Pascoal Lemme, 355 - Ilha do Fundão - Cid. Universitária - Rio de Janeiro/RJ - Brasil CEP: 21941-918 - E-mail: carlos.heitor@coppead.ufrj.br

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This article assesses the impact of exogenous variables in GARCH models, when applied to volatility forecasts for the Brazilian USD-BRL currency market. As exogenous variables, we used the realized variance, based on high frequency data, and the FXVol index, based on market implied volatility data. This is the first study to use the FXVol index and to investigate its effects on Brazilian foreign exchange volatility. The results indicate statistical significance of the superiority of the extended models when predicting volatility. We conclude that high frequency data and market implied volatility contain relevant information with respect to USD-BRL currency volatility. These find ings are relevant for hedgers, speculators and practitioners in general.

Keywords
Volatility forecasts; Extended GARCH models; Implied volatility indices; Brazilian foreign exchange market

	Models
	_GARCH	_GJR	_eGARCH	_eGARCH+RV	_eGARCH+IV	_eGARCH+RV+IV
ω	0.0107	0.0114	-0.0036	-0.0493	-0.0485	-0.0688
ω	(0.004)	(0.001)	(0.357)	(0.023)	(0.074)	(0.210)
α	0.0997	0.1317	0.0605	0.0682	0.0736	0.0751
α	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.001)
β	0.8916	0.8992	0.9783	0.9463	0.9486	0.9328
β	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
γ		-0.0839	0.1834	0.1527	0.1743	0.1562
γ		(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
δ				0.0379		0.0310
δ				(0.026)		(0.177)
φ					0.0355	0.0217
φ					(0.084)	(0.428)
InL	-2,044.63	-2,033.96	-2,034.81	-2,029.17	-2,030.41	-2,028.31
AIC	4,095.26	4,075.91	4,077.62	4,068.35	4,070.82	4,068.61
BIC	4,111.40	4,097.42	4,099.13	4,095.24	4,097.71	4,100.88

Models	Criterion					Ranking (1:Best, 8:Worst)					Sum of Rankings	Final Ranking
Models	RMSE	MAE	RMSPE	MAPE	MdAPE	RMSE	MAE	RMSPE	MAPE	MdAPE	Sum of Rankings	Final Ranking
SD	0.0196	0.0016	0.7369	0.5288	0.4110	8	8	2	2	5	25	5
EWMA	0.0188	0.0109	0.7171	0.5214	0.4028	4	5	1	1	3	14	2
GARCH	0.0188	0.0109	0.9335	0.6325	0.4278	7	4	6	6	6	29	6
GJR	0.0188	0.0110	0.9554	0.6461	0.4301	6	6	7	7	7	33	7
eGARCH	0.0188	0.0112	0.9821	0.6675	0.4336	5	7	8	8	8	36	8
eGARCH+RV	0.0185	0.0107	0.9275	0.6275	0.4100	3	3	5	5	4	20	4
eGARCH+IV	0.0185	0.0105	0.8714	0.5919	0.3901	2	2	4	4	2	14	2
eGARCH+RV+IV	0.0184	0.0103	0.8548	0.5795	0.3871	1	1	3	3	1	9	1

Models	Criterion					Ranking (1:Best, 8:Worst)					Sum of Rankings	Final Ranking
Models	RMSE	MAE	RMSPE	MAPE	MdAPE	RMSE	MAE	RMSPE	MAPE	MdAPE	Sum of Rankings	Final Ranking
SD	0.0166	0.0110	1.1490	0.6654	0.4049	8	8	8	4	2	30	7
EWMA	0.0159	0.0106	1.1147	0.6566	0.3859	7	7	7	2	1	24	4
GARCH	0.0145	0.0101	1.0063	0.7016	0.4604	6	4	3	6	6	25	5
GJR	0.0144	0.0102	1.0314	0.7138	0.4819	5	5	5	7	7	29	6
eGARCH	0.0143	0.0103	1.0387	0.7270	0.4869	4	6	6	8	8	32	8
eGARCH+RV	0.0142	0.0101	1.0102	0.6987	0.4591	3	3	4	5	5	20	3
eGARCH+IV	0.0140	0.0097	0.9552	0.6579	0.4394	1	2	1	3	4	11	2
eGARCH+RV+1V	0.0140	0.0097	0.9562	0.6540	0.4296	2	1	2	1	3	9	1

Models		j
Models		SD	EWMA	GARCH	GJR	eGARCH	eGARCH+RV	eGARCH+IV	eGARCH+RV+IV
i	SD		3.0828	2.0266	2.0996	2.0684	2.8190	2.9151	3.3131
	SD		(0.002)	(0.043)	(0.036)	(0.039)	(0.005)	(0.004)	(0.001)
	EWMA	-3.0828		-0.1437	-0.0645	-0.0160	0.6489	0.7166	1.0345
	EWMA	(0.002)		(0.886)	(0.949)	(0.987)	(0.517)	(0.474)	(0.302)
	GARCH	-2.0266	0.1437		0.3384	0.3989	2.8713	2.0918	3.2261
	GARCH	(0.043)	(0.886)		(0.735)	(0.690)	(0.004)	(0.037)	(0.001)
	GJR	-2.0996	0.0645	-0.3384		0.2822	4.1574	2.2446	3.5315
	GJR	(0.036)	(0.949)	(0.735)		(0.778)	(0.000)	(0.025)	(0.000)
	eGARCH	-2.0684	0.0160	-0.3989	-0.2822		4.2519	2.8433	4.2281
	eGARCH	(0.039)	(0.987)	(0.690)	(0.778)		(0.000)	(0.005)	(0.000)
	eGARCH+RV	-2.8190	-0.6489	-2.8713	-4.1574	-4.2519		0.5827	2.1951
	eGARCH+RV	(0.005)	(0.517)	(0.004)	(0.000)	(0.000)		(0.560)	(0.029)
	eGARCH+IV	-2.9151	-0.7166	-2.0918	-2.2446	-2.8433	-0.5827		1.8963
	eGARCH+IV	(0.004)	(0.474)	(0.037)	(0.025)	(0.005)	(0.560)		(0.059)
	eGARCH+RV+IV	-3.3131	-1.0345	-3.2261	-3.5315	-4.2281	-2.1951	-1.8963
	eGARCH+RV+IV	(0.001)	(0.302)	(0.001)	(0.000)	(0.000)	(0.029)	(0.059)

Models		j
Models		SD	EWMA	GARCH	GJR	eGARCH	eGARCH+RV	eGARCH+IV	eGARCH+RV+IV
i	SD		3.1916	1.8440	1.4913	0.9619	2.2717	2.7842	3.3404
	SD		(0.002)	(0.066)	(0.137)	(0.337)	(0.024)	(0.006)	(0.001)
	EWMA	-3.1916		0.1899	-0.1964	-0.6768	0.6798	1.2348	1.7962
	EWMA	(0.002)		(0.850)	(0.844)	(0.499)	(0.497)	(0.218)	(0.073)
	GARCH	-1.8440	-0.1899		-1.4709	-2.8449	1.8688	3.3933	5.2654
	GARCH	(0.066)	(0.850)		(0.142)	(0.005)	(0.062)	(0.001)	(0.000)
	GJR	-1.4913	0.1964	1.4709		-2.9483	4.8847	6.0395	7.6759
	GJR	(0.137)	(0.844)	(0.142)		(0.003)	(0.000)	(0.000)	(0.000)
	eGARCH	-0.9619	0.6768	2.8449	2.9483		7.3480	9.0032	9.0786
	eGARCH	(0.337)	(0.499)	(0.005)	(0.003)		(0.000)	(0.000)	(0.000)
	eGARCH+RV	-2.2717	-0.6798	-1.8688	-4.8847	-7.3480		3.3721	8.0125
	eGARCH+RV	(0.024)	(0.497)	(0.062)	(0.000)	(0.000)		(0.001)	(0.000)
	eGARCH+IV	-2.7842	-1.2348	-3.3933	-6.0395	-9.0032	-3.3721		4.1862
	eGARCH+IV	(0.006)	(0.218)	(0.001)	(0.000)	(0.000)	(0.001)		(0.000)
	eGARCH+RV+IV	-3.3404	-1.7962	-5.2654	-7.6759	-9.0786	-8.0125	-4.1862
	eGARCH+RV+IV	(0.001)	(0.073)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)

Models		j
Models		SD	EWMA	GARCH	GJR	jeGARCH	eGARCH+RV	eGARCH+IV	eGARCH+RV+IV
i	SD		2.8644	4.2542	4.3423	4.1941	4.7584	4.8284	5.0789
	SD		(0.004)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)	(0.000)
	EWMA	-2.8644		3.1936	3.5394	3.4625	4.0242	4.0134	4.2580
	EWMA	(0.004)		(0.002)	(0.000)	(0.001)	(0.000)	(0.000)	(0.000)
	GARCH	-4.2542	-3.1936		0.5684	0.8222	2.0203	3.3261	3.5494
	GARCH	(0.000)	(0.002)		(0.570)	(0.411)	(0.044)	(0.001)	(0.000)
	GJR	-4.3423	-3.5394	-0.5684		0.8596	2.7043	3.7586	3.6856
	GJR	(0.000)	(0.000)	(0.570)		(0.391)	(0.007)	(0.000)	(0.000)
	eGARCH	-4.1941	-3.4625	-0.8222	-0.8596		1.5582	3.6355	2.8593
	eGARCH	(0.000)	(0.001)	(0.411)	(0.391)		(0.120)	(0.000)	(0.004)
	eGARCH+RV	-4.7584	-4.0242	-2.0203	-2.7043	-1.5582		2.4431	3.3110
	eGARCH+RV	(0.000)	(0.000)	(0.044)	(0.007)	(0.120)		(0.015)	(0.001)
	eGARCH+IV	-4.8284	-4.0134	-3.3261	-3.7586	-3.6355	-2.4431		-0.3195
	eGARCH+IV	(0.000)	(0.000)	(0.001)	(0.000)	(0.000)	(0.015)		(0.750)
	eGARCH+RV+IV	-5.0726	-4.2580	-3.5494	-3.6856	-2.8593	-3.3110	0.3195
	eGARCH+RV+IV	(0.000)	(0.000)	(0.000)	(0.000)	(0.004)	(0.001)	(0.750)

Models		j
Models		SD	EWMA	GARCH	GJR	eGARCH	eGARCH+RV	eGARCH+IV	eGARCH+RV+IV
i	SD		2.0254	2.3394	2.0378	1.6774	2.4855	3.2683	3.4941
	SD		(0.043)	(0.020)	(0.042)	(0.094)	(0.013)	(0.001)	(0.001)
	EWMA	-2.0254		1.4112	1.1529	0.8294	1.6197	2.4636	2.6473
	EWMA	(0.043)		(0.159)	(0.250)	(0.407)	(0.106)	(0.014)	(0.008)
	GARCH	-2.3394	-1.4112		-0.8951	-1.5395	0.8874	3.7987	4.0510
	GARCH	(0.020)	(0.159)		(0.371)	(0.124)	(0.375)	(0.000)	(0.000)
	GJR	-2.0378	-1.1529	0.8951		-1.4989	2.7156	6.3132	5.9250
	GJR	(0.042)	(0.250)	(0.371)		(0.135)	(0.007)	(0.000)	(0.000)
	eGARCH	-1.6774	-0.8294	1.5395	1.4989		3.7673	7.9018	6.2532
	eGARCH	(0.094)	(0.407)	(0.124)	(0.135)		(0.000)	(0.000)	(0.000)
	eGARCH+RV	-2.4855	-1.6197	-0.8874	-2.7156	-3.7673		5.7867	7.5518
	eGARCH+RV	(0.013)	(0.106)	(0.375)	(0.007)	(0.000)		(0.000)	(0.000)
	eGARCH+IV	-3.2683	-2.4636	-3.7987	-6.3132	-7.9018	-5.7867		0.3720
	eGARCH+IV	(0.001)	(0.014)	(0.000)	(0.000)	(0.000)	(0.000)		(0.710)
	eGARCH+RV+IV	-3.4941	-2.6473	-4.0510	-5.9250	-6.2532	-7.5518	-0.3720
	eGARCH+RV+IV	(0.001)	(0.008)	(0.000)	(0.000)	(0.000)	(0.000)	(0.710)

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Acompanhe os números deste periódico no seu leitor de RSS

[TFN1] The complete models specification is: σ̂t2=ω̂+α̂+γ̂Nt−1εt−12+β̂σ̂t−12, for models I and II, and lnσ̂t2=ω̂+α̂εt−1+γε̂t−1/σ̂t−1β̂lnσ̂t−12+δ̂lnσ˜t−12+φ̂lnIVt−12 for the remaining models. Parameters estimates we report together with p-values in parenthesis. Those were estima ted maximizing the log likelihood function. The Akaike information criterion (AIC) is calculated as -2*(lnL) + 2p, where p is the number of parameters estimated in each model (Akaike 1974). The Bayesian information criterion (BIC), proposed in Schwarz (1978), is calculated as -2(lnL) + p(lnN), where N is the sample size. Further discussion on AIC and BIC can be found in Tsay (2005)Tsay, Ruey S. 2005. Analysis of Financial Time Series. Wiley.. Numbers in bold indicate statistical significance at the 10% significance level.