Pricing Crop Revenue Insurance Using Parametric Copulas

Duarte, Gislaine Vieira; Ozaki, Vitor Augusto

doi:10.5935/0034-7140.20190015

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Artigos • Rev. Bras. Econ. 73 (3) • Jul-Sep 2019 • https://doi.org/10.5935/0034-7140.20190015 copy

Pricing Crop Revenue Insurance Using Parametric Copulas^* * We thank the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for financial support.

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Crop revenue insurance has been widely discussed recently. It has become an important mechanism for risk; management of crop yielO anp prices. However, a more comprehensive study is needed to investigate the dependence stmcture between thu variables analyzed ro celculate the premium rate actearially fair for revenue insurance. Tleis study proposes alternatives ao calculate premium rates for revenue insurance using parametric copula functions. The results nuuunsts that the average commnndal rates calculated by the insurer aru undnrestimftnd when compared to tce copula model. The underesSimation om rates can lead to seriou losses to insurers, sinca segy consiher a lower risk than should be tamen into account.

Keywords
Crop risk management; OLLN distribution; parametric copulas; revenue insurance

Series	Coefficientes	Estimates	p-value	R ²
Toledo Yield	α β	-76,362.08 39.53	5.83E-9 2.86E-9	0.6629
Guarapuava Yield	α β	-100,300 51.48	2.68E-15 1.33E-15	0.8549
Cascavel Yield	α β	-79,534.999 41.112	4.79E-8 2.51E-8	0.6033
Castro Yield	α β	-81,924.200 42.429	4.41E-14 1.74E-14	0.8306
Deflated Price	α β γ	-81,763.886 42.348 42.348	3.53E-13 1.46E-13 1.46E-13	0.8172

Series	p-value for Series	p-value for Series²
Price	0.0763	0.0842
Toledo Yield	0.2619	0.1273
Guarapuava Yield	0.0509	0.0437
Cascavel Yield	0.3746	0.2975
Castro Yield	0.0936	0.0866

Copulas	Toledo × Price δ (standard error)	Guarapuava × Price δ (standard error)	Cascavel × Price δ (standard error)	Castro × Price δ (standard error)
Clayton	-0.0889 (0.2006)		-0.0243 (0.2254)	-0.0585 (0.1718)
Frank	-1.0141 (1.0215)	-1.7589 (1.0390)	-0.6834 (1.0198)	-0.4189 (0.9830)
AMH	-0.7185 (0.5505)		-0.4077 (0.5709)	-0.2753 (0.5408)
Gaussian t_v	-0.1569 (0.1685)	-0.3218 (0.1685) -0.3087 (0.1662) v = 10.8119 (29.6171)	-0.0768 (0.1863)	-0.0808 (0.1755)

	Criteria	Clayton	Frank	AMH	Gaussiana	t
	AIC	1.7429	0.9995	0.6766	1.1871
	BIC	3.2983	2.5549	2.232	2.7425
Toledo × Price	LLV	0.1285	0.5002	0.6616	0.4064
	Sn	0.0164	0.03224		0.03338
	p-value	0.7188	0.5609		0.6978
	AIC	1.9797	1.5366	1.4797	1.8071
	BIC	3.535	3.0919	3.035	3.3625
Cascavel × Price	LLV	0.1016	0.2317	0.2601	0.0964
	Sn	0.0244	0.0246	0.0262	0.02238
	p-value	0.6188	0.8936	0.2672	0.9446
	AIC	1.9017	1.8356	1.7945	- 1.7865
	BIC	3.4571	3.3909	3.3498	3.3418
Castro × Price	LLV	0.0491	0.0822	0.1027	0.1067
	Sn	0.0490	0.0566	0.05981	0.0588
	p-value	0.2592	0.02048	0.0449	0.05145
	AIC		-0.8457		-1.5938	0.267
	BIC		0.7097		-0.0384	3.377
Guarapuava × Price	LLV		1.4228		1.7968	1.8665
	Sn		0.02713		0.0324	0.0414
	p-value		0.8323		0.7904	0.6618

Variable	Model	AICc	BIC	A*	W*
Yield Toledo	Normal	554.4212	557.1569	0.7902	0.1208
	SN	556.8204	560.7120	0.7902	0.1208
	OLLN	555.9902	559.8864	0.6605	0.1063
Price	Log Normal	281.5256	284.2630	0.8458	0.1518
Price	ST2	280.2308	286.4522	0.8215	0.0987

	Criteria	Clayton	Frank	AMH	Gaussiana	t
	AIC	1.4722	0.1345	-0.2317	0.6865
	BIC	3.0276	1.6898	1.3236	2.2419
Toledo × Price	Sn	0.0164	0.03224		0.03338
	p-valor	0.7228	0.5929		0.7058
	AIC	1.8011	0.8069	0.7161	1.3959
	BIC	3.3564	2.3623	2.2715	2.9513
Cascavel × Price	Sn	0.0244	0.0246	0.0262	0.02238
	p-valor	0.6386	0.8886	0.2393	0.9466
	AIC	1.9338	1.8133	1.78	1.7859
	BIC	3.4892	3.3686	3.3353	3.3412
Castro × Price	Sn	0.0490	0.0566	0.05981	0.0588
	p-valor	0.2552	0.0244	0.0148	0.0624
	AIC		-1.1173		-1.5327	0.3152
	BIC		0.4338		-0.0227	3.4259
Guarapuava × Price	Sn		0.02713		0.0324	0.0414
	p-valor		0.8323		0.7887	0.6317

	Copula	δ
Toledo × Price	AMH (SPI) AMH (PI)	-1 -0.92021
Cascavel × Price	AMH (SPI) AMH (PI)	-0.4811 -0.6452
Castro × Price	Gaussian (SPI) AMH (PI)	-0.0695 -0.4260
Guarapuava × Price	Gaussian (SPI) Gaussian (PI)	-0.3218 -0.3058

Inference	Sn	δ	p-value
Semi-parametric (EM)	0.058886	-0.0767	0.05445
Parametric (PM)	0.059819	-0.24817	0.03247

		Level Coverage
Municipalities	Model	60-69%	70-79%
	AMH Copula (PM)	12.351	19.032
Toledo × price	Normal Bivariate	6.164	19.747
	Insurer A	6.26	5.68
	AMH Copula (MP)	13.838	21.088
Cascavel × price	Normal Bivariate	2.004	9.157
	Insurer A		5.52
	AMH Copula (EM)	5.772	9.491
Guarapuava × price	Normal Bivariate	0.039	1.621
	Insurer A		4.85
	Gaussian Copula(EM)	9.166	13.684
Castro × price	Normal Bivariate	1.268 × 10^-4	0.1117
	Insurer A	5.20	5.24

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	Toledo × price		Cascavel × price
CL	AMH Copula (PM)	Normal Bivariate	AMH Copula (PM)	Normal Bivariate
60%	3.43	2.03	6.10	0.48
65%	4.36	4.03	7.73	1.52
70%	5.41	7.16	9.54	3.26
75%	6.56	11.21	11.54	5.89
80%	7.83	15.71	13.75	10.11
	Guarapuava × price		Castro × price
CL	Gaussian Copula(EM)	Normal Bivariate	Gaussian Copula(EM)	Normal Bivariate
60%	2.52	0.020	4.06	6.3 × 10^-6
65%	3.32	0.135	5.10	1.2 × 10^-4
70%	4.23	0.710	6.22	0.0048
75%	5.25	2.713	7.45	0.1070
80%	6.40	8.589	8.78	1.0915

Municipalities × Price	Castro	Guarapuava	Toledo	Cascavel
Model of Copula	Gaussian (SPI)	Gaussian (SPI)	AMH (PI)	AMH (PI)

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Pricing Crop Revenue Insurance Using Parametric Copulas* * We thank the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for financial support.

Abstract

Pricing Crop Revenue Insurance Using Parametric Copulas^* * We thank the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for financial support.