The value of resilience bond in financing flood resilient infrastructures: a case study of Towyn

Figures & data

Figure 1. Resilience bond mechanism. Source: Re:Focus (2015).

Figure 2. Flood barriers in Towyn, Wales. Source: adapted from Dawson, Peppe, and Wang (2011).

Table 1. Distribution fitness tests.

Surge Level	Distributions / Tests	Kolmogorov Smirnov	Anderson Darling	Chi-Squared
4 metres	GEV	0.222	1.2863	1.5086
	Normal	0.34338	3.6219	1.1773
	Lognormal	0.33616	4.0887	0.22018
	Weibull	0.32209	3.6727	0.46816
5 metres	GEV	0.11914	7.8505	N/A
	Normal	0.294	3.7763	11.62
	Lognormal	0.35885	5.0038	2.6767
	Weibull	0.33049	4.5405	0.37505
6 metres	GEV	0.12766	0.55678	0.1787
	Normal	0.24911	1.7497	4.1259
	Lognormal	0.26659	2.6924	7.4065
	Weibull	0.27207	2.4088	5.1501

Table 2. Probability of surge levels.

Surge level (m)	Return period	Probability of occurrence
4.0	< 20 years	0.9512261
5.0	20 years to 75 years	0.0355289
6.0	> 75 years	0.0132451

Table 3. Probability of breach for each flood barrier.

Barrier	F	G	H	I	J
Breach probability	0.370879	0.027855	0.019714	0.333368	0.246095

Table 4. Parameters of flood resilience bond pricing model.

	Parameter set A
Cox-Ingersoll-Ross model	a = 0.0241, b = 0.0539, $\sigma$ = 0.0141, $r_0$ = 0.0614
Intensity under HPP	$\lambda =7.85$
4 m surge GEV distribution	k = −1.15308, $\sigma$ = 3.31024e + 05, $\mu$ = 2.03156e + 06
5 m surge GEV distribution	k = −1.10344, $\sigma$ = 1.17273e + 06, $\mu$ = 7.40161e + 06
6 m surge GEV distribution	k = −1.16737, $\sigma$ = 1.40609e + 07, $\mu$ = 4.03551e + 07
Trigger range	[8,000,000 to 28,000,000]

Figure 3. Prices of catastrophe/resilience bonds for Towyn under GEV distribution.

Table 5. Price of a flood catastrophe bond.

Period/Threshold	≈8 million	≈14 million	≈20 million	≈28 million
Year 1	25.68	37.69	51.44	57.82
Year 2	27.35	40.14	54.78	61.58
Year 3	29.11	42.72	58.31	65.55
Year 4	30.98	45.46	62.05	69.75
Year 5	32.95	48.36	66.00	74.19

Table 6. Price of flood resilience bond with 50% resilience.

Period/Threshold	≈8 million	≈14 million	≈20 million	≈28 million
Year 1	42.39	58.06	59.03	59.38
Year 2	45.14	61.82	62.86	63.23
Year 3	48.06	65.81	66.91	67.31
Year 4	51.14	70.03	71.20	71.63
Year 5	54.39	74.49	75.74	76.18

Figure 4. Price of flood resilience bond for Towyn with 10% resilience.

Table 7. Price of flood resilience bond (10%) under different thresholds.

Period/Threshold	≈8 million	≈14 million	≈20 million	≈28 million
Year 1	27.56	42.40	55.28	59.42
Year 2	29.35	45.14	58.86	63.27
Year 3	31.24	48.05	62.66	67.35
Year 4	33.24	51.13	66.67	71.66
Year 5	35.35	54.38	70.90	76.21

Figure 5. Price of resilience bond for Towyn with 90% resilience.

Table 8. Price of flood resilience bond (90%) under different thresholds.

Period/Threshold	≈8 million	≈14 million	≈20 million	≈28 million
Year 1	60.84	61.05	61.11	61.23
Year 2	64.78	65.01	65.08	65.20
Year 3	68.95	69.20	69.27	69.40
Year 4	73.36	73.62	73.70	73.84
Year 5	78.03	78.30	78.38	78.53

Table 9. Parameters of flood resilience bond under Vasicek/CIR models.

	Parameter set B
Vasicek model	a = 0.212, b = 1.085, $\sigma$ = 0.4208, $r_0$ = 0.011
Cox-Ingersoll-Ross model	a = 0.212, b = 1.085, $\sigma$ = 0.4208, $r_0$ = 0.011
Intensity under HPP	$\lambda =7.85$
4 m surge GEV distribution	k = −1.15308, $\sigma$ = 3.31024e + 05, $\mu$ = 2.03156e + 06
5 m surge GEV distribution	k = −1.10344, $\sigma$ = 1.17273e + 06, $\mu$ = 7.40161e + 06
6 m surge GEV distribution	k = −1.16737, $\sigma$ = 1.40609e + 07, $\mu$ = 4.03551e + 07
Trigger range	[8,000,000 to 28,000,000]

Figure 6. Price of resilience bond with 50% resilience under Vasicek (left) and CIR model (right).

Figure 7. Value difference between applying Vasicek and CIR model.

Re:Focus. 2015. Leveraging catastrophe bonds: As a mechanism for resilient infrastructure project finance. RE bound insurance report.

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Dawson, R.J., R. Peppe, and M. Wang. 2011. An agent-based model for risk-based flood incident management. Natural Hazards 59: 167–89.

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