Vancouver, British Columbia, Canada June 16 - 18, 2013

www.iarfic.org

Hosts:

Keynote Speech – Martin Odening

CHALLENGES OF INSURING WEATHER RISK IN AGRICULTURE

Martin Odening Department of Agricultural Economics, Humboldt-Universität zu Berlin

2nd International Agricultural Risk, Finance, and Insurance Conference,

Vancouver, June 16-18, 2013

Motivation

2

Outline

1. Covariate Risk due to Systemic Weather Risk

2. Non-stationary loss distributions due to Climate Change

3. Model Risk due to Data Scarcity

3

Challenge 1: Systemic Weather Risk

Problem: Systemic risk can lead to a breakdown of a

private crop insurance market (e.g. Duncan & Myers)

Remedies: Spatial diversification (Wang & Zhang) Time diversificaton (Chen & Goodwin) Product diversification Reinsurance Securitization (Barieu & El Karoui)

4

Case Study: Weather Risk in China

Quantification of the dependence structure of weather events at different locations by means of copulas

Is spatial diversification of systemic weather risk possible?

Weather risk indicators: Growing Degree days; Frost Index

Insurer‘s risk exposure: Buffer Fund

5

6

( )

( )( )ii

iii

n

iiii

LEVKIfL

LwNTL

NTLVaRBF

=⋅=

−⋅=

=

∑=

π

π

α

,

}{1

fund;buffer =BF

loss; =Lpremium;fair =π

index; weather =Ilevel; trigger =Ke; tick valu=V

level; confidence =α

loss; net total=NTL region; =iweight;=w

Buffer Fund

Flow Chart of the Computational Procedure

7

(4)

Buffer fund, buffer load and spatial diversification effect

Simulated weather index for each weather station

Net total losses for several aggregation levels

Standardized residuals

Copula

Simulated dependent standardized residuals of daily temperature

Temperature models

Daily temperature records

Simulated daily temperature

(1) (2)

(3)

(5)

(6) (7) (8)

Source: Okhrin, Odening, Xu (2012)

Location of Selected Weather Stations

8

Structure of Hierarchical Archimedean Copula

9

C7,1

C6,1

C5,1

C4,1

C4,2

C3,1

C3,2

C2,1 C2,2

C2,3

C2,4

Source: Okhrin, Odening, Xu (2012)

Buffer Loads for Different Regional Aggregation Levels: GDD

10

0

40

80

120

160

0 1 2 3 4 5 6

Mon

etar

y un

its

Aggregation level

GaussianGumbelRotated GumbelStrike level: 50%

Strike level: 15%

Source: Okhrin, Odening, Xu (2012)

Conclusions

Copulas allow a flexible modeling of the dependence structure of joint weather risks

Significant stochastic dependence of temperature related insurance losses in China

Systemic weather risk can be mitigated by regional diversification but is still high

Supplementary tools for risk reduction are required

11

(Time) Diversification of insurance losses by multi-year insurance contracts

Argument: Multi-year insurance contracts can be offered at lower premia than single-year contracts due to time diversification (e.g. Chen & Goodwin 2010)

But: The fallacy of time diversification (e.g. Samuelson 1969); Multi-year insurance contracts are more expensive than single-year contracts due to loss of flexibility of premium adjustments

Question: What are the benefits of multi-year insurance contracts, if any?

12

13

Insurance Market Model (adapted from Kleindorfer et al. 2012)

Competitive insurance market; area yield insurance; two-period model

Risk averse farmers; differ in basis risk Risk averse insurers specialized on

single-year or multi-year contracts MY: price constant,

compensation in each period SY: price in period 2 depends on loss in period 1

Choice set farmers: MY, SY in one or both years, no insurance

Optimal decision rule by dynamic programming

14

Insurance Market Model (cont’d)

Results: • SY and MY contracts co-exist • choice of optimal contract depends on

basis risk and risk aversion • more farmers demand insurance

if both contract types are offered Extension:

• multiple periods • shifting loss distribution

Challenge 2: Increasing Weather Risk

Problem: Climate change → increasing weather risk → non-stationary loss distribution → historical loss models underestimate risks and rate risks incorrectly → insurance contract adjustment required

Remedies: Risk projections using climate models local tests

15

Classification of Statistical Tests for Changing Weather Risk

Aspect Characteristics

Subject of risk measurement

Mean of extreme weather indices

Quantiles of basic weather variables

Time increment Global Local

Kind of change Continuous Jump

Statistical test procedure

Mann-Kendall

test

Change point test

t- test

Quantile regression

Extreme value theory

16

Local versus Global Test of Changes in Monthly Rainfall (Berlin)

0

20

40

60

80

100

120

140

160

1948 1958 1968 1978 1988 1998 2008

Prec

ipita

tion

(mm

/mon

th)

Time

observations 1948-2008 1948-1962

1963-1977 1978-1992 1993-2007

Local Test Results for GDD (Mason, Iowa)

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0

0,2

0,4

0,6

0,8

1

1-p-

valu

es

0

1

2

3

4

5

6

1920 1930 1940 1950 1960 1970 1980 1990Cum

ulat

ive

1-p

-val

ues

Time

Mann-Kendall test treshold M.-K. test

Source: Wang et al. (2013)

Trends of Indices C = change point test, M = Mann-Kendall Test, T = t-test

19

Indices GDD FDI CRI PFI Cities From-To Sign Test From-To Sign Test From-To Sign Test From-To Sign Test Taipei 1939-1949 + C,T,M n.a. n.a. n.a. 1953-1966 + C 1949-1959 - C 1959-1960 - C 1960-1965 + C

1981-2008 + C

Mason 1932-1941 - C 1986-1987

+ T 1928-1933 + C 1928-1929 + C

1958-1959 - T 1939-1939 - C 1961-1964 + C 1965-1965 + C 1948-1950 + C 1968-1971 + C 1970-1971 + M 1988-1989 + C 1977-1980 - C

1978-2009 - C 1981-1983 - M,T Berlin 1977-1982 + T none none none 1956-1958 + C none none none

1979-2009 + C 1963-1966 + C 1988-1989 + M,T

Source: Wang et al. (2013)

10% Quantile CRI Mason (upper panel) and Berlin (lower panel)

20

0

20

40

60

80

100

120

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

prec

ipita

tion

(mm

)

time

0

20

40

60

1948 1958 1968 1978 1988 1998 2008

prec

ipita

tion

(mm

)

time

10% quantile upper confidence band observations lower confidence band

Source: Wang et al. (2013)

Conclusions

The „Increasing-Weather-Risk-Hypothesis“ has to be qualified

Local test procedures: → more detailed information when changes of weather conditions occur; → facilitate the adjustment of insurance contracts

21

Challenge 3: Data Scarcity

Problem: limited yield data → parameter uncertainty may increase risk loadings

Remedies: (daily) weather data crop yield models bootstrapping procedures expert knowledge

22

Bayesian Copula Estimation with Expert Knowledge (Arbenz & Canestraro 2012)

𝜽𝜽:copula parameters 𝝍𝝍:parameters of marginal distributions 𝑶𝑶:observation set 𝓔𝓔:set of expert knowledge

23

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Area Yield Insurance for Rice Producers in China

24

China

Jilin

Heilongjiang

Liaoning

Elicitation of joint probabilities from insurance experts

„What is your estimate of the joint probability

that a shortfall of average rice yield,

which occurs less than once in a decade,

is simultaneously observed

in Heilongjiang and in Jilin?“

25

Estimation of Buffer Loads with Different Data Sets

26

a) estimation with regional data Expert

knowledge Dependence parameters

Regional crop yield

data Copula

Posterior distribution

of parameters

Simulated aggregated

loss distribution

Buffer fund, buffer load

b) estimation with sub-regional data Disaggre-gated crop yield data

Resampling Empirical

aggregated loss

distribution

Buffer fund, buffer load

Source: Shen, Odening, Okhrin (2013)

Estimated Loss Distributions

27 Source: Shen, Odening, Okhrin (2013)

Estimated Loss Distributions

28 Source: Shen, Odening, Okhrin (2013)

Conclusion

Expert knowledge can be combined with yield data in a Bayesian framework.

Inclusion of expert knowledge corrects risk premia (in our application)

Generalization of the “treatment effect” is difficult Increased model complexity

29

References

Okhrin, O., Odening, M., Xu, W. (2012): Systemic Weather Risk and Crop Insurance: The Case of China. Journal of Risk and Insurance.

Osipenko, M., Shen, Z., Odening, M. (2013): Is there a Demand for Multi-year Crop Insurance? CRC 649 Discussion Paper, HU Berlin (forthcoming)

Wang, W., Bobojonov, I., Härdle, W.K., Odening, M. (2013): Testing for Increasing Weather Risk. Stochastic Environmental Research and Risk Assessment.

Shen, Z., Odening, M., Okhrin, O. (2013): Can Expert Knowledge Compensate Data Scarcity in Crop Insurance Pricing? Selected Paper, AEEA Annual Meeting 2013, Washington DC.

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