keynote speech – martin odening · vancouver, british columbia, canada. june 16 - 18, 2013. ....
TRANSCRIPT
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
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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)
18
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.
30