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Weather Business andWeather Risk Opportunities in
Latin America
AGROASEMEX
Jorge L. VazquezLuisarturo Castellanos
Latin American Panel, WRMA Annual Meeting 2007
I. Weather data and climate-related strategies
In Mexico, the major agro-reinsurance risks are related to climate variability and extremes
Disasters in agriculture 1995-2003 related to climate extremes
(based on info by SAGARPA).
Risk transference priorities in MEX agriculture
A view on weather data-policy in Latin America
•Weather data-policy is diverse across the region.
•Several observation networks exist: official, specific purpose, academic and private among others.
•In some countries there are almost no restrictions about sharing weather-data (v.gr. Mexico), but in others strong comercial limitations apply (mostly in Central American countries).
•Broadly speaking, the number of weather stations is decreasing as time goes by.
•Synoptic data are usually available.
•Climate data usually require some work previously to be usable in weather-business.
•Weather and climate agencies welcome cooperation agreements to improve the networks.
•But … not every measurement has to be useful in weather-business.
The issue of Climate data in Mexico
Considerations on WS for agro-reinsurance in Mexico:
•Official observation network•At least 25 years of data•90% of records available.•Nearness to crop-areas•Updated metadata•Real-time reports
A subset of 345 was visited and selected from a total of 3,000
weather stations in the country for agro-weather business.
•Quality control and homogeinity matter and several approaches are available for that purpose (from proprietary to public).
•Mexico selected the QC public approach proposed by the WMO-ETCCDI, encouraging local-experts participation.
•Overcome of data-series incompleteness as part of the pricing strategy.
•Need of joining the Weather Service in data-rescue and data-processing activities.
Climate indexes (rainfall tresholds) are determined for each region surrounding a selected weather station. To do so, simulations are made using biophysical growth models. The simulations consider the vegetal species,soil type and climate.
Stage 1
SowingSowing
Stage 2
FloweringFlowering
Stage 3
Valor Cat
HarvestingHarvesting
Valor CatValor Cat
Climate
Genetics
Soil features
Byophisical Model
Production rates
The agro-product core: linking weather, agriculture and economic parameters in a single treshold.
Field Calibration
How much rainfall is the treshold to damage a specific crop production?
The agro-product core: linking weather, agriculture and economic parameters in a single treshold.
The answer is not unique, since it varies for each region, crop and season.
However, regional tresholds can be found by mean ofClimate data + Byophisical models + Production
statistics
Figure. Regions affected by extreme drought during spring-
summer 2005 in Mexico.
Above.- SPI for May & June exhibiting severe (orange) and extreme (red) drought in central Mexico.
Right.- Federal States where indemnities took place upon AGROASEMEX’s
parametric insurance.
Not AffectedAffectedNot insured
New parametric schemes could be developed using climate tools like the Standardized Precipitation Index (SPI)
among other indices.
However, operation of such schemes are strongly dependent on previous field-
experiments to prove success.
Possibility of new products development using climate concepts and indices
•Priority to massive instruments instead of individual risk-transference contracts.
•Progressive migration to parametric schemes based on remote sensing
technology (satellite and radar data merged with observations).
•New approaches using both, observational and model info (data-assimilation, social &
economic data sampling, improved vulnerability assessments).
•Taking advantage of knowledge increases about climate variability and change.
•Flexible, multi-scaled and tailored products for different applications /sectors.
The eye on the future Latin America
II. Parametric Agriculture Insurance
•The Mexican Agriculture Insurance Market is covered directly by the Agriculture and Livestock Insurance Funds (approximately 150 funds per cycle) and by a few Private Insurance Companies.
•Traditional insurance schemes have been offered by both the Funds and Private Companies in which the loss is determined upon field supervision.
•Since 2001 Agroasemex participates only as reinsurance (stop loss and quota share) of the market. In 2004 the Weather Parametric Insurance was first introduced into the Mexican market by Agroasemex.
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•Since 2002 Agroasemex has developed the Agriculture Parametric Insurance based upon Weather Stations throughout the country.
•Only drought is currently covered;
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•Triggers were established as the minimum precipitation needed to get a catastrophic yield (30% of average yield).
•Catastrophic scheme adopted; i.e. the whole Sum Insured is paid (no partial payments) if the accumulated rainfall for a particular time lapse is less than the trigger.
•The Insurance is offered to Federal and/or State Governments.
•The Sum Insured is fixed at approximately $80 / ha.
•3 phases per year are covered according to the growth phases of the crops, each with a different trigger.
•If on any of the phases the trigger is pulled the loss is determined, but only once during the cycle can the payment be done;
•As of today, risk units are only conventional weather stations that report in real time, operated by CNA (Mexican Weather Service).P
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•Further research is currently being done to cover heavy rainfall events, and for drought based upon alternative technologies.
•The Government determines the number of hectares covered by each Weather Station insured.
Geographic Evolution2
003
Geographic Evolution2
004
Geographic Evolution2
005
Geographic Evolution2
006
Geographic Evolution2
007
Potential Surface Insured Surface
•The potentially-insured surface rises to 8 million hectares, in 2006, only 18% of that was insured.
Po
ten
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l De
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Insured Weather Stations
Insured Surface (‘000 Hectares)
626
186
226
2003 2004 2005 2006
108248.5
1,200
1,400
2003 2004 2005 2006
230
2007
1,900
2007
Ev
olu
tio
n
Sum Insured (USD Million)
3.616.9
59.6
84.7
2003 2004 2005 2006
Premiums (USD Million)
0.3
2.1
9.19.5
2003 2004 2005 2006
90.0
2007
9.7
2007
Ev
olu
tio
n
Indemnities (USD Millions)
Since 2004, Agroasemex has transferred the risk to international markets through proportional and non proportional schemes
0.0 0.0
10.5
2003 2004 2005 2006
2.1
Ev
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n
III. Risk Pricing Model
Ris
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The model used to price the risk is based upon the following characteristics.
a.Non parametric fits (Gaussian Kernel).
b.Spearman rank correlations.
c.Correlated Monte Carlo simulations.
d.Regional portfolio integration.
For each station-crop-phase the probability of payment is:
Pt = P1 + (1-P1)*P2 + (1-P1)*(1-P2)*P3
Where,
Pt = Total ProbabilityPi = Probability of rainfall < Trigger in phase i
Ke
rne
ls
Año St15076 St150861961 41.9 78.91963 119.5 116.51964 110.1 74.41965 63.4 991967 99 78.21968 101.2 711971 76.6 149.81972 132.8 1131973 67.7 87.51975 176.8 219.61977 74.2 57.51979 82.6 67.61980 61.9 105.51982 81.9 184.11983 57.5 36.91984 63.8 1131985 68 87.91986 188.3 211.11987 124.3 128.81988 40.1 491989 14.2 471991 30.2 811992 125.1 183.71994 75.9 69.21995 53.8 1071996 26.1 741997 55.6 1161998 4.6 281999 22.4 272000 95.4 2232003 67.9 90.5
Año R15076 R150861961 25 191963 6 81964 7 211965 20 141967 9 201968 8 231971 13 61972 3 101973 18 171975 2 21977 15 261979 11 251980 21 131982 12 41983 22 291984 19 101985 16 161986 1 31987 5 71988 26 271989 30 281991 27 181992 4 51994 14 241995 24 121996 28 221997 23 91998 31 301999 29 312000 10 12003 17 15
Original Data
= .711
Rank Data
= .607
Sp
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Co
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Est 12_1 12_2 12_3 14_1 14_2 14_3 22_1 22_2 22_3 89_1 89_2 89_3 93_1 93_2 93_3 116_1 116_2 116_312_1 1 0.203 0.622 0.259 -0.140 0.315 0.608 0.406 -0.084 0.566 0.112 0.462 0.399 -0.126 0.196 0.182 -0.224 0.16812_2 0.203 1 -0.168 -0.042 0.252 0.014 0.084 0.692 -0.280 0.063 0.175 -0.385 0.601 0.524 -0.007 0.706 0.378 -0.12612_3 0.622 -0.168 1 0.028 -0.580 0.301 0.713 -0.077 0.070 0.203 -0.140 0.497 0.336 -0.315 0.392 -0.217 -0.727 0.21014_1 0.259 -0.042 0.028 1 0.322 -0.126 0.175 0.203 0.224 -0.238 -0.294 0.028 0.182 -0.329 -0.098 0.462 -0.098 -0.04914_2 -0.140 0.252 -0.580 0.322 1 -0.077 -0.294 0.476 -0.091 0.035 0.406 -0.301 -0.007 0.406 -0.105 0.336 0.594 -0.14014_3 0.315 0.014 0.301 -0.126 -0.077 1 -0.147 -0.210 -0.406 0.133 0.042 0.259 0.573 0.000 0.601 0.077 0.056 0.69222_1 0.608 0.084 0.713 0.175 -0.294 -0.147 1 0.280 0.510 0.350 0.210 0.545 0.112 -0.014 0.084 -0.070 -0.364 0.00022_2 0.406 0.692 -0.077 0.203 0.476 -0.210 0.280 1 -0.259 0.420 0.517 -0.105 0.259 0.329 0.021 0.657 0.182 -0.07022_3 -0.084 -0.280 0.070 0.224 -0.091 -0.406 0.510 -0.259 1 -0.105 0.028 0.238 -0.280 0.056 -0.413 -0.364 0.042 -0.21089_1 0.566 0.063 0.203 -0.238 0.035 0.133 0.350 0.420 -0.105 1 0.741 0.650 -0.091 0.000 0.392 -0.119 0.098 0.37889_2 0.112 0.175 -0.140 -0.294 0.406 0.042 0.210 0.517 0.028 0.741 1 0.392 -0.154 0.392 0.294 0.007 0.392 0.37889_3 0.462 -0.385 0.497 0.028 -0.301 0.259 0.545 -0.105 0.238 0.650 0.392 1 -0.196 -0.301 0.566 -0.294 -0.161 0.60193_1 0.399 0.601 0.336 0.182 -0.007 0.573 0.112 0.259 -0.280 -0.091 -0.154 -0.196 1 0.147 0.322 0.545 -0.035 0.25993_2 -0.126 0.524 -0.315 -0.329 0.406 0.000 -0.014 0.329 0.056 0.000 0.392 -0.301 0.147 1 -0.133 0.266 0.713 -0.06393_3 0.196 -0.007 0.392 -0.098 -0.105 0.601 0.084 0.021 -0.413 0.392 0.294 0.566 0.322 -0.133 1 0.112 -0.105 0.790
116_1 0.182 0.706 -0.217 0.462 0.336 0.077 -0.070 0.657 -0.364 -0.119 0.007 -0.294 0.545 0.266 0.112 1 0.294 0.168116_2 -0.224 0.378 -0.727 -0.098 0.594 0.056 -0.364 0.182 0.042 0.098 0.392 -0.161 -0.035 0.713 -0.105 0.294 1 0.091116_3 0.168 -0.126 0.210 -0.049 -0.140 0.692 0.000 -0.070 -0.210 0.378 0.378 0.601 0.259 -0.063 0.790 0.168 0.091 1
Regional Correlation Matrix
Co
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Sim
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isto
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Mean = 9.1%
IV. Pasture Satellite Insurance
•Since 2005 Agroasemex has been developing the Pasture Livestock Insurance based upon Satellite Images.
•NDVI (Normalized Differentiated Vegetation Index) is used to measure the amount of biomass available as cattle food.
Pa
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•Triggers were established as 64% of the accumulated NDVI of the previous year.
•Catastrophic scheme adopted offered exclusively to Federal and/or State Governments.
•The Sum Insured is fixed at approximately $38 / animal unit.
•The risk unit is the municipality (county), but different animal units are insured per municipality accordingly.
•The domestic livestock inventory (milk and meat cattle) is compound by 30.6 million heads, out of which 93% are meat cattle breeders.
200
7 G
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State Pasture Surface(millions of hectares)
Animal Units(Heads)
Sum Insured(USD millions)
Chihuahua 5.95 353,000 8.5 Coahuila 1.01 45,500 1.1 Durango 2.40 167,400 4.0 Jalisco 0.85 85,100 2.1 Sonora 1.55 178,700 4.3 Zacatecas 1.30 98,500 2.4
TOTAL 13.06 928,200 22.44200
7 P
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V. Risk Pricing Model
Dy
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•State-space models a.k.a. Dynamic Linear Models was the methodology proposed to price the risk.
•Unlike static models, dynamic models are explicitly formulated in order to allow changes in the parameters as time passes by.
•As time passes by, new observations are available, hence new knowledge and information is at hand; these are assimilated into the model through changes in the model parameters.
•The models allow for changes in the relationships as well as adjustments for minor errors or omissions coming from a lack of model specificity.
DL
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•They are a good alternative to forecast time series, which are the type of data we are currently using for this insurance.
•Because they are open models, they allow for parameter updating, expert intervention and monitoring.
•They forecast the future, as a combination of history (data) and a time series model of the phenomenon.
•The forecast they provide is not a point estimate but rather the whole probability distribution.
•The probability that the “trigger” is affected does not depend on how many times in history it has occurred.
•The forecast is not strongly affected by the fact that the series has missing values.
•Expert information can be incorporated into the model.
•Parameterization. All the key information is captured in t
•Parametric information through probability distributions.
•Conditional Independence
Yt-2 Yt-1 Yt Yt+1 Yt+2
t-2 t-1 t t+1 t+2
•Sequential parametric model. All the dependence in the
data Yt’s is modeled by the system (tt-1).
Ch
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Let Yt be a vector (rx1) of observations in time and t a vector (nx1) of parameters, t=1, 2, …
The general dynamic linear model (normal) is characterized by
{Ft, Gt, Vt, Wt}
(Ytt) N[FtTt, Vt]
(tt-1) N[Gtt-1,Wt]
Co
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With prior distribution
(0D0) ~ N[m0, C0]
Dt is all the past and present information at time t.
Yt = FtTt + vt, vt N[0, Vt] observation equation
t = Gtt-1 + wt, wt N[0,Wt] system equation
Yt-2 Yt-1 Yt Yt+1 Yt+2
t-2 t-1 t t+1 t+2
Co
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Ft design matrix (nxr) of known independent variables
t is the ‘(nx1) state vector’
t = FtTt mean response or level
vt observational error
Gt evolution or system matrix
Wt system variance matrix.
Co
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E(Yt+1|Dt) = E(Ft+1Tt+1 + vt+1 |Dt)
= E(Ft+1Tt+1|Dt)+E(vt+1 |Dt)
= Ft+1T E(t+1|Dt)+0
= Ft+1T E(Gt+1t+ wt+1 |Dt)
=Ft+1T Gt+1 E(t |Dt)Fo
rec
as
t
Var(Yt+1|Dt) = Var(Ft+1Tt+1 + vt+1 |Dt)
= Var(Ft+1Tt+1|Dt)+Var(vt+1 |Dt)
= Ft+1TVar(t+1|Dt)Ft+1+ Vt+1
= Ft+1TVar(Gt+1t+ wt+1 |Dt)Ft+1+ Vt+1
= Ft+1T(Gt+1Var(t |Dt)Gt+1
T+Wt+1) Ft+1 + Vt+1
Posterior for t-1: (t-1 |Dt-1) ~ N(mt-1 , Ct-1)
Prior for t: (t |Dt-1) ~ N(at , Rt)
where at =Gt mt-1 ; Rt = Gt Ct-1 Gt T+ Wt
Forecast: (Yt |Dt-1) ~ N(ft , Qt)
where ft = FtT
at ; Qt = FtT
Rt Ft + Vt
Posterior for t: (t |Dt) ~ N(mt , Ct)
with mt = at + At et ; Ct = Rt – At Qt AtT
where At = Rt Ft Qt-1 ; et = Yt – ft
Le
arn
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0
2
4
6
8
10
12
14
16
18
1979 1984 1989 1994 1999 2004
Año
Índi
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Yt Pronóstico Límite Inferior Límite Superior
Ex
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P(ft<7.69) = 3.5%
Ex
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Thanks!
Questions and comments are welcome
