Business Principles, Tools, and Techniques in Participating in Various Types...
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Rational & Mechanics of CAT Swap
1. Rationale and Mechanics for
Peak Natural Catastrophe
Variance Swaps in Insurance
Ivelin Zvezdov
Sebastian Rath
Igor Cizelj
2. Agenda
1. Motivation
2. Simulated insurance loss
3. Defining capital reserve shortage & the swap contract
4. Historical stress test
5. Using the variance swap contract
6. Convergence
7. Spatial risk metrics
3. Theoretical and Economic
Motivation
3
1. Geo-spatial variability of insurance risk
2. A low priority for insurance practitioners, focused on first order risk
3. Climate variability - a new significant and measurable factor in geo-
spatial risk variability
4. Support measuring of inter-dependence and clustering of insurance
risk, for risk management practitioners
5. Operational efficiencies in reserve capital management
6. Arbitrage opportunities for capital market firms
4. Historical simulation of known
significant events
4
Storm track & footprint
of ETC Daria, 26/26โth of
January 1990
Perturbations of
ETC Daria
Historical tracks 1999-2008
and a single perturbation of
each track
5. Physical intensity downscaling
and insurance loss computation
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Downscaling of intensity to 10m grid, 14 km above ground, & 6 hours of
temporal resolution
6. Natural catastrophe simulation
for insurance loss
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โข CRESTA zones in Holland
โข Notional insurance company -
10% of industry insured
exposure by geo-zone
(business unit)
Number of simulated events
in a 10K stochastic scenarios /
years
7. Defining available and required
capital reserves
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Available capital reserve ๐ ๐๐=2%; ๐ธ๐ 2% = ๐ ๐ฟ๐๐ ๐ โง ๐ ๐๐=2%
Required capital reserve ๐พ๐๐=1%; ๐ 1% = ๐ ๐ฟ๐๐ ๐ โง ๐พ๐๐=1%
Capital reserves observe both super and sub additivity properties
๐ ๐๐=2% > ฯ๐= 1
90
๐ต๐ ๐ ๐๐=2%; and ๐พ๐๐=1% < ฯ ๐=1
90
๐ต๐ ๐พ๐๐=1%
TVaR remains strictly sub-additive
๐๐๐๐ ๐๐=1% < เท
๐=1
90
๐ต๐ ๐๐๐๐ ๐๐=1%
8. Capital reserves back-allocation
from portfolio to business unit
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- Traditional industry practice based on contributing ratios of modeled
expected values of loss EL
- Captures inter-dependence for risk factors within the portfolio
๐ธ๐ฟ = เท
๐=1
90
๐ต๐ ๐ธ๐ฟ๐
๐ต๐๐ ๐ ๐๐ 2% = ๐ ๐๐ 2%
๐ต๐ ๐ธ๐ฟ ๐
ฯ ๐=1
90 ๐ต๐ ๐ธ๐ฟ ๐
๐ต๐๐ ๐พ๐๐ 2% = ๐พ๐๐ 2%
๐ต๐ ๐ธ๐ฟ๐
ฯ ๐=1
90
๐ต๐ ๐ธ๐ฟ๐
9. Defining capital reserves
shortages and rates
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๐ต๐ ๐ โ๐๐๐ก๐๐๐ ๐๐๐ก๐ =
๐ต๐ ๐ ๐๐=2% โ ๐ต๐ ๐พ๐๐=1% +
๐ต๐ ๐๐๐ ๐ข๐๐๐ ๐๐ฅ๐๐๐ ๐ข๐๐
10. Historical stress tests for
spatial variability
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๐ต๐๐ ๐ท๐๐๐๐ ๐ฟ๐๐ ๐
๐ต๐๐ ๐ ๐๐=1%
11. Stress tested rate-on-line
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๐๐๐ ๐ต๐๐ ๐พ๐๐=1%, max(๐ต๐๐ ๐ท๐๐๐๐ ๐ฟ๐๐ ๐ โ ๐ต๐๐ ๐ ๐๐=2%, 0)
๐ต๐๐ ๐พ๐๐=1%
12. Interpretations for practitioners
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Available and required capital reserve bands imposed on historical
losses from Daria by BU
13. More interpretations for practitioners
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- For 40 business units, historical losses breach the thresholds of available
capital reserve
- For another 30 business units historical ROL(s) exceeds a threshold of
30%, what should be considered as a very high market price
- For 8 business units the ROL is 100% and for another 4 it exceeds 80% -
historical loss breaches or approaches required capital reserves.
14. Inefficiencies for insurers and
opportunities for optimal outcomes
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- Business units with extreme shortages of capital reserve post
extreme catastrophe event will require fund transfer and raised
internal cost.
- Underwriting limits are overexposed to losses in some business
units
- In other business units, lower underwriting limits may lead to
underestimating of business opportunity and market share
- Rationale for seeking both internal risk and underwriting
management optimal solutions
17. Convergence
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Variance swap rates derived for simulated strike variances from business unit
modeled required capital reserves in the exceedance probability interval
EP5% to EP1%
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
-50.0% -40.0% -30.0% -20.0% -10.0% 0.0% 10.0% 20.0% 30.0% 40.0% 50.0%
EPofrequiredreserves
Variance swap rate
18. Second order risk management
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Covariance ratio by each pair of company units
๐ถ๐๐[๐1,๐: ๐2,๐]
๐๐ด๐ ๐1,๐ + ๐๐ด๐ ๐2,๐
Inland North
Inland Central 0.39
Inland South 0.50 0.37
Coastal South 0.49 0.49 0.41
Coastal Central
0.50 0.49 0.49 0.38
Coastal
Central
Coastal
South
Inland
South
Inland
Central
Inland
North
19. Covariance measure
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Covariance percent share, by each pair of company units
๐ถ๐๐[๐1,๐: ๐2,๐]
ฯ ฯ ๐ถ๐๐[๐1โฆ5;๐โฆ๐: ๐2โฆ4;๐โฆ๐]
Inland North 100%
Inland Central 100% 5.99%
Inland South 100% 13.39% 6.43%
Coastal South 100% 12.35% 11.52% 5.64%
Coastal
Central 100% 12.02% 13.65% 12.74% 6.26%
Coastal
Central
Coastal
South
Inland
South
Inland
Central
Inland
North
20. Marginal covariance measure
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Marginal covariance percent share for each company unit
๐ถ๐๐[๐1,๐: ๐2,๐ + ๐3,๐ + ๐4,๐ + ๐5,๐]
๐๐ด๐ ๐1,๐ + ๐๐ด๐ ๐2,๐ + ๐3,๐ + ๐4,๐ + ๐5,๐
Inland North 0.16
Inland Central 0.35
Inland South 0.37
Coastal South 0.33
Coastal Central 0.37
All without
Coastal Central
All without
Coastal South
All without
Inland South
All without
Inland Central
All without
Inland North
21. Continuing work
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Expand the effort to define coherent second order geo-spatial risk
measurement processes, and metrics for (re)insurance.
Stimulate knowledge exchange among practitioners and academics
Design of practical risk transfer and hedging strategies
Work towards consensus on underlying standards and sources of data for
modeling and pricing.