Parameterization and Calibration of Actuarial Models

57 Pages·2008·0.79 MB·English

Parameterization and Calibration of Actuarial Models
Paul Kneuer
2008 Enterprise Risk Management Seminar
Tuesday, April 15, 11:45 a.m. - 1:00 p.m.
ERM Symposium
Paul Kneuer
April 15, 2008
Parametizing Models:
Volatility Measures
ERM Symposium
Paul Kneuer
April 15, 2008
Parametizing Models:
Volatility Measures
(cid:137) The bad news: It’s hard
(cid:137) The good news: It’s impossible
08_Parametizing_PJK_Speech.ppt 3
An integrated and dynamic view of the volatility of transactions would be a powerful
insight:
Overall portfolio capital needs, real time
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Relative capital usage of transactions
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Marginal cost pricing
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08_Parametizing_PJK_Speech.ppt 4
(cid:137) Unfortunately, data is a poor source for the volatility of the next period. “Past
performance is not a promise of future returns.”
(cid:137) In real world situations, what we don’t know that we don’t know can have more
cost (and value) than what we do know.
(cid:137) “It’s hard.”
08_Parametizing_PJK_Speech.ppt 5
A simple model:
Define a loss process so that it is a Poisson (counting) function: frequency, not severity.
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Look at an historical period and estimate the Poisson mean.
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Project the distribution of counts next year.
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Measure the value as E(X) + R x SD(X)
(cid:137)
Contract Value
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1 2 3 4 5
Known Frequency
Risk Charges:
15% 20% 25% 30%
08_Parametizing_PJK_Speech.ppt 6
Now, acknowledge that the data from last year is only sample from a distribution that
we can never know.
Prior Mean Observation Exposure
? ?
08_Parametizing_PJK_Speech.ppt 7
The Value of Next Year’s Contract Reflects the Risk
that We have a Poor Estimate of Last Year’s Mean
The value of parameter risk is proportional to:
C.V. of uncertainty around prior mean
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Square root of annual observed claims
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Correlation between this risk and overall market
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Market premium risk charges
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Square root of 1/experience period (in years)
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Relative Increase in Value
(Value of Parameter Risk/Expected Loss)
3503.%5
3003.%0
2502.%5
2002.%0
1501.%5
1001.%0
500.%5
00..00
1 2 3 4 5
Observed Frequency
CV of Prior Gamma: 0.5 1 2 4 8 16
08_Parametizing_PJK_Speech.ppt 8
Required Reading
“The Black Swan” by Nassim Taleb
(cid:137) In many areas, the next data observations can be so discontinuous that it
invalidates the form of distribution you would have chosen.
(cid:137) For the population of ERM Symposium attendees, would you bet on the relative
increase in the overall average size following the next arrival, based on:
Height?
(cid:137)
Career experience?
(cid:137)
Journal citations?
(cid:137)
Net worth?
(cid:137)
08_Parametizing_PJK_Speech.ppt 9
Black Swans
(cid:137) Maximum swing to average from next observation:
Observation Swing to Average
Aaron Gray (7’ Center for Bulls) < ¼ inch part of six feet, 0.3%
Charles Hewitt (FCAS, 1951) < 1 week part of 20 years, 0.1%
Merton Miller (U. of C. Nobelist) > 100 part of < 5, 20x
Bill Gates (Harvard Drop-out) > $100Mn part of < $1Mn, 100x
(cid:137) Fields of analysis exposed to black swans cannot be approximated with small,
unbiased, normal errors.
(cid:137) “It’s impossible”
08_Parametizing_PJK_Speech.ppt 10