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 (cid:137) Relative capital usage of transactions (cid:137) Marginal cost pricing (cid:137) 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. (cid:137) Look at an historical period and estimate the Poisson mean. (cid:137) Project the distribution of counts next year. (cid:137) 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 (cid:137) Square root of annual observed claims (cid:137) Correlation between this risk and overall market (cid:137) Market premium risk charges (cid:137) Square root of 1/experience period (in years) (cid:137) 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