1. Mortality Regimes and Pricing Samuel H. Cox University of Manitoba Yijia Lin University of Nebraska - Lincoln Andreas Milidonis University of Cyprus & University of Manchester Presented at Fifth International Longevity Risk and Capital Markets Solutions Conference New York City, NY September 26, 2009 1

2. Figure 1. US population mortality index from 1901 to 2005 Mortality Regimes and Pricing2 Mortality Regimes - Motivation

3.  Describe mortality changes through different means and volatilities in the various switching states  Reflect different natures of mortality evolutions  Accommodate non-normality features Mortality Regimes and Pricing3 Mortality Regime Switching Model

4.  Regime Switching models have been constructed to:  Model dynamics in population mortality indices  Extend the Lee-Carter (1992) model  Results of proposed Regime Switching models have been benchmarked to existing models  Price mortality/longevity security to show the economic significance of modeling different mortality regimes through Changes in market price of risk Changes in call option premiums Mortality Regimes and Pricing4 Outline

5.  Mortality log change rate  Markov process with two regimes:  Markovian probability transition matrix where, j = 1 or 2; k = 1 or 2. Mortality Regimes and Pricing5 RS-GBM model for Modeling US Population Mortality Index

6. Figure 2 Conditional Probability of US Population Mortality Index Classified in High Volatility Regime Mortality Regimes and Pricing6

7.  Geometric Brownian motion  Lin and Cox (2008) Model where Mortality Regimes and Pricing7 Competing Models for US Population Mortality Index

8. Table 2 Maximum Likelihood Parameter Estimates of Competing Models Mortality Regimes and Pricing8

9. 9 Is Modeling Changes in Mortality Regimes Important?

10. Mortality Regimes and Pricing10 Is Modeling Changes in Mortality Regimes Important? (Cont’)  Wang transform

11.  Lee-Carter (1992) model where  We model as RS-normal where and Mortality Regimes and Pricing11 Improving the Lee-Carter Model with Regime Switching Model

12. Figure 4 Conditional Probability of Error Term Classified in Low Volatility Regime Mortality Regimes and Pricing12

13. Table 7 Maximum Likelihood Parameter Estimates of Competing Models Mortality Regimes and Pricing13

14.  Longevity Call Option  Esscher Transform Mortality Regimes and Pricing14 Pricing Longevity Securities with RS Models

15. Mortality Regimes and Pricing15 Table 8 15-year Longevity Call Option Premiums on per $100,000 Notional Amount Table 9 20-year Longevity Call Option Premiums on per $100,000 Notional Amount

16.  We propose two regime switching models in the mortality context  Model the dynamics of the population mortality index  Extend the Lee-Carter (1992) model  We find the statistical improvement provided by our proposed regime switching models relative to some existing mortality stochastic models.  We show how to apply mortality regime switching models to price longevity securities. Mortality Regimes and Pricing16 Conclusions