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,

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

 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

 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

 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

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

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

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

9 Is Modeling Changes in Mortality Regimes Important?

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

 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

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

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

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

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

 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