Mortality Regimes and PricingSamuel H. Cox
University of Manitoba
Yijia LinUniversity of Nebraska - Lincoln
Andreas MilidonisUniversity of Cyprus
& University of Manchester
Presented at Fifth International Longevity Risk and Capital Markets Solutions Conference
New York City, NY
September 26, 20091
Figure 1. US population mortality index from 1901 to 2005
Mortality Regimes and Pricing 2
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 Pricing 3
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 Pricing 4
Outline
Mortality log change rate Markov process with two regimes:
Markovian probability transition matrix
where , j = 1 or 2; k = 1 or 2.
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RS-GBM model for Modeling US Population Mortality Index
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Figure 2
Conditional Probability of US Population Mortality Index Classified in High Volatility Regime
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Geometric Brownian motion
Lin and Cox (2008) Model
where
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Competing Models for US Population Mortality Index
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yprobabilitwith
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Mortality Regimes and Pricing 10
Is Modeling Changes in Mortality Regimes Important? (Cont’)
Wang transform
]))(([)( 1* ii LFGLF
Lee-Carter (1992) model
where
We model as RS-normal
where and
Mortality Regimes and Pricing 11
Improving the Lee-Carter Model with Regime Switching Model
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Figure 4
Conditional Probability of Error Term Classified in Low Volatility Regime
Mortality Regimes and Pricing 12
te
Longevity Call Option
Esscher Transform
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Pricing Longevity Securities with RS Models
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Mortality Regimes and Pricing 15
Table 815-year Longevity Call Option Premiums on per $100,000 Notional Amount6515
~p
Table 920-year Longevity Call Option Premiums on per $100,000 Notional Amount6520
~p
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 Pricing 16
Conclusions