For life insurance and annuity products whose payoffs depend on the future mortality rates, there is a risk that realized
mortality rates will be different from the anticipated rates
accounted for in their pricing and reserving calculations. This is
termed as mortality risk. Since mortality risk is difficult to
diversify and has significant financial impacts on insurance
policies and pension plans, it is now a well-accepted fact that
stochastic approaches shall be adopted to model the mortality risk
and to evaluate the mortality-linked securities.
The objective of this thesis is to propose the use of a
time-changed Markov process to describe stochastic mortality
dynamics for pricing and risk management purposes. Analytical and
empirical properties of this dynamics have been investigated using
a matrix-analytic methodology. Applications of the proposed model
in the evaluation of fair values for mortality linked securities
have also been explored.
To be more specific, we consider a finite-state Markov process
with one absorbing state. This Markov process is related to an
underlying aging mechanism and the survival time is viewed as the
time until absorption. The resulting distribution for the survival
time is a so-called phase-type distribution. This approach is
different from the traditional curve fitting mortality models in
the sense that the survival probabilities are now linked with an
underlying Markov aging process. Markov mathematical and
phase-type distribution theories therefore provide us a flexible
and tractable framework to model the mortality dynamics. And the
time-changed Markov process allows us to incorporate the
uncertainties embedded in the future mortality evolution.
The proposed model has been applied to price the EIB/BNP Longevity
Bonds and other mortality derivatives under the independent
assumption of interest rate and mortality rate. A calibrating
method for the model is suggested so that it can utilize both the
market price information involving the relevant mortality risk and
the latest mortality projection. The proposed model has also been
fitted to various type of population mortality data for empirical
study. The fitting results show that our model can interpret the
stylized mortality patterns very well.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/11117 |
| Date | 28 July 2008 |
| Creators | Liu, Xiaoming |
| Contributors | Lin, X. Sheldon |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
| Format | 1306284 bytes, application/pdf |
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