This thesis addresses the absence of explicit pricing formulae and the complexity of proposed
models (incomplete markets framework) in the area of mortality risk management requiring
the application of advanced techniques from the realm of Financial Mathematics and Actuarial
Science. In fact, this is a multi-essay dissertation contributing in the direction of designing and
pricing mortality-linked derivatives and offering the state of art solutions to manage longevity
risk. The first essay investigates the valuation of Catastrophic Mortality Bonds and, in particular,
the case of the Swiss Re Mortality Bond 2003 as a primary example of this class of
assets. This bond was the first Catastrophic Mortality Bond to be launched in the market
and encapsulates the behaviour of a well-defined mortality index to generate payoffs for bondholders.
Pricing this type of bond is a challenging task and no closed form solution exists in
the literature. In my approach, we adapt the payoff of such a bond in terms of the payoff of
an Asian put option and present a new methodology to derive model-independent bounds for
catastrophic mortality bonds by exploiting the theory of comonotonicity.
While managing catastrophic mortality risk is an upheaval task for insurers and re-insurers,
the insurance industry is facing an even bigger challenge - the challenge of coping up with
increased life expectancy. The recent years have witnessed unprecedented changes in mortality
rate. As a result academicians and practitioners have started treating mortality in a stochastic
manner. Moreover, the assumption of independence between mortality and interest rate has
now been replaced by the observation that there is indeed a correlation between the two rates.
Therefore, my second essay studies valuation of Guaranteed Annuity Options (GAOs) under the
most generalized modeling framework where both interest rate and mortality risk are stochastic
and correlated. Pricing these types of options in the correlated environment is an arduous
task and a closed form solution is non-existent. In my approach, I employ the use of doubly
stochastic stopping times to incorporate the randomness about the time of death and employ
a suitable change of measure to facilitate the valuation of survival benefit, there by adapting
the payoff of the GAO in terms of the payoff of a basket call option. I then derive general
price bounds for GAOs by employing the theory of comonotonicity and the Rogers-Shi (Rogers
and Shi, 1995) approach. Moreover, I suggest some `model-robust' tight bounds based on the
moment generating function (m.g.f.) and characteristic function (c.f.) under the affine set up.
The strength of these bounds is their computational speed which makes them indispensable
for annuity providers who rely heavily on Monte Carlo simulations to calculate the fair market
value of Guaranteed Annuity Options. In fact, sans Monte Carlo, the academic literature does
not offer any solution for the pricing of the GAOs. I illustrate the performance of the bounds
for a variety of affine processes governing the evolution of mortality and the interest rate by
comparing them with the benchmark Monte Carlo estimates.
Through my work, I have been able to express the payoffs of two well known modern
mortality products in terms of payoffs of financial derivatives, there by filling the gaps in the
literature and offering state of art techniques for pricing of these sophisticated instruments