Model-Independent Price Bounds for Catastrophic Mortality Bonds

TL;DR

This paper develops model-independent bounds for pricing catastrophic mortality bonds, using comonotonic theory and Monte Carlo simulations, with a focus on the Swiss Re Mortality Bond 2003.

Contribution

It introduces a novel approach to derive model-independent bounds for mortality bonds using comonotonic theory, applicable to complex payoff structures.

Findings

Bounds are tight and effective for valuation.

Monte Carlo simulations validate the bounds' accuracy.

The method applies to bonds with similar payoff structures.

Abstract

In this paper, we are concerned with the valuation of Catastrophic Mortality Bonds and, in particular, we examine 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 these type of bonds is a challenging task and no closed form solution exists in the literature. In our approach, we express the payoff of such a bond in terms of the payoff of an Asian put option and present a new approach to derive model-independent bounds exploiting comonotonic theory as illustrated in \cite{prime1}, \cite{2} and \cite{Simon} for the pricing of Asian options. We carry out Monte Carlo simulations to estimate the bond price and illustrate the quality of the bounds.