Financial Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Pricing Pure Endowments

TL;DR

This paper introduces a new method for pricing mortality risk in incomplete markets using an instantaneous Sharpe ratio, providing a consistent valuation framework for pure endowments with stochastic hazard rates.

Contribution

It develops a novel valuation formula for non-diversifiable mortality risk that accounts for stochastic hazard rates and satisfies key financial properties.

Findings

Risk-adjusted survival probability exceeds physical probability with stochastic hazard rates.

Valuation formula is subadditive in the number of contracts.

Method applies to pricing pure endowments in incomplete markets.

Abstract

We develop a theory for pricing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We prove that our ensuing valuation formula satisfies a number of desirable properties. For example, we show that it is subadditive in the number of contracts sold. A key result is that if the hazard rate is stochastic, then the risk-adjusted survival probability is greater than the physical survival probability, even as the number of contracts approaches infinity.