Insurance valuation: a computable multi-period cost-of-capital approach

TL;DR

This paper introduces a multi-period valuation method for insurance liabilities using a two-stage process that incorporates market replication, residual cash flow management, and risk considerations, with explicit formulas and computational insights.

Contribution

It develops a comprehensive framework for the cost-of-capital margin in insurance valuation, linking it to dynamic risk measurement and providing explicit formulas and computational methods.

Findings

Explicit formulas for the cost-of-capital margin under certain assumptions

Properties of the margin related to risk measures and utility functions

Application example in life insurance illustrating computational aspects

Abstract

We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replication using only cash funds. The latter part takes capital requirements and costs into account, as well as limited liability and risk averseness of capital providers. The cost-of-capital margin is the value of the residual cash flow. We set up a general framework for the cost-of-capital margin and relate it to dynamic risk measurement. Moreover, we present explicit formulas and properties of the cost-of-capital margin under further assumptions on the model for the liability cash flow and on the conditional risk measures and utility functions. Finally, we highlight computational aspects of the cost-of-capital margin, and related quantities, in terms of an example from life insurance.