Fair Value of Liabilities
How Do We Define “Closest” Asset
Match?
David Service

FIA, FIAA

& Jie Sun

B Act S (Hons), B Comm, AIAA

Presented to the Institute of Actuaries of Australia
XIV General Insurance Seminar 2003
9-12 November 2003

This paper has been prepared for issue to, and discussion by, Members of the Institute of Actuaries of Australia
(IAAust). The IAAust Council wishes it to be understood that opinions put forward herein are not necessarily those of the IAAust and the Council is not responsible for those opinions.

 2003 Institute of Actuaries of Australia

The Institute of Actuaries of Australia
Level 7 Challis House 4 Martin Place
Sydney NSW Australia 2000
Telephone: +61 2 9233 3466 Facsimile: +61 2 9233 3446
Email: insact@actuaries.asn.au Website: www.actuaries.asn.au

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Fair Value of Liabilities - How Do We Define “Closest”
Asset Match?
Abstract
“Fair value” of liabilities is becoming an increasingly important concept for the accounts of insurance companies. The fair value of assets can, in most cases, be determined by taking the market value but there is no practical market value for insurance liabilities. This leads to various alternative approaches. While the theory is still under active discussion, all approaches use the concept of the asset portfolio which is the “closest match” to the liability portfolio. The discount rate implied by that asset portfolio is used as the discount rate for the liability cashflows to give a “fair value” of liabilities for the insurer’s balance sheet.
In this paper we suggest an approach to find the asset portfolio with the “closest match” to a particular liability portfolio when both are comprised of stochastic cashflows. Since these portfolios are stochastic the approach results in “closest match” being measured on a probabilistic basis.
Our definition of “closest match” is
The asset portfolio which, for a given probability of ultimate surplus being negative, requires the lowest initial asset amount. This definition leads also to the conclusion that the “closest match” asset portfolio can be different for different probabilities of insolvency.
A worked example using stochastic models for both asset and liability cashflows shows the “closest match” portfolios for various probabilities of insolvency.
David Service
Centre for Actuarial Research
Australian National University david.service@anu.edu.au Jie Sun
Centre for Actuarial Research
Australian National University jie.sun@anu.edu.au 2

1. Introduction
“Fair value” of liabilities is becoming an increasingly important concept for the accounts of insurance companies. The fair value of assets can, in most cases, be determined by taking the market value but there is no practical market value for insurance liabilities. This leads to various alternative approaches. While the theory is still under active discussion all approaches use the concept of the asset portfolio which is the “closest match” to the liability portfolio. The discount rate implied by that asset portfolio is used as the discount rate for the liability cashflows to give a “fair value” of liabilities for the insurer’s balance sheet.
When a future insurance liability is known with certainty, (for example, it is known that exactly $4000 liability is due in 2 years’ time), the fair value will be very straightforward to determine, i.e. the value of 2-year zero coupon bond. However, few general insurance liabilities are known with certainty. In particular, for long tail business there are very large uncertainties surrounding the liability cashflows. Therefore, a perfect match usually does not exist for most general insurance liabilities and the idea of identifying the asset portfolio with the “closest match” forms an important component of determining the fair value of liabilities.
This particular scenario is representative of a more general problem which is relevant not only to the fair value of liabilities but to the overall concept of asset / liability