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

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-ofcapital 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-ofcapital margin, and related quantities, in terms of an example from life insurance.

Valuation of Non-Life Liabilities from Claims Triangles

“…The purpose of the present paper is to describe how the cost-of-capital approach from Engsner et al (2017), which builds on the approach to market-consistent liability valuation from Möhr (2011), may be implemented using non-life claims triangle data covering both premium and reserve risk. In Engsner et al (2017), general formulas for cost-of-capital valuation of liability cash flows are provided.…”

“…In Engsner et al (2017), general formulas for cost-of-capital valuation of liability cash flows are provided. For this to become practically relevant in a non-life insurance context, we need to define cash flow dynamics that are consistent with those seen in actual non-life insurance applications.…”

“…One can here note that these methods do not necessarily have a one-to-one correspondence with the assumptions underlying, e.g., the standard chain-ladder method. We can also remark that there are connections between the consistent multi-period valuation approach from Engsner et al (2017) and the simplified inconsistent multi-period valuation approach provided by EIOPA; see the definition of the so-called "risk margin" in (European Commission 2015, Article 37).…”

“…Moreover, the valuation formulas from Engsner et al (2017) are based on the payment process dynamics and the resulting capital costs from repeated capital requirements. In practice, we need to define a specific model, estimate parameters and assess both process and estimation uncertainty.…”

“…In practice, we need to define a specific model, estimate parameters and assess both process and estimation uncertainty. Further, in Engsner et al (2017), it is shown that the general cost-of-capital valuation formulas become analytically tractable when the underlying class of models describing the payment dynamics are Gaussian. Due to this, we give two examples of Gaussian time series payment process models.…”