A combined analysis of hedge effectiveness and capital efficiency in longevity hedging

On the economics of the longevity risk transfer market

“…Taking the associated cost of capital (and its uncertainty arising from stochastic future mortality) properly into account, the primary hedger's time‐zero random present value of all future cash flows that are exposed to longevity risk is given by (cf. Börger, Freimann, et al, 2021) $$${\rm{\Pi }}:= L(0)+CoC,$$$ where $$L(0)$$ denotes the random present value of all future liabilities, that is, benefit payments to surviving annuitants, and CoC represents the random present value of all cost of capital for supporting the annuity portfolio over its lifetime based on a cost‐of‐capital rate of $${r}_{CoC}$$. Note that the definition of $${\rm{\Pi }}$$ coincides in terms of its mean with the Technical Provisions under Solvency II, which are defined as the sum of the best estimate liabilities and a risk margin computed with a cost‐of‐capital approach (cf.…”

“…In this section, we introduce longevity swaps, annuity forwards, and q ‐forwards as hedging instruments for the primary hedger. Following Börger, Freimann et al (2021), we rely on different IPs for constructing customized as well as index‐based versions of the same base instrument that involve varying levels of population basis risk for the hedger.…”

“…Since annuity forwards and q ‐forwards are structurally intended for shorter hedge horizons, we consider times to maturity of up to 25 years (cf. Börger, Freimann, et al, 2021).…”

“…Since then, this concept has been taken up in several studies, including Blake et al (2019), Cairns and El Boukfaoui (2021), and the references cited therein. However, previous studies are either limited to qualitative descriptions and discussions of a functioning longevity risk transfer market or solely focus on one link of this risk transfer chain, that is, on transactions between a longevity hedger and a hedge provider who is typically left unspecified (see, e.g., Börger, Freimann, et al, 2021; Cairns et al, 2014; Cairns & El Boukfaoui, 2021; Meyricke & Sherris, 2014; Ngai & Sherris, 2011). To the best of our knowledge, a comprehensive quantitative analysis of the dynamics of the longevity risk transfer market that simultaneously encompasses both links of this risk transfer chain has not been conducted in the literature yet.…”

“…In this paper, we fill this gap in the literature by proposing a comprehensive stochastic model of a longevity risk transfer market that consists of the following components: Market participants : We consider the following three different types of market participants with own characteristics and (partly opposing) objectives: Primary longevity hedgers : On the demand side, we consider primary writers of longevity risk, such as pension funds or life insurers, that evaluate a (partial) transfer of their longevity risk exposure. In the spirit of Börger, Freimann et al (2021), we assume that they simultaneously seek a high hedge effectiveness (measuring the achieved level of risk reduction) and a high capital efficiency (measuring the reduction in the cost of capital after deduction of the hedging costs). Hypothetically speaking, primary hedgers would aim for a complete risk transfer, which reduces their capital charges to zero, if such a perfect hedge was available on a cost‐free basis.…”