Practical valuation of long-term guarantees in inactive financial markets

Bierbaum, Jürgen; Bartel, Hans-Georg; Dennstedt, Nils; Dillmann, Tobias; Engel, Wolfgang; Keller, Marcus; Musialik, Karol; Pauls, Thorsten; Quapp, Norbert; Winter, Jens

doi:10.1007/s13385-014-0089-9

Cited by 1 publication

(2 citation statements)

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“…The existence of a state-price deflator ϕ ∈ L 2 (F) fully specifies no-arbitrage prices with respect to ϕ at the market M F . However, this does not say anything about optimal replication of zero-coupon bonds with times to maturity that are not attainable by trading at the market M F according to (2). This is exactly what we would like to discuss in an insurance setting (i.e., where accounting and solvency regulation for insurance companies applies).…”

Section: Bond Market With Reinvestment Riskmentioning

confidence: 90%

“…When liabilities cannot be marked to market, a popular approach is to "mark-to-model", that is, to fit a model using information available in active markets and to use this model to price the liabilities (see, for example, Bierbaum et al [2] and Martin [3]). This approach disregards the impossibility to completely hedge long-term payoffs, even deterministic ones, using only the short-and medium-term bonds traded in active markets.…”

Section: Introductionmentioning

confidence: 99%

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Best-Estimates in Bond Markets with Reinvestment Risk

MacKay

Wüthrich

2015

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The concept of best-estimate, prescribed by regulators to value insurance liabilities for accounting and solvency purposes, has recently been discussed extensively in the industry and related academic literature. To differentiate hedgeable and non-hedgeable risks in a general case, recent literature defines best-estimates using orthogonal projections of a claim on the space of replicable payoffs. In this paper, we apply this concept of best-estimate to long-maturity claims in a market with reinvestment risk, since in this case the total liability cannot easily be separated into hedgeable and non-hedgeable parts. We assume that a limited number of short-maturity bonds are traded, and derive the best-estimate price of bonds with longer maturities, thus obtaining a best-estimate yield curve. We therefore use the multifactor Vasiček model and derive within this framework closed-form expressions for the best-estimate prices of long-term bonds.

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Section: Bond Market With Reinvestment Riskmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%