Best-Estimates in Bond Markets with Reinvestment Risk

Anne MacKay and Mario V. Wüthrich
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Anne MacKay: ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
Mario V. Wüthrich: ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland

Risks, 2015, vol. 3, issue 3, 1-27

Abstract: 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 Vasi?cek model and derive within this framework closed-form expressions for the best-estimate prices of long-term bonds.

Keywords: best-estimate price; reinvestment risk; dynamic hedging; sequential local risk minimization; incomplete market; state-price deflator; long-term bonds (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2015
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