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Best-Estimates in Bond Markets with Reinvestment Risk

1
ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
2
Swiss Finance Institute SFI Professor, 8006 Zurich, Switzerland
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Academic Editor: Mogens Steffensen
Risks 2015, 3(3), 250-276; https://doi.org/10.3390/risks3030250
Received: 10 April 2015 / Accepted: 10 July 2015 / Published: 16 July 2015
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 Vasiˇcek model and derive within this framework closed-form expressions for the best-estimate prices of long-term bonds. View Full-Text
Keywords: best-estimate price; reinvestment risk; dynamic hedging; sequential local risk minimization; incomplete market; state-price deflator; long-term bonds best-estimate price; reinvestment risk; dynamic hedging; sequential local risk minimization; incomplete market; state-price deflator; long-term bonds
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MacKay, A.; Wüthrich, M.V. Best-Estimates in Bond Markets with Reinvestment Risk. Risks 2015, 3, 250-276.

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