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Risks 2015, 3(3), 250-276; doi:10.3390/risks3030250

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
*
Author to whom correspondence should be addressed.
Academic Editor: Mogens Steffensen
Received: 10 April 2015 / Accepted: 10 July 2015 / Published: 16 July 2015
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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 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

MacKay, A.; Wüthrich, M.V. Best-Estimates in Bond Markets with Reinvestment Risk. Risks 2015, 3, 250-276.

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