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Best-Estimates in Bond Markets with Reinvestment Risk

Author

Listed:
  • Anne MacKay

    (ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland)

  • Mario V. Wüthrich

    (ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland
    Swiss Finance Institute SFI Professor, 8006 Zurich, Switzerland)

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.

Suggested Citation

  • Anne MacKay & Mario V. Wüthrich, 2015. "Best-Estimates in Bond Markets with Reinvestment Risk," Risks, MDPI, vol. 3(3), pages 1-27, July.
    • Handle: RePEc:gam:jrisks:v:3:y:2015:i:3:p:250-276:d:52709
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    References listed on IDEAS

    as
    1. K. Ben Nowman, 2011. "Estimation of one-, two- and three-factor generalized Vasicek term structure models for Japanese interest rates using monthly panel data," Applied Financial Economics, Taylor & Francis Journals, vol. 21(14), pages 1069-1078.
    2. Michael Martin, 2013. "Assessing the model risk with respect to the interest rate term structure under Solvency II," Journal of Risk Finance, Emerald Group Publishing, vol. 14(3), pages 200-233, May.
    3. Malamud, Semyon & Trubowitz, Eugene & Wüthrich, Mario V., 2008. "Market Consistent Pricing of Insurance Products," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 483-526, November.
    4. Dahl, Mikkel, 2007. "A Discrete-Time Model for Reinvestment Risk in Bond Markets," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 235-264, November.
    5. repec:eme:jrfpps:v:14:y:2013:i:2:p:200-233 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

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