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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
    as

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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. Föllmer, H. & Schweizer, M., 1988. "Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 147-160, November.
    5. repec:eme:jrfpps:v:14:y:2013:i:2:p:200-233 is not listed on IDEAS
    6. 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.
    Full references (including those not matched with items on IDEAS)

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