Best-Estimates in Bond Markets with Reinvestment Risk

Risks

Anne MacKay¹  Mario V. Wüthrich¹ 

[1] ETH Zurich, RiskLab, Department of Mathematics, 8092 Zurich, Switzerland; E-Mail:

关键词: best-estimate price;    reinvestment risk;    dynamic hedging;    sequential local risk minimization;    incomplete market;    state-price deflator;    long-term bonds;   

DOI  :  10.3390/risks3030250

来源: mdpi

【 摘 要 】

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 Vasiček model and derive within this framework closed-form expressions for the best-estimate prices of long-term bonds.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.