Best-estimates in bond markets with reinvestment risk - Anne MacKay; Mario V. Wüthrich (Risks, 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 Vasicek model and derive within this framework closed-form expressions for the best-estimate prices of long-term bonds.
Keywords: 330; best-estimate price; reinvestment risk; dynamic hedging; sequential local risk minimization; incomplete market; state-price deflator; long-term bonds