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MacKay, Anne
Wüthrich, Mario V.
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[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 3 [Year:] 2015 [Issue:] 3 [Pages:] 250-276
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 Vasi¡cek model and derive within this framework closed-form expressions for the best-estimate prices of long-term bonds.
best-estimate price
reinvestment risk
dynamic hedging
sequential local risk minimization
incomplete market
state-price deflator
long-term bonds
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