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Hedging of long term zero-coupon bonds in a market model with reinvestment risk. (English) Zbl 1307.91192

The authors present a method to value and hedge long-term deterministic cash-flows with short and medium term zero-coupon bonds. The classical stochastic term structure models assume that bonds with unlimited time to maturity are traded at each time point. So, they do not provide the right framework for the problem. Instead, the authors develop a discrete-time stochastic yield curve model with limited availability of maturity dates and with new bonds, issued at each point in time with a maturity date unavailable at the previous time points. This involves reinvestment risk and there is a perfect hedging for long term liabilities. The model is calibrated to market data about Swiss government bonds and optimal hedging strategies are described under a given risk tolerance. The considerations provide a natural extrapolation of the yield curve beyond the last liquid maturity date and a framework for valuing long term insurance liabilities, for instance under Solvency 2. Also, the optimal replication strategy for liabilities is determined under the given risk tolerance.

MSC:

91G60 Numerical methods (including Monte Carlo methods)
91G30 Interest rates, asset pricing, etc. (stochastic models)
91B70 Stochastic models in economics
91G20 Derivative securities (option pricing, hedging, etc.)
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References:

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