Hedging of long term zero-coupon bonds in a market model with reinvestment risk

We present a computational methodology to value and hedge long term zero-coupon bonds trading in short and medium term ones. For this purpose we develop a discrete time stochastic yield curve model with limited availability of maturity dates at a fixed time point and newly issued bonds at future tim...

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Bibliographic Details
Published in:	European actuarial journal 2014-07, Vol.4 (1), p.49-75
Main Authors:	Stefanovits, David, Wüthrich, Mario V.
Format:	Article
Language:	eng
Subjects:	Actuarial science Applications of Mathematics Arbitrage Bond markets Calibration Economics Financial instruments Financial Services Game Theory Government bonds Hedging Investment policy Market prices Mathematics Mathematics and Statistics Original Research Paper Quantitative Finance Social and Behav. Sciences Solvency Valuation Volatility Yield curve Zero coupon bonds
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Summary:	We present a computational methodology to value and hedge long term zero-coupon bonds trading in short and medium term ones. For this purpose we develop a discrete time stochastic yield curve model with limited availability of maturity dates at a fixed time point and newly issued bonds at future time points. This involves reinvestment risk and there is no perfect hedging strategy available for long term liabilities. We calibrate the model to market data and describe optimal hedging strategies under a given risk tolerance. These considerations provide a natural extrapolation of the yield curve beyond the last liquid maturity date, and a framework which allows to value long term insurance liabilities, for instance, under Solvency 2. Moreover, we determine the optimal trading strategy replicating the liabilities under the given risk tolerance.
ISSN:	2190-9733 2190-9741