Risk management for a bond using bond put options

Abstract. This paper studies a strategy that minimizes the risk of a position in a zero coupon bond by buying a percentage of a put option, subject to a fixed budget available for hedging. We consider two popular risk measures: Value-at-Risk(VaR) and Tail Value-at-Risk (TVaR). We elaborate a formula for determining the optimal strike price for this put option in case of a Hull-White stochastic interest rate model. We calibrate the Hull-White model parameters to a set of cap prices, in order to provide a credible numerical illustration. We demonstrate the relevance of searching the optimal strike price, since moving away from the optimum implies a loss, due to an increased (T)VaR. In this way, we extend the results of [Ahn et al., 1999], who minimize VaR for a position in a share