Dual analysis on hedging Value at Risk of bond portfolio using options

In this paper, I propose the optimal hedging of bond portfolio VaR using bond options based on dual theory in non-linear optimization and I clarify the relation between the implicit price of bond options in VaR hedging and the price, which is derived by arbitrage pricing theory. Through the dual analysis I provide insight into why out-of-the-money options tend to remain rich and the options on super-long bonds are quite often traded richer than other options. The focus is to investigate the background of these bond market observations from the viewpoint of the managerial decision-making in hedging the VaR of their bond portfolio. As supported by the numerical examples, the optimal hedging strategy derived in the framework quite convincingly explains the reason for the bond market phenomenon even though it does not fully represent the actual bond market.