Risk measures and behaviors for bonds under stochastic interest rate models

This paper develops a model for measuring the risk inherent from trading a bond position under some important stochastic interest rate models. We employ the value at risk (VaR) and expected shortfall (ES) as proxies for the extreme risk inherent from trading a bond position. In particular, we concern ourselves with the average tail behavior of the real-world profit/loss distribution for a bond position. We investigate the risk behaviors of a bond position under some stochastic interest rate models including the Merton model, the Vasicek model, and the Cox–Ingersoll–Ross (CIR) model.