A simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility

The aim of this paper is to propose a simple framework for analyzing the mean escape time of interest rate product in different term structures with stochastic volatility. In the modeling perspective, we utilize the one factor Hull-White model to design the dynamics of interest rate returns whose stochastic volatility term is assumed to follow the Cox-Ingersoll-Ross process. Furthermore, we apply the Nelson-Siegel function to simulate various scenarios of term structure based on the US Treasury bill and European bond. Then, we analyze the mean escape time surfaces of different term structures for theoretical flat yield curves and two empirical S-shaped yield curves whose term structures of short-, mid-, and long-term maturities are shifted by the modified parameters of the Nelson-Siegel function. We observe that the survival probability begins with one and reduces to zero with different rate of decay for different interest rates and volatilities. Furthermore, the results of empirical term structures imply that the adjustment in the yield of long-term maturity changes the structure of MET surface more significantly than that of short- and long-term maturities. Lastly, we detect the noise enhanced stability phenomenon from the mean escape time for all cases of flat yield, Treasury bill, and European bond.