In this paper we study the two-dimensional joint distribution of the first passage time of a constant level by spectrally negative generalized Ornstein–Uhlenbeck processes and their primitive stopped at this first passage time. By using martingales techniques, we show an explicit expression of the Laplace transform of the distribution in terms of new special functions. Finally, we give an appli...

Term structure models describe the evolution of the yield curve through time, without considering the influence of risk, tax, etc. Recently, uncertain processes were initialized and applied to option pricing and currency model. Under the assumption of short interest rate following uncertain processes, this paper investigates the term-structure equation. This equation is first derived for valuin...

We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumpti...

In this work, we consider the issue of pricing exchange options and spread options with stochastic interest rates. We provide the closed form solution for the exchange option price when interest rate is stochastic. Our result holds when interest rate is modeled with a stochastic term structure of general form, which includes Vasicek model, CIR term structure, and other well-known term structure...

We study the generalized Fong–Vasicek two-factor interest rate model with stochastic volatility. In this model dispersion is assumed to follow a non-negative process with volatility proportional to the square root of dispersion, while the drift is assumed to be a general function. We consider averaged bond prices with respect to the limiting distribution of stochastic dispersion. The averaged b...

This paper applies dynamic programming principle and Legendre transform to study a dynamic asset allocation problem with liability process and stochastic interest rate model, where interest rate is assumed to be driven by the Ho-Lee model or the Vasicek model. By using variable change technique, we obtain the closed-form solutions to the optimal investment strategies in the quadratic utility fr...

This paper shows that the expectations hypothesis (EH) of the term structure of interest rates is defensible despite the robust evidence on the predictability of excess bond returns. This is achieved through the introduction of regime-dependent heteroscedasticity into the discrete Vasicek model. The empirical purpose of this paper is to reexamine the adequacy of the EH. The restrictions implied...