A three-factor interest rate model defined on a finite domain has been provided. All the functions in the model can be obtained from the real markets. It has been proven that a final-value problem of the corresponding partial differential equation on a finite domain has a unique solution. Because the formulation of the problem is on a finite domain and correct, it is not difficult to design eff...

Observe that the forward rate F (t, T0, T1) and the swap rate R(t) are known today (time t = 0) from today’s yield curve, but for t > 0 they are unknown and are therefore random variables. In order to value interest rate derivatives we need to model these random variables. To see how we might go about this we consider one of the simplest interest rate derivativesan interest rate cap on a loan. ...

Main purpose of this paper is to describe the background of interest rate modeling, i.e. introduce main division of interest rate models, explain what is the instantaneous interest rate and what is its suitable representative. We will deeply focus on Vaš́ıček and Hull-White model and analyze problem of the calibration of these models. Introduction It is well known that interest rates and their s...

made significant efforts to establish and improve their procedures for interest rate risk management, including using economic models of interest rates and related models of credit risk (Lopez 2001a, b).At the same time, bank supervisors worldwide, including the Federal Reserve, have been expanding their knowledge and oversight of interest rate risk management techniques. For example, U.S. bank...

In this paper, a novel quadratic assignment-based mathematical model is developed for concurrent design of robust inter and intra-cell layouts in dynamic stochastic environments of manufacturing systems. In the proposed model, in addition to considering time value of money, the product demands are presumed to be dependent normally distributed random variables with known expectation, variance, a...