Interest Rate Models

Interest-Rate Models

In this article we will describe some of the main developments in interest-rate modelling since Black & Scholes’ (1973) and Merton’s (1973) original articles on the pricing of equity derivatives. In particular, we will focus on continuoustime, arbitrage-free models for the full term structure of interest rates. Other models which model a limited number of key interest rates or which operate in ...

Chapter Iv - Interest Rate Models

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. ...

Applications of Interest Rate Models

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...

Three-factor Interest Rate Models

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...

Calibration of Interest Rate Models