# Dynamic correlation in a convergence model of interest rates

## Main Article Content

Beáta Stehlíková Zuzana Bučková

## Abstract

Short rate models are formulated in terms of stochastic differential equations governing the instantaneous interest rate, so called short rate. The bond prices, as well as other derivatives, are then given as a solution to a parabolic partial differential equation with a terminal condition equal to the payoff of the derivative. Convergence models are used to model a situation where a country is going to enter a monetary union and its short rate is affected by the short rate in the monetary union. In addition, Wiener processes which model random shocks in the behaviours of the short rates can be correlated. In this paper we consider a dynamic correlation (i.e., the correlation is a given function of time) in a convergence model with volatilities proportional to powers of the respective short rates. Firstly, we consider a special case with constant volatilities which is analytically tractable. Based on observations made in this case, we propose an approximate analytical solution for the bond prices in the general model and derive order of its accuracy.

## Article Details

How to Cite
Stehlíková, B., & Bučková, Z. (2020). Dynamic correlation in a convergence model of interest rates. Proceedings Of The Conference Algoritmy, , 201 - 210. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/1584/837
Section
Articles

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