On Non-Existence of a One Factor Interest Rate Model for Volatility Averaged Generalized Fong-Vasicek Term Structures

Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2008 Takachiho / University of Miyazaki, Miyazaki, Japan, September 1-7, pp. 40-48, 2008

9 Pages Posted: 5 Nov 2008 Last revised: 12 Jun 2009

See all articles by Beata Stehlikova

Beata Stehlikova

Comenius University - Department of Applied Mathematics and Statistics

Daniel Sevcovic

Comenius University - Faculty of Mathematics, Physics and Informatics

Date Written: 2006

Abstract

The purpose of this paper is to study the generalized Fong - Vasicek two-factor interest rate model with stochastic volatility. In this model the dispersion of the stochastic short rate (square of volatility) is assumed to be stochastic as well and it follows a non-negative process with volatility proportional to the square root of dispersion. The drift of the stochastic process for the dispersion is assumed to be in a rather general form including, in particular, linear function having one root (yielding the original Fong - Vasicek model or a cubic like function having three roots (yielding a generalized Fong - Vasicek model for description of the volatility clustering). We consider averaged bond prices with respect to the limiting distribution of stochastic dispersion. The averaged bond prices depend on time and current level of the short rate like it is the case in many popular one-factor interest rate model including in particular the Vasicek and Cox - Ingersoll-Ross model. However, as a main result of this paper we show that there is no such one-factor model yielding the same bond prices as the averaged values described above.

Keywords: two-factor term structure models, generalized Fong--Vasicek interest rate model, stochastic volatility, stochastic differential equation, averaging, limiting density

Suggested Citation

Stehlikova, Beata and Sevcovic, Daniel, On Non-Existence of a One Factor Interest Rate Model for Volatility Averaged Generalized Fong-Vasicek Term Structures (2006). Proceedings of the Czech-Japanese Seminar in Applied Mathematics 2008 Takachiho / University of Miyazaki, Miyazaki, Japan, September 1-7, pp. 40-48, 2008 , Available at SSRN: https://ssrn.com/abstract=1295557 or http://dx.doi.org/10.2139/ssrn.1295557

Beata Stehlikova

Comenius University - Department of Applied Mathematics and Statistics ( email )

Mlynská dolina
SK-842 48 Bratislava, 842 48
Slovakia

Daniel Sevcovic (Contact Author)

Comenius University - Faculty of Mathematics, Physics and Informatics ( email )

Mlynská dolina
SK-842 48 Bratislava, 842 48
Slovakia

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
101
Abstract Views
1,040
Rank
481,522
PlumX Metrics