On the Singular Limit of Solutions to the Cox-Intersoll-Ross Interest Rate Model with Stochastic Volatility

Kybernetika, Vol. 40, 2008

10 Pages Posted: 5 Nov 2008

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: November 4, 2008

Abstract

In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox-Ingersoll-Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution to the two factors generalized CIR model and we show that the first two terms in the expansion are independent of the variable representing stochastic volatility.

Keywords: Cox-Ingersoll-Ross two factors model, rapidly oscillating volatility, singular, limit of solution, asymptotic expansion

Suggested Citation

Stehlikova, Beata and Sevcovic, Daniel, On the Singular Limit of Solutions to the Cox-Intersoll-Ross Interest Rate Model with Stochastic Volatility (November 4, 2008). Kybernetika, Vol. 40, 2008, Available at SSRN: https://ssrn.com/abstract=1295524

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

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