On the singular limit of solutions to the CIR interest rate model with stochastic volatility

TL;DR

This paper investigates the asymptotic behavior of zero coupon bond prices in a two-factor CIR interest rate model with rapidly oscillating stochastic volatility, deriving a second-order expansion that simplifies the influence of volatility.

Contribution

It provides the first detailed second-order asymptotic expansion for the generalized CIR model with stochastic volatility, revealing the independence of initial terms from volatility variables.

Findings

Second-order asymptotic expansion of bond prices derived.

First two terms of expansion are independent of stochastic volatility.

Model captures clustering of interest rate volatilities.

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.