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

2008/11/04 by Beáta Stehlí­ková, Stehlikova, B., Sevcovic, D.
Economics, Econometrics and Finance · Mathematics · #35C20 35B25 62P05 60H10 35K05 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Numerical Analysis (math.NA) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0811.0591

openalex publication_date 2008/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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