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

Classification:

35C20, 35B25, 62P05, 60H10, 35K05
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