关于具有随机波动率的CIR利率模型解的奇异极限
On the singular limit of solutions to the CIR interest rate model with stochastic volatility
AI总结：
本文针对快速振荡随机波动率下的零息债券定价，通过奇异摄动展开推导广义CIR双因子模型的渐近解，并证明前两项与随机波动率变量无关。
摘要：
本文关注快速振荡随机波动率下零息债券定价的期限结构模型。我们分析了描述利率波动率聚集性的广义Cox-Ingersoll-Ross双因子模型的解。主要目标是推导债券价格关于代表随机波动率过程快尺度的奇异参数的渐近展开。我们推导了广义CIR双因子模型解的二阶渐近展开，并证明展开式的前两项与代表随机波动率的变量无关。
英文摘要：
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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