arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2402.07503math.PRq-fin.MF
收藏

由独立Lévy过程驱动的仿射期限结构模型

Affine term structure models driven by independent Lévy processes

Michał Barski, Rafał Łochowski

备注：
arXiv admin note: substantial text overlap with arXiv:2303.08477, arXiv:2204.07245
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文刻画了由独立Lévy鞅驱动的非负短期利率仿射期限结构模型，证明在Laplace变换正则变化假设下其解可由稳定过程驱动，包含更可靠的$α$-CIR模型，并验证了重尾性、极限分布及市场校准表现。

摘要：

我们刻画了非负短期利率R的仿射期限结构模型，该模型可作为由独立的一维Lévy鞅驱动的自治SDE的解获得，即形如$$ dR(r)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=r_0\geq 0, \quad t>0, \quad (1)$$的方程，其中$F,G_1,...,G_d$为确定性实函数，$Z_1,...,Z_d$为独立的一维Lévy鞅。利用Filipović关于仿射期限结构模型生成器形式的一般性结果，在驱动噪声的Laplace变换正则变化的假设下，证明了方程(1)的所有可能解R也可作为由独立稳定过程驱动的自治SDE的解获得，其稳定性指数在$(1,2]$范围内。所得模型特别包括由Jiao等人引入的$α$-CIR模型，该模型被证明仍然简单但比经典CIR模型更可靠。我们证明了关于R的重尾性及其以稳定性指数表示的极限分布的结果。最后，展示了所得模型对市场利率期限结构的数值校准结果，并与CIR和$α$-CIR模型进行了比较。

英文摘要：

We characterize affine term structure models of non-negative short rate $R$ which may be obtained as solutions of autonomous SDEs driven by independent, one-dimensional Lévy martingales, that is equations of the form $$ dR(r)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=r_0\geq 0, \quad t>0, \quad (1)$$ with deterministic real functions $F,G_1,...,G_d$ and independent one-dimensional Lévy martingales $Z_1,...,Z_d$. Using a general result on the form of the generators of affine term structure models due to Filipović, it is shown, under the assumption that the Laplace transforms of the driving noises are regularly varying, that all possible solutions $R$ of (1) may be obtained also as solutions of autonomous SDEs driven by independent stable processes with stability indices in the range $(1,2]$. The obtained models include in particular the $α$-CIR model, introduced by Jiao et al., which proved to be still simple yet more reliable than the classical CIR model. Results on heavy tails of $R$ and its limit distribution in terms of the stability indices are proven. Finally, results of numerical calibration of the obtained models to the market term structure of interest rates are presented and compared with the CIR and $α$-CIR models.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑