Classification and calibration of affine models driven by independent L\'evy processes

Micha{\l} Barski and Rafa{\l} {\L}ochowski

Papers from arXiv.org

Abstract: The paper is devoted to the study of the short rate equation of the form $$ dR(t)=F(R(t))dt+\sum_{i=1}^{d}G_i(R(t-))dZ_i(t), \quad R(0)=x\geq 0, \quad t>0, $$ with deterministic functions $F,G_1,...,G_d$ and independent L\'evy processes of infinite variation $Z_1,...,Z_d$ with regularly varying Laplace exponents. The equation is supposed to have a nonnegative solution which generates an affine term structure model. A precise form of the generator of $R$ is characterized and a related classification of equations which generate affine models introduced in the spirit of Dai and Singleton \cite{DaiSingleton}. Each class is shown to have its own canonical representation which is an equation with the same drift and the jump diffusion part based on a L\'evy process taking values in $\mathbb{R}^{g}, 1\leq g\leq d$, with independent coordinates being stable processes with stability indices in the range $(1,2]$. Numerical calibration results of canonical representations to the market term structure of interest rates are presented and compared with the classical CIR model. The paper generalizes the classical results on the CIR model from \cite{CIR}, as well as on its extended version from \cite{BarskiZabczykCIR} and \cite{BarskiZabczyk} where $Z$ was a one-dimensional L\'evy process.

Date: 2023-03
New Economics Papers: this item is included in nep-des and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2303.08477 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2303.08477

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().