Interest Rate Models on Lie Groups

Title
Interest Rate Models on Lie Groups
Authors
박종우전창묵한철우Nick Webber
Keywords
Financial mathematics; Financial engineering; Interest rate modelling; Affine term structure models
Issue Date
2011-04
Publisher
Quantitative finance
Citation
VOL 11, NO 4, 559-572
Abstract
This paper examines an alternative approach to interest rate modeling, in which the nonlinear and random behavior of interest rates is captured by a stochastic differential equation evolving on a curved state space. We consider as candidate state spaces the matrix Lie groups; these offer not only a rich geometric structure, but—unlike general Riemannian manifolds— also allow for diffusion processes to be constructed easily without invoking the machinery of stochastic calculus on manifolds. After formulating bilinear stochastic differential equations on general matrix Lie groups, we then consider interest rate models in which the short rate is defined as linear or quadratic functions of the state. Stochastic volatility is also augmented to these models in a way that respects the Riemannian manifold structure of symmetric positive-definite matrices. Methods for numerical integration, parameter identification, pricing, and other practical issues are addressed through examples.
URI
http://pubs.kist.re.kr/handle/201004/41317
ISSN
1469-7688
Appears in Collections:
KIST Publication > Article
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