Abstract
In this chapter we develop a framework for term structure modelling that allows factors other than the instantaneous spot rate itself to influence the evolution of the term structure of interest rates. The framework allows for multi-factor generalisations of the Hull–White model as well as of the CIR model. First we present a two-factor extension of the Hull–White model. Then we develop a general multi-factor term structure model and the corresponding bond option pricing model. Finally as a specific application, we consider the so called Duffie–Kan affine class of term structure models, which is widely applied in practice.
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Notes
- 1.
It is important to stress that the measure now is not unique because of the market incompleteness, which manifests itself through the market prices of risk λ k .
References
Duffie, D., & Kan, R. (1996). A yield-factor model of interrest rates. Mathematical Finance, 6(4), 379–406.
Hull, J., & White, A. (1994). Numerical procedures for implementing term structure models II: Two-factor models. Journal of Derivatives, 2, 37–48.
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Chiarella, C., He, XZ., Nikitopoulos, C.S. (2015). Interest Rate Derivatives: Multi-Factor Models. In: Derivative Security Pricing. Dynamic Modeling and Econometrics in Economics and Finance, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45906-5_24
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DOI: https://doi.org/10.1007/978-3-662-45906-5_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-45905-8
Online ISBN: 978-3-662-45906-5
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