Affine term structure model: Difference between revisions

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{{expert-subject|date=December 2012|reason=Confirmation, details on the Affine Term Structure Model.}}

An '''affine term structure model''' is a [[financial model]] that relates [[zero-coupon bond]] prices (i.e. the discount curve) to a [[spot rate]] model. It is particularly useful for ''deriving the [[yield curve]]'' – the process of determining spot rate model inputs from observable [[bond market]] data. The affine class of term structure models implies the convenient form that log bond prices are linear functions of the spot rate<ref>{{Cite journal|last=Duffie|first=Darrell|last2=Kan|first2=Rui|date=1996|title=A Yield-Factor Model of Interest Rates|url=https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9965.1996.tb00123.x|journal=Mathematical Finance|language=en|volume=6|issue=4|pages=379–406|doi=10.1111/j.1467-9965.1996.tb00123.x|issn=1467-9965}}</ref> (and potentially additional state variables).

== Background ==

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== Arbitrage-Free Nelson-Siegel ==

One approach to affine term structure modeling is to enforce an [[arbitrage-free]] condition on the proposed model. In a series of papers,<ref>{{Cite journal|last=Christensen|first=Jens H. E.|last2=Diebold|first2=Francis X.|last3=Rudebusch|first3=Glenn D.|date=2011-09-01|title=The affine arbitrage-free class of Nelson–Siegel term structure models|url=http://www.sciencedirect.com/science/article/pii/S0304407611000388|journal=Journal of Econometrics|series=Annals Issue on Forecasting|language=en|volume=164|issue=1|pages=4–20|doi=10.1016/j.jeconom.2011.02.011|issn=0304-4076}}</ref><ref>{{Cite journal|last=Christensen|first=Jens H. E.|last2=Rudebusch|first2=Glenn D.|date=2012-11-01|title=The Response of Interest Rates to US and UK Quantitative Easing|url=https://academic.oup.com/ej/article/122/564/F385/5079473|journal=The Economic Journal|language=en|volume=122|issue=564|pages=F385–F414|doi=10.1111/j.1468-0297.2012.02554.x|issn=0013-0133}}</ref><ref>{{Cite journal|last=Christensen|first=Jens H. E.|last2=Krogstrup|first2=Signe|date=2019-01-01|title=Transmission of Quantitative Easing: The Role of Central Bank Reserves|url=https://academic.oup.com/ej/article/129/617/249/5250963|journal=The Economic Journal|language=en|volume=129|issue=617|pages=249–272|doi=10.1111/ecoj.12600|issn=0013-0133}}</ref> a proposed dynamic yield curve model was developed using an arbitrage-free version of the famous Nelson-Siegel model,<ref>{{Cite journal|last=Nelson|first=Charles R.|last2=Siegel|first2=Andrew F.|date=1987|title=Parsimonious Modeling of Yield Curves|url=http://www.jstor.org/stable/2352957|journal=The Journal of Business|volume=60|issue=4|pages=473–489|doi=10.1086/296409|jstor=2352957|issn=0021-9398}}</ref> which the authors label AFNS. To derive the AFNS model, the authors make several assumptions:

# There are three latent factors corresponding to the ''level'', ''slope'', and ''curvature'' of the [[yield curve]]