Pang, Kin (1997) Calibration of interest rate term structure and derivative pricing models. PhD thesis, University of Warwick.

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Abstract

We argue interest rate derivative pricing models are misspecified so
that when they are fitted to historical data they do not produce prices
consistently with the market. Interest rate models have to be calibrated to
prices to ensure consistency. There are few published works on calibration
to derivatives prices and we make this the focus of our thesis.
We show how short rate models can be calibrated to derivatives
prices accurately with a second time dependent parameter. We analyse the
misspecification of the fitted models and their implications for other models.
We examine the Duffle and Kan Affine Yield Model, a class of short
rate models, that appears to allow easier calibration. We show that, in fact,
a direct calibration of Duffle and Kan Affine Yield Models is exceedingly
difficult. We show the non-negative subclass is equivalent to generalised
Cox, Ingersoll and Ross models that facilitate an indirect calibration of nonnegative
Duffle and Kan Affine Yield Models.
We examine calibration of Heath, Jarrow and Morton models. We
show, using some experiments, Heath, Jarrow and Morton models cannot
be calibrated quickly to be of practical use unless we restrict to special
subclasses. We introduce the Martingale Variance Technique for
improving the accuracy of Monte Carlo simulations.
We examine calibration of Gaussian Heath Jarrow and Morton
models. We provide a new non-parametric calibration using the Gaussian
Random Field Model of Kennedy as an intermediate step. We derive new
approximate swaption pricing formulae for the calibration.
We examine how to price resettable caps and floors with the market-
Libor model. We derive a new relationship between resettable caplets and
floorlets prices. We provide accurate approximations for the prices. We
provide practical approximations to price resettable caplets and floorlets
directly from quotes on standard caps and floors. We examine how to
calibrate the market-Libor model.

Item Type:	Thesis (PhD)
Subjects:	H Social Sciences > HB Economic Theory
Library of Congress Subject Headings (LCSH):	Interest rates -- Econometric models, Derivative securities -- Prices -- Econometric models
Official Date:	June 1997
Dates:	Date Event June 1997 Submitted
Institution:	University of Warwick
Theses Department:	Warwick Business School
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Hodges, Stewart
Sponsors:	Economic and Social Research Council (Great Britain) (ESRC) ; Financial Options Research Centre (Great Britain)
Extent:	[222] leaves
Language:	eng

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