Libor and Swap Market Models for the Pricing of Interest Rate Derivatives: An Empirical Analysis

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Abstract

In this paper we empirically analyze and compare the Libor and Swap Market Models, developed by Brace, Gatarek, and Musiela (1997) and Jamshidian (1997), using paneldata on prices of US caplets and swaptions.A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices.For both one-factor and two-factor models we analyze how well they price caplets and swaptions that were not used for calibration.We show that the Libor Market Models in general lead to better prediction of derivative prices that were not used for calibration than the Swap Market Models.A one-factor Libor Market Model that exhibits mean-reversion gives a good fit of the derivative prices, and adding a second factor only decreases pricing errors to a small extent.We also find that models that are chosen to exactly match certain derivative prices are overfitted. Finally, a regression analysis reveals that the pricing errors are correlated with the shape of the term structure of interest rates.
Original languageEnglish
Place of PublicationTilburg
PublisherFinance
Number of pages46
Volume2000-35
Publication statusPublished - 2000

Publication series

NameCentER Discussion Paper
Volume2000-35

Fingerprint

Market model
Empirical analysis
Interest rate derivatives
Pricing
Swaps
Derivatives
LIBOR market model
Swaption
Factors
Calibration
Pricing errors
Term structure of interest rates
Prediction
Mean reversion
Panel data
Regression analysis

Keywords

  • Term Structure Models
  • Interest Rate Derivatives
  • Lognormal Pricing Models
  • Black Formula

Cite this

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title = "Libor and Swap Market Models for the Pricing of Interest Rate Derivatives: An Empirical Analysis",
abstract = "In this paper we empirically analyze and compare the Libor and Swap Market Models, developed by Brace, Gatarek, and Musiela (1997) and Jamshidian (1997), using paneldata on prices of US caplets and swaptions.A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices.For both one-factor and two-factor models we analyze how well they price caplets and swaptions that were not used for calibration.We show that the Libor Market Models in general lead to better prediction of derivative prices that were not used for calibration than the Swap Market Models.A one-factor Libor Market Model that exhibits mean-reversion gives a good fit of the derivative prices, and adding a second factor only decreases pricing errors to a small extent.We also find that models that are chosen to exactly match certain derivative prices are overfitted. Finally, a regression analysis reveals that the pricing errors are correlated with the shape of the term structure of interest rates.",
keywords = "Term Structure Models, Interest Rate Derivatives, Lognormal Pricing Models, Black Formula",
author = "{de Jong}, F.C.J.M. and J.J.A.G. Driessen and A. Pelsser",
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year = "2000",
language = "English",
volume = "2000-35",
series = "CentER Discussion Paper",
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Libor and Swap Market Models for the Pricing of Interest Rate Derivatives : An Empirical Analysis. / de Jong, F.C.J.M.; Driessen, J.J.A.G.; Pelsser, A.

Tilburg : Finance, 2000. (CentER Discussion Paper; Vol. 2000-35).

Research output: Working paperDiscussion paperOther research output

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T1 - Libor and Swap Market Models for the Pricing of Interest Rate Derivatives

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AU - Pelsser, A.

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N2 - In this paper we empirically analyze and compare the Libor and Swap Market Models, developed by Brace, Gatarek, and Musiela (1997) and Jamshidian (1997), using paneldata on prices of US caplets and swaptions.A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices.For both one-factor and two-factor models we analyze how well they price caplets and swaptions that were not used for calibration.We show that the Libor Market Models in general lead to better prediction of derivative prices that were not used for calibration than the Swap Market Models.A one-factor Libor Market Model that exhibits mean-reversion gives a good fit of the derivative prices, and adding a second factor only decreases pricing errors to a small extent.We also find that models that are chosen to exactly match certain derivative prices are overfitted. Finally, a regression analysis reveals that the pricing errors are correlated with the shape of the term structure of interest rates.

AB - In this paper we empirically analyze and compare the Libor and Swap Market Models, developed by Brace, Gatarek, and Musiela (1997) and Jamshidian (1997), using paneldata on prices of US caplets and swaptions.A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices.For both one-factor and two-factor models we analyze how well they price caplets and swaptions that were not used for calibration.We show that the Libor Market Models in general lead to better prediction of derivative prices that were not used for calibration than the Swap Market Models.A one-factor Libor Market Model that exhibits mean-reversion gives a good fit of the derivative prices, and adding a second factor only decreases pricing errors to a small extent.We also find that models that are chosen to exactly match certain derivative prices are overfitted. Finally, a regression analysis reveals that the pricing errors are correlated with the shape of the term structure of interest rates.

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KW - Lognormal Pricing Models

KW - Black Formula

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