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Arbitrage Theory in Continuous Time$
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Tomas Björk

Print publication date: 2004

Print ISBN-13: 9780199271269

Published to Oxford Scholarship Online: October 2005

DOI: 10.1093/0199271267.001.0001

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Martingale Models for the Short Rate

Martingale Models for the Short Rate

Chapter:
(p.326) 22 Martingale Models for the Short Rate
Source:
Arbitrage Theory in Continuous Time
Author(s):

Tomas Björk (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0199271267.003.0022

This chapter analyses the martingale modelling approach for the short rate of interest rate model. It considers an interest rate model where the P-dynamics of the short rate of interest are given by d r (t) = μ (t, r (t)) dt + σ (t, r(t)) d W-. The term structure (i.e., the family of bond price processes), as well as the prices of all other interest rate derivatives are determined by specifying the r-dynamics under the martingale measure Q, a procedure known as martingale modelling. Practice exercises are included.

Keywords:   martingale modelling, short rate, interest rate model, yield, price

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