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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

(p.326) 22 Martingale Models for the Short Rate
Arbitrage Theory in Continuous Time

Tomas Björk (Contributor Webpage)

Oxford University Press

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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