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The equivalent martingale measure conditions in a general model for interest rates

Part of: Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Kais Hamza ,
Saul Jacka  and
Fima Klebaner
Kais Hamza*
Affiliation:
Monash University
Saul Jacka*
Affiliation:
University of Warwick
Fima Klebaner*
Affiliation:
Monash University
*
∗ Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3800, Australia.
∗∗∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK. Email address: [email protected]
∗ Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3800, Australia.
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Abstract

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Assuming that the forward rates ftu are semimartingales, we give conditions on their components under which the discounted bond prices are martingales. To achieve this, we give sufficient conditions for the integrated processes ftu=∫0uftvdv to be semimartingales, and identify their various components. We recover the no-arbitrage conditions in models well known in the literature and, finally, we formulate a new random field model for interest rates and give its equivalent martingale measure (no-arbitrage) condition.

Keywords

No arbitrageforward ratesemimartingaleHeath-Jarrow-Morton conditions

MSC classification

Primary: 60H15: Stochastic partial differential equations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 2 , June 2005 , pp. 415 - 434
Copyright
Copyright © Applied Probability Trust 2005 

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