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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: s.d.jacka@warwick.ac.uk
∗ 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 f t u 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 f t u =∫0 uf t v dv 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

Information

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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