Annals of Finance

, Volume 14, Issue 2, pp 223–251 | Cite as

On the implied market price of risk under the stochastic numéraire

  • Nikolai Dokuchaev
Research Article


This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. An equivalent martingale measure is not unique for this market, and there are non-replicable claims. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from bond prices constructed as a risk-free investment with deterministic payoff at the terminal time. This leads to possibility to infer a implied market price of risk process from observed historical bond prices.


Implied parameters Market price of risk Random numéraire Stochastic bond price Incomplete market 

JEL Classification




This work was supported by ARC grant of Australia DP120100928 to the author. The author would like to thank the anonymous reviewers for the detailed suggestions that improved the manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia
  2. 2.National Research University ITMOSaint PetersburgRussia

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