Mathematics and Financial Economics

, Volume 9, Issue 1, pp 57–83 | Cite as

Liquidity risk and the term structure of interest rates



This paper develops an arbitrage-free pricing theory for a term structure of fixed income securities that incorporates liquidity risk. In our model, there is a quantity impact on the term structure of zero-coupon bond prices from the trading of any single zero-coupon bond. We derive a set of conditions under which the term structure evolution is arbitrage-free. These no arbitrage conditions constrain both the risk premia and the term structure’s volatility. In addition, we also provide conditions under which the market is complete, and we show that the replication cost of an interest rate derivative is the solution to a backward stochastic differential equation.


Liquidity risk Fixed income markets Completeness  No arbitrage 

JEL subject classification

D40 G13 



The second author’s research is partly supported by the Institute for Financial Mathematics of Montreal (IFM2), the Caisse de dépot et placement du Québec Chair in Portfolio Management and the Natural Sciences and Engineering Research Council of Canada.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Samuel Curtis Johnson Graduate School of ManagementCornell UniversityIthacaUSA
  2. 2.Finance DepartmentESG UQAMMontrealCanada

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