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.
KeywordsLiquidity risk Fixed income markets Completeness No arbitrage
JEL subject classificationD40 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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