135 Term Structure Review ARFE 2009

135 Term Structure Review ARFE 2009 - Review in Advance...

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The Term Structure of Interest Rates Robert A. Jarrow Johnson Graduate School of Management, Cornell University, Ithaca, New York 14853; email: [email protected] Annu. Rev. Financ. Econ. 2009. 12:1–28 First published online as a Review in Advance on The Annual Review of Financ. Econ. is online at financial.annualreviews.org This article’s doi: 10.1146/annurev . financial . 050808 . 114513 Copyright © 2009 by Annual Reviews. All rights reserved 1941-1367/09/1205-0000$20.00 Key Words arbitrage-free term structures, HJM model, expectations hypothesis, LIBOR model, futures and forward contracts Abstract This paper reviews the term structure of interest rates literature relating to the arbitrage-free pricing and hedging of interest rate derivatives. Term structure theory is emphasized. Topics included are the HJM model, forward and futures contracts, the expecta- tions hypothesis, and the pricing of caps/floors. Directions for future research are discussed. 12.1 Review in Advance first posted online on October 22 , 200 9 . (Minor changes may still occur before final publication online and in print.) Changes may still occur before final publication online and in print. Annu. Rev. Fin. Econ. 2009.1. Downloaded from arjournals.annualreviews.org by Robert A. Jarrow on 11/12/09. For personal use only.
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1. INTRODUCTION The term structure of interest rates literature studies the evolution of default-free interest rates of different maturities (the term structure) across time. Alternatively stated, the term structure of interest rates studies the evolution of default-free bond prices of different maturities. There are two related approaches to understanding this evolution: equilibrium and arbitrage-free pricing models. Equilibrium models are more complex, requiring more assumptions about investor preferences and market structures. This additional structure enables equilibrium models to characterize interest rate risk premia or, equivalently, the expected returns on zero- coupon bonds of all maturities (the price evolution under the statistical probability mea- sure). To test these models, one needs to estimate the interest rate risk premia because these differentiate the various models. In contrast, complete market arbitrage-free pricing models study the evolution of the term structure of interest rates to price interest rate derivatives given the initial prices for a collection of zero-coupon bonds. For this reason, the arbitrage-free pricing methodology is often termed a relative pricing theory. The arbitrage-free pricing models are also useful for understanding interest rate risk management, in particular the hedging of interest rate risk. These models are valid for arbitrary interest rate risk premia; hence, they are consistent with numerous equilibrium models. To test these models, one needs to estimate only volatilities and correlations of default-free interest rates and validate (or reject) the model’s hedging accuracy.
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135 Term Structure Review ARFE 2009 - Review in Advance...

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