The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks

Pedro Santa-Clara

New University of Lisbon - Nova School of Business and Economics; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR)

Didier Sornette

Swiss Finance Institute; ETH Zurich

December, 1999

Review of Financial Studies, 2000

This paper offers a new class of models for the term structure of forward interest rates. We allow each instantaneous forward rate to be driven by a different stochastic shock, but constrain the shocks so that the forward rate curve is kept continuous. We term the shocks to the forward curve ``stochastic string shocks'', and construct them as solutions to stochastic partial differential equations. The paper offers a variety of parameterizations that can produce, with parsimony, any correlation pattern among forward rates of different maturities. We derive the no-arbitrage condition on the drift of forward rates shocked by stochastic strings and show how to price interest rate derivatives. Although derivatives can be easily priced, they can be perfectly hedged only by trading in an infinite number of bonds of all maturities. We show that the strings model is consistent with any panel dataset of bond prices, and does not require the addition of error terms in econometric models. Finally, we empirically calibrate some versions of the model and price the delivery option embedded in long bond futures. We show that the delivery option is much more valuable in string models than in a similar one-factor model. This is due to the greater variety of shapes of the term structure that string models can produce, which induces more changes in the cheapest-to-deliver bond.

JEL Classification: E43, G12, G13

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Date posted: March 27, 2000  

Suggested Citation

Santa-Clara, Pedro and Sornette, Didier, The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks (December, 1999). Review of Financial Studies, 2000. Available at SSRN: http://ssrn.com/abstract=216752

Contact Information

Pedro Santa-Clara (Contact Author)
New University of Lisbon - Nova School of Business and Economics ( email )
HOME PAGE: http://docentes.fe.unl.pt/~psc/
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
Centre for Economic Policy Research (CEPR) ( email )
77 Bastwick Street
London, EC1V 3PZ
United Kingdom
Didier Sornette
Swiss Finance Institute ( email )
c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
ETH Zurich ( email )
Department of Management, Technology and Economics
Scheuchzerstrasse 7
8092 Zurich
41446328917 (Phone)
41446321914 (Fax)
HOME PAGE: http://www.er.ethz.ch/
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