The Term Structure of Simple Forward Rates with Jump Risk

37 Pages Posted: 7 Jun 2000

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Steven Kou

Boston University

Date Written: April 2000

Abstract

This paper characterizes the arbitrage-free dynamics of interest rates, in the presence of both jumps and diffusion, when the term structure is modeled through simple forward rates (i.e., through discretely compounded forward rates evolving continuously in time) or forward swap rates. Whereas instantaneous continuously compounded rates form the basis of most interest rate models, simply compounded rates and their parameters are more directly observable in practice. We consider very general types of jump processes, allowing randomness in jump sizes and dependence between jump sizes, jump times, and interest rates. We make explicit how jump and diffusion risk premia enter into the dynamics of simple forward rates. We also formulate reasonably tractable subclasses of models and provide pricing formulas for some derivative securities, including interest rate caps and options on swaps. Through these formulas, we illustrate the effect of jumps on implied volatilities in interest rate derivatives.

JEL Classification: G13, G12, E43

Suggested Citation

Glasserman, Paul and Kou, Steven, The Term Structure of Simple Forward Rates with Jump Risk (April 2000). Available at SSRN: https://ssrn.com/abstract=223773 or http://dx.doi.org/10.2139/ssrn.223773

Paul Glasserman

Columbia Business School ( email )

3022 Broadway
403 Uris Hall
New York, NY 10027
United States
212-854-4102 (Phone)
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Steven Kou (Contact Author)

Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
6173583318 (Phone)

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