 The Term Structure of Simple Forward Rates with Jump RiskPaul Glasserman and S. G. Kou Mathematical Finance, 2003, vol. 13, issue 3, 383-410 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 traditional interest rate models, simply compounded rates and their parameters are more directly observable in practice and are the basis of recent research on “market models.” We consider very general types of jump processes, modeled through marked point 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. Date: 2003 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:13:y:2003:i:3:p:383-410 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematical Finance is currently edited by Jerome Detemple More articles in Mathematical Finance from Wiley Blackwell |
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