The Term Structure of Simple Forward Rates with Jump Risk
研究了在跳跃和扩散并存下，基于简单远期利率（离散复利）的利率期限结构无套利动态，给出了跳跃风险溢价如何影响利率动态，并提供了利率上限和互换期权的定价公式，展示了跳跃对隐含波动率的影响。
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.