Communications in Mathematical Finance

Interest rate modeling with fractional Levy process

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•                                           Abstract
  
  We propose a new interest rate model driven by fractional Levy process. We derive the joint characteristic function for spot rate and its integral, which enables us to obtain the analytical formula for the prices of bonds and interest rate derivatives. We numerically study a particular type of long memory interest rate model, namely fractional normal inverse Gaussian (NIG) model. We show that the higher fractional integration parameter leads to the slower decay of term structure of volatilities. We also find the long memory parameter has significant effects on the prices of bonds and interest rate derivatives.