Derivatives Pricing Under a New Macro-Financial Square-Root Process for the Term Structure of Interest Rates

Abstract

This paper develops a new macro-financial continuous-time model for the term structure of interest rates assuming that the instantaneous interest rate converges to a certain long-term mean level that depends on the business cycle and that the interest rate volatility depends on the interest rate level. In short, both the mean reversion level and the interest rate volatility are modeled by the physic equation of harmonic waves. Under these assumptions, we compute closed-form expressions for the prices of different fixed income and interest rate derivatives and for relevant risk management measures.

Keywords: square-root process, interest rates, term structure, continuous-time model, harmonic waves, martingale

JEL Classification: G12, G13