Stochastic Volatility Corrections for Interest Rate Derivatives

Peter Cotton, Jean‐Pierre Fouque, George Papanicolaou and Ronnie Sircar

Mathematical Finance, 2004, vol. 14, issue 2, 173-200

Abstract: We study simple models of short rates such as the Vasicek or CIR models, and compute corrections that come from the presence of fast mean‐reverting stochastic volatility. We show how these small corrections can affect the shape of the term structure of interest rates giving a simple and efficient calibration tool. This is used to price other derivatives such as bond options. The analysis extends the asymptotic method developed for equity derivatives in Fouque, Papanicolaou, and Sircar (2000b). The assumptions and effectiveness of the theory are tested on yield curve data.

Date: 2004
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