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Stochastic Volatility Corrections for Interest Rate Derivatives
Author(s) -
Cotton Peter,
Fouque JeanPierre,
Papanicolaou George,
Sircar Ronnie
Publication year - 2004
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2004.00188.x
Subject(s) - vasicek model , yield curve , short rate model , short rate , econometrics , interest rate , volatility (finance) , sabr volatility model , stochastic volatility , economics , rendleman–bartter model , affine term structure model , bond , bond valuation , mean reversion , forward rate , mathematics , finance , monetary economics
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.