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Volatility and Time Series EconometricsEssays in Honor of Robert Engle$
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Tim Bollerslev, Jeffrey Russell, and Mark Watson

Print publication date: 2010

Print ISBN-13: 9780199549498

Published to Oxford Scholarship Online: May 2010

DOI: 10.1093/acprof:oso/9780199549498.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 22 September 2021

A Multifactor, Nonlinear, Continuous‐Time Model of Interest Rate Volatility *

A Multifactor, Nonlinear, Continuous‐Time Model of Interest Rate Volatility *

(p.296) 14 A Multifactor, Nonlinear, Continuous‐Time Model of Interest Rate Volatility*
Volatility and Time Series Econometrics

Jacob Boudoukh

Christopher Downing

Matthew Richardson

Richard Stanton

Robert F. Whitelaw

Oxford University Press

This chapter provides a method for estimating multifactor continuous-time Markov processes. Using Milshtein's (1978) approximation schemes for writing expectations of functions of the sample path of stochastic differential equations in terms of the drift, volatility, and correlation coefficients, it provides nonparametric estimation of the drift and diffusion functions of multivariate stochastic differential equations. This technique is applied to the short- and long-end of the term structure for a general two-factor, continuous-time diffusion process for interest rates.

Keywords:   continuous-time Markov processes, Milshtein, approximation, volatility, interest rates

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