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Unformatted text preview: Asymmetry and Long Memory in Dynamics of Interest Rate Volatility Pei-Shih Weng a, * a Department of Finance, National Central University, Jhongli, TY 32001, Taiwan May 2008 Abstract Empirically, the conditionally heteroskedastic volatility effect in short rate volatility process has been presented for broad discussion, and the long memory phenomena is also tested. However, these two effects have been never involved together to model the dynamics of short rate volatility. This paper introduces a asymmetry and long memory conditional variance model, says FIEGARCH, to model the dynamics of short-term interest rate volatility on the three-month U.S. Treasury bills. By finding the significant estimates, we recognize the necessity of the asymmetric volatility function with the long memory property. Our results also show that the nonlinearity is not a necessary fact for the short rate drift, instead, the asymmetric specification plays an important role in the mean function. Finally, according to the comparison for the prediction of the volatility dynamics, the FIEGARCH shows better forecasting ability, especially in monthly frequency. JEL Classification: C51; C52; G12 Keywords : Short-Term Interest Rate, Volatility, Long Memory, Asymmetry 1 Introduction The short-term riskless rate of interest and its estimated volatility, driving the changes in the entire term structure, are the fundamental variables in continuous time models. This makes the choice of a volatility model for the risk-free rate crucial to pricing interest rate derivatives and hedging interest rate risk. The use of an incorrect volatility model could * The author is currently Ph.D. candidates. Contact: Tel.: +88634227151 ext. 66283; E-mail address: [email protected] 1 lead to incorrect inferences, mishedged or unhedged risks, or pricing errors. In continuous time diffusion models, the short-term interest rate is usually based on Brownian motion. In a general framework, the dynamics of the short rate can be described by the stochastic differential equation: dr t = μ ( r t , t ) dt + σ ( r t , t ) dW t (1) were r t is the instantaneous spot rate, W t is a standard Brownian motion, and μ ( r t , t ) and σ ( r t , t ) are the drift and diffusion functions that depend on the short rate and possibly other state variables. Many single-factor term structure models imply dynamics for the short-term riskless rate that can be nested within the following model proposed by Chan et al. (1992) (henceforth CKLS), dr t = ( α + α 1 r t ) dt + σr φ t dW t (2) where α , α 1 , σ , and φ are fixed parameters. CKLS estimate the parameters of the continuous time model given in (2) using a discrete time econometric specification: r t- r t- 1 = α + α 1 r t- 1 + ε t (3) E ( ε t | Ω t- 1 ) = 0 , E ( ε 2 t | Ω t- 1 ) = h t = σ 2 r 2 φ t- 1 (4) However, a major limitation in CKLS model is that they restrict volatility to be a function of the interest rate level only, and not of the news arrival process.function of the interest rate level only, and not of the news arrival process....
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This note was uploaded on 02/28/2010 for the course ECO 211 taught by Professor Gilo during the Spring '10 term at Young Harris.
- Spring '10