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A two‐mean reverting‐factor model of the term structure of interest rates
Author(s) -
Moreno Manuel
Publication year - 2003
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.10088
Subject(s) - vasicek model , rendleman–bartter model , interest rate , short rate model , econometrics , yield curve , term (time) , affine term structure model , bond , bond valuation , economics , short rate , interest rate risk , volatility (finance) , interest rate derivative , cox–ingersoll–ross model , mathematics , mathematical economics , monetary economics , physics , finance , quantum mechanics
This article presents a two‐factor model of the term structure of interest rates. It is assumed that default‐free discount bondprices are determined by the time to maturity and two factors, the long‐term interest rate, and the spread (i.e., the difference)between the short‐term (instantaneous) risk‐free rate of interest and the long‐term rate. Assuming that both factorsfollow a joint Ornstein‐Uhlenbeck process, a general bond pricing equation is derived. Closed‐form expressions for prices of bonds andinterest rate derivatives are obtained. The analytical formula for derivatives is applied to price European options on discount bonds and morecomplex types of options. Finally, empirical evidence of the model's performance in comparison with an alternative two‐factor(Vasicek‐CIR) model is presented. The findings show that both models exhibit a similar behavior for the shortest maturities.However, importantly, the results demonstrate that modeling the volatility in the long‐term rate process can help to fit the observed data,and can improve the prediction of the future movements in medium‐ and long‐term interest rates. So it is not so clear which is the bestmodel to be used. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23: 1075–1105, 2003