Term‐structure estimation in markets with infrequent trading

Abstract

There are two issues that are of central importance in term-structure analysis. One is the modelling and estimation of the current term structure of spot rates. The second is the modelling and estimation of the dynamics of the term structure. These two issues have been addressed independently in the literature. The methods that have been proposed assume a sufficiently complete price data set and are generally implemented separately. However, there are serious problems when these methods are applied to markets with sparse bond prices. We develop a method for jointly estimating the current term-structure and its dynamics for markets with infrequent trading. We propose solving both issues by using a dynamic term-structure model estimated from incomplete panel-data. To achieve this, we modify the standard Kalman filter approach to deal with the missing-observation problem. In this way, we can use historic price data in a dynamic model to estimate the current term structure. With this approach we are able to obtain an estimate of the current term structure even for days with an arbitrary low number of price observations. The proposed methodology can be applied to a broad class of continuous-time term-structure models with any number of stochastic factors. To show the implementation of the approach, we estimate a three-factor generalized-Vasicek model using Chilean government bond price data. The approach, however, may be used in any market with infrequent trading, a common characteristic of many emerging markets. Copyright © 2007 John Wiley & Sons, Ltd.

Why Do Emerging Economies Borrow Short Term?

“…1 2 Cortázar, Schwartz, and Naranjo (2007) discuss the di¢ culties of estimating the term structure in markets with infrequent trading and suggest an alternative methodology that uses data for more dates than the ones for which the yield curve is being estimated. We address this issue by working with countries with many bonds and liquid markets.…”

Why Do Emerging Economies Borrow Short Term?

“…12 12 Cortázar, Schwartz, and Naranjo (2007) discuss the difficulties of estimating the term structure in markets with infrequent trading and suggest an alternative methodology that uses data for more dates than the ones for which the yield curve is being estimated. We address this issue by working with countries with many bonds and liquid markets.…”

A multicommodity model of futures prices: Using futures prices of one commodity to estimate the stochastic process of another

“…As Cortazar et al (2007) pointed out, the above optimal estimates can be obtained even if the number of observations varies with time. The Kalman filter allows the dimension u t of vectors z t , d t , v t and of matrices H t and R t to be a function of time.…”

“…In this section it is shown how the Kalman filter can be used to estimate a model, even if data are incomplete and for some days there are no prices (Cortazar, Schwartz, & Naranjo, 2007). Let the following measurement equation relate a vector of observable variables z t with a vector of state variables, x t : (15) where H t is a u t ϫ n matrix, d t is a u t ϫ 1 vector, and v t is a u t ϫ 1 vector of uncorrelated Gaussian disturbances with mean 0 and covariance matrix R t .…”