Abstract
Zero coupon rates are not observable in the market for a range of maturities. Therefore, an estimation methodology is required to derive the zero coupon yield curves from observable data. If we deal with approximations of empirical data to create yield curves it is necessary to choose suitable mathematical functions. We use parametric model of Nelson and Siegel. The current mathematical apparatus employed for this kind of approximation is outlined. This theoretical background is applied to an estimation of the zero-coupon yield curve derived from the Czech coupon bond market. There are many methodologies and each can provide surprisingly different results. Nevertheless, each seeks to provide an estimation that fit the data well while maintaining an easily interpretable form. On an initial test data sample we have not faced any problems, reported elsewhere, of not having found the global optimum or having found multiple local minima.
Highlights
The term structure of interest rates is defined as the relationship between the yields of default-free pure discount bonds and their time to maturity
The minimization problem is stated in terms of the observed and computed prices rather than in terms of the observed and computed yields to maturity (YTM’s)
For the solution obtained by NS-11 we computed the discount, forward and spot yield curves (Fig. 4)
Summary
There are three equivalent descriptions of the term structure of interest rates (Málek, 2005): the discount function which specifies zero-coupon bond (with a par value $1) prices as a function of maturity, the spot yield curve which specifies zero-coupon bond yields (spot rates) as a function of maturity, the forward yield curve which specifies zero-coupon bond forward yields (forward rates) as a function of maturity. P Bid i time to payment (measured in years) time to maturity the discount function, that is the present value of a unit payment due in time t spot rate of maturity t, expressed as the continuously compounded annual rate continuously compounded instantaneous forward rate at time t number of bonds observed price (offer), price (ask). There are three equivalent descriptions of the term structure of interest rates: the discount function d, the spot yield curve z and forward yield curve f.
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