Hrvatsko društvo ekonomista

ARTICLES ::: AUTHORS ::: ARTICLES SEARCH

April 2003. ::: Vol.54 No.03-04

    Zdravka Aljinović
    Snježana Pivac
    Boško Šego

THE CIR MODEL AND ITS APPLICATION TO GOVERNMENT SECURITIES OF THE REPUBLIC OF CROATIA Izvorni znanstveni članak The term structure of interest rates has a long history of traditional theories. It is important to economists because the relationship among interest rates on default free securities that differ in their term to maturity, reflects the information available to the market about the future course of events. The spread of inherently risky instruments (variable rate securities and options) in the seventies, posed critical questions for traditional theories, based on the hypotheses of certainty, and gave rise to a golden decade of revolution in the methods of financial analysis on the basis of probability theory. In this paper we present the basic new term structure model as one of the key products of this golden decade. It was developed in this framework: continuous time, perfect and frictionless markets, diffusion processes, no-arbitrage condition i.e. prices constrained by the hypotheses that equivalent assets (or portfolios) in terms of cash flows and other characteristics must earn the same return. We also show how Cox, Ingersoll and Ross specialize the basic model. The CIR model is then used to extract the term structure of interest rates from observed prices of (fixed rate) Croatian Government bonds. We assume, as the model requires, that the risk of default can be ignored. The parameters of the model and the spot rate value are estimated using cross-sections of prices for two dates in 1997 and 1998. The resulting yield curves, corresponding to the estimated parameters, are the so-called inverse yield curves, for both dates. In many examples of the CIR model application in the countries with developed financial markets, it is rather rare to find the results with falling yield curve. If there is such a result, it may forecast the economic recession and reflect the existing state of instability. The results in the present study show that in Croatia interest rates decrease with maturity for both chosen dates, indicating that long term investment is not favourable. The trend of falling interest rates is even more pronounced for the later date. It is also important to emphasize that there is a significant difference between our results and the results of similar research in countries with long tradition of developed financial markets. Although the used model is the same, as well as the method for parameters estimation, there is a difference between the quality of data. While in those countries the observed prices and interest rates were taken from very frequent and liquid secondary markets, we had to use the data from primary market, because the data on secondary markets were very scarce. - Puni tekst (Hrvatski) Str. 249 - 287 (pdf, 358.67 KB)

THE CIR MODEL AND ITS APPLICATION TO GOVERNMENT SECURITIES OF THE REPUBLIC OF CROATIA

Izvorni znanstveni članak

The term structure of interest rates has a long history of traditional theories. It is important to economists because the relationship among interest rates on default free securities that differ in their term to maturity, reflects the information available to the market about the future course of events. The spread of inherently risky instruments (variable rate securities and options) in the seventies, posed critical questions for traditional theories, based on the hypotheses of certainty, and gave rise to a golden decade of revolution in the methods of financial analysis on the basis of probability theory. In this paper we present the basic new term structure model as one of the key products of this golden decade. It was developed in this framework: continuous time, perfect and frictionless markets, diffusion processes, no-arbitrage condition i.e. prices constrained by the hypotheses that equivalent assets (or portfolios) in terms of cash flows and other characteristics must earn the same return. We also show how Cox, Ingersoll and Ross specialize the basic model. The CIR model is then used to extract the term structure of interest rates from observed prices of (fixed rate) Croatian Government bonds. We assume, as the model requires, that the risk of default can be ignored. The parameters of the model and the spot rate value are estimated using cross-sections of prices for two dates in 1997 and 1998. The resulting yield curves, corresponding to the estimated parameters, are the so-called inverse yield curves, for both dates. In many examples of the CIR model application in the countries with developed financial markets, it is rather rare to find the results with falling yield curve. If there is such a result, it may forecast the economic recession and reflect the existing state of instability. The results in the present study show that in Croatia interest rates decrease with maturity for both chosen dates, indicating that long term investment is not favourable. The trend of falling interest rates is even more pronounced for the later date. It is also important to emphasize that there is a significant difference between our results and the results of similar research in countries with long tradition of developed financial markets. Although the used model is the same, as well as the method for parameters estimation, there is a difference between the quality of data. While in those countries the observed prices and interest rates were taken from very frequent and liquid secondary markets, we had to use the data from primary market, because the data on secondary markets were very scarce.

Puni tekst (Hrvatski) Str. 249 - 287 (pdf, 358.67 KB)