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# Aplikácia teórie matíc v determinácií časovej štruktúry úrokových sadzieb

## Finance

### Aplikácia teórie matíc v determinácií časovej štruktúry úrokových sadzieb

Name and surname of author:

#### Jozef Glova

Year:
2011
Issue:
2
Keywords:
yield curve, interest rate term structure analysis, bootstrapping method.
JEL clasification:
DOI (& full text):
Anotation:
This paper focuses on the term structure of interest rates. We show that the term structure of interest rates is a static function that relates the term to maturity to the yield to maturity for a sample of bonds at a given point of time. We also short describe four mainstream theories attempt to explain the shape of the yield curve. The yield curve is a basic instrument for understanding the relationship between the interest rate of bonds and the maturity of a financial instrument. It has the same relevance for all economic subjects in the form of interest rates determination. Estimation of the term structure discussed in the paper involves obtaining zero coupon interest rates, or discount functions from a set of coupon bond prices. The bootstrapping method is used here to determinate the particular zero coupon interest rates of bonds, where the method consists of iteratively extracting zero coupon interest rates using a sequence of increasing maturity coupon bond prices. Using these rates it becomes possible to derive interest rates for all maturities by making a few assumptions including linear interpolation as we discuss in conclusion of this paper. The particular spot and forward zero coupon interest rates resulting from the bootstrapping method can be used as input in different economic categories like financial management, portfolio management, actuary science, company valuation, management of firm value, financial risk management, etc. The matrix approach derived and described in this paper can be used instead of solving the zero coupon rates sequentially for obtaining a direct solution with particular zero coupon rates. This helps us to diminish the computing severity related to the sequential determination of interest rates using an iterative approach. Fortunately, however, the application of matrix theory helps us to solve this issue very well.
This paper focuses on the term structure of interest rates. We show that the term structure of interest rates is a static function that relates the term to maturity to the yield to maturity for a sample of bonds at a given point of time. We also short describe four mainstream theories attempt to explain the shape of the yield curve. The yield curve is a basic instrument for understanding the relationship between the interest rate of bonds and the maturity of a financial instrument. It has the same relevance for all economic subjects in the form of interest rates determination. Estimation of the term structure discussed in the paper involves obtaining zero coupon interest rates, or discount functions from a set of coupon bond prices. The bootstrapping method is used here to determinate the particular zero coupon interest rates of bonds, where the method consists of iteratively extracting zero coupon interest rates using a sequence of increasing maturity coupon bond prices. Using these rates it becomes possible to derive interest rates for all maturities by making a few assumptions including linear interpolation as we discuss in conclusion of this paper. The particular spot and forward zero coupon interest rates resulting from the bootstrapping method can be used as input in different economic categories like financial management, portfolio management, actuary science, company valuation, management of firm value, financial risk management, etc. The matrix approach derived and described in this paper can be used instead of solving the zero coupon rates sequentially for obtaining a direct solution with particular zero coupon rates. This helps us to diminish the computing severity related to the sequential determination of interest rates using an iterative approach. Fortunately, however, the application of matrix theory helps us to solve this issue very well.
Section:
Finance
Appendix (online electronic version):