termstrc (version 1.1.1)

spotrates: Function for the Calculation of the Spot Rates

Description

The function calculates the spot rates for the chosen approach, a provided maturity vector and parameter set.

Usage

spotrates(method, beta, m)

Arguments

method

"Nelson/Siegel" or "Svensson".

beta

parameter set $\bm{\beta}$.

m

maturity or a vector of maturities.

Value

• Returns a vector with the calculated spot rates.

Details

The spot rates according to Nelson/Siegel are defined as: $$s(m,\text{bm}\beta )={\beta }_0+{\beta }_1\frac{1-\exp (-\frac{m}{{\tau }_1})}{\frac{m}{{\tau }_1}}+{\beta }_2(\frac{1-\exp (-\frac{m}{{\tau }_1})}{\frac{m}{{\tau }_1}}-\exp (-\frac{m}{{\tau }_1})).$$ Svensson defines the spot rate function as follows: $$s(m,\text{bm}\beta )={\beta }_0+{\beta }_1\frac{1-\exp (-\frac{m}{{\tau }_1})}{\frac{m}{{\tau }_1}}+{\beta }_2(\frac{1-\exp (-\frac{m}{{\tau }_1})}{\frac{m}{{\tau }_1}}-\exp (-\frac{m}{{\tau }_1}))+{\beta }_3(\frac{1-\exp (-\frac{m}{{\tau }_2})}{\frac{m}{{\tau }_2}}-\exp (-\frac{m}{{\tau }_2}))$$

References

Charles R. Nelson and Andrew F. Siegel (1987): Parsimonious Modeling of Yield Curves. The Journal of Business, 60(4):473--489. Lars E.O. Svensson (1994): Estimating and Interpreting Forward Interest Rates: Sweden 1992 -1994. Technical Reports 4871, National Bureau of Economic Research.