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:
$$s(m,\bm{\beta}) = \beta_0 + \beta_1\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} + \beta_2\left(\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} - \exp(-\frac{m}{\tau_1})\right).$$
Svensson defines the spot rate function as follows:
$$s(m,\bm{\beta}) = \beta_0 + \beta_1\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} + \beta_2\left(\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} - \exp(-\frac{m}{\tau_1})\right) + \beta_3\left(\frac{1-\exp(-\frac{m}{\tau_2})}{\frac{m}{\tau_2}} - \exp(-\frac{m}{\tau_2})\right)$$
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.