svensson: Spot Rate Function according to Svensson
Description
This function calculates the spot rates for certain maturity dates and a parameter vector
according to Svensson (1994).
Usage
svensson(beta, m)
Arguments
beta
a vector of parameters $\bm{\beta} = (\beta_0, \beta_1,\beta_2,\tau_1, \beta_3, \tau_2)$.
m
one maturity (or a vector of maturities).
Value
Returns a vector consisting of the calculated spot rates.
Details
The spot rate according to Svensson for a maturity $m$ is calculated using the following function:
$$s(m,\bm{\beta}) = \beta_0 + \beta_1\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} + \beta_2\left(\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} - \exp(-\frac{m}{\tau_1})\right) + \beta_3\left(\frac{1-\exp(-\frac{m}{\tau_2})}{\frac{m}{\tau_2}} - \exp(-\frac{m}{\tau_2})\right)$$
References
Lars E.O. Svensson (1994):
Estimating and Interpreting Forward Interest Rates: Sweden 1992 -1994.
Technical Reports 4871, National Bureau of Economic Research.