termstrc (version 1.3.7)

spr_ns: Spot Rate Function according to Nelson and Siegel

Description

This function calculates the spot rates for certain maturity dates and a parameter vector according to Nelson/Siegel (1987).

Usage

spr_ns(beta, m)

Arguments

beta

a vector of parameters ${\bm{\beta}} = \left(\beta_0,\beta_1,\beta_2,\tau_1\right)$.

m

one maturity (or a vector of maturities).

Value

• Returns a vector consisting of the calculated spot rates.

Details

The spot rate according to Nelson/Siegel for a maturity $m$ is defined as:

$$s(m,\bm{\beta}) = \beta_0 + \beta_1\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} + \beta_2\left(\frac{1-\exp(-\frac{m}{\tau_1})}{\frac{m}{\tau_1}} - \exp(-\frac{m}{\tau_1})\right).$$

References

Charles R. Nelson and Andrew F. Siegel (1987): Parsimonious Modeling of Yield Curves. The Journal of Business, 60(4):473--489.

Examples

spr_ns(rep(0.01,4),1:30)