Spot rates from forward one-year rates

Converts annual effective forward one-year rates \(f_{0,1}, f_{1,1}, \dots, f_{n-1,1}\) into annual effective spot rates \(z_1, z_2, \dots, z_n\).

Usage

z_from_fn1(fn1)

Arguments

fn1

Numeric vector of annual effective forward one-year rates.

Value

Numeric vector of annual effective spot rates.

Details

Since $$ (1+z_n)^n = \prod_{j=0}^{n-1}(1+f_{j,1}), $$ the spot rates are recovered directly.

Examples

z_from_fn1(c(0.04, 0.05, 0.06, 0.07, 0.08))
#> [1] 0.04000000 0.04498804 0.04996825 0.05494075 0.05990565