Forward rate implied by spot rates

Computes the annual effective forward rate for the interval from time n to time n + k: $$ (1+z_{n+k})^{n+k} = (1+z_n)^n(1+f_{n,k})^k. $$

Usage

fnk_from_z(z, n, k)

Arguments

z

Numeric vector of annual effective spot rates for maturities 1, ..., length(z). Each value must be greater than -1.

n

Nonnegative integer forward-start time.

k

Positive integer forward period.

Value

A numeric scalar.

Examples

z <- c(0.03, 0.04, 0.05, 0.06, 0.07)
fnk_from_z(z, n = 1, k = 4)
#> [1] 0.0802404
fnk_from_z(z, n = 2, k = 2)
#> [1] 0.08038462