FRN Single-Coupon Replication

Replicate the date-$T$ coupon of a floating-rate note with two zeros and a one-period reinvestment. Face $N = \$100$.

$\mathrm{PV}_0(\text{coupon}) = N\big[\mathrm{DF}(T{-}\Delta) - \mathrm{DF}(T)\big] = N\,\Delta\, f(0, T{-}\Delta, T)\,\mathrm{DF}(T)$

Replication step

Maturity $T$ (years) 5.0

Period $\Delta$ 0.5

$r(0, T{-}\Delta)$ annual 3.50%

$r(0, T)$ annual 4.00%

Realized $r$ at $T{-}\Delta$ 4.50%

DF(T−Δ)

DF(T)

Implied forward f

Coupon at T

PV today
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