I am going through J.C.Hull for swaps. Where he says we can value a swap using bonds. Let $B_{fl}$: value of floating rate bond, $L$ notional principal. Why is $B_{fl} = L$ just after a payment ? What about between payments ? In nutshell how can I calculate the value of such a bond ?
eg. ( notional principal $L=100$ ) If a floating rate bond has expiry in 15 months. And coupon payments are in next 3,9 and 15 months. The LIBOR at preceeding coupon payment date was $3$% (semi annual compounding rate ). Also say the current 3 month LIBOR is $2$% in continuous compounding. The why is bond value/price = $(100+1.5)*e^{-2*(3/12)}$ ? Why aren't the rest of cash flows taken in for pricing, with coupon rates taken to be forward rates ? Is this an approximation ? Or is it the same as even if I take all cash flows into account ? If so how do I prove it ?