I think I understand how to value a fixed rate bond w/ forward rates but is it possible to value a value a floating bond (e.g. LIBOR) w/ forward rates? I only know the formula L*exp(r*(t-t’)) where L is the notional principal r is the forward rate t is the time between payments t’ is the time to the next payment, so when t=t’, the value of the bond becomes L but I can’t prove this using forward rates. Can someone help? Thanks!
i believe its like a floating rate swap. It goes to par at every payment date… maybe im wrong…
urymoto1 Wrote: ------------------------------------------------------- > i believe its like a floating rate swap. > > It goes to par at every payment date… > > maybe im wrong… Yes it is but I don’t know how to explain the fact that it goes to par with forward rates.
just like you would with a swap…
Let’s put it another way. What are the cash flows of this floating bond? Are they related to the forward rates at all?
Well, according the CFA text, at level II we can simply assume that the floating rate bond is worth par at next reset. So why do we need forward rates at all?
plyon Wrote: ------------------------------------------------------- > Well, according the CFA text, at level II we can > simply assume that the floating rate bond is worth > par at next reset. So why do we need forward > rates at all? I think I really want to understand this as oppose to just memorizing it…
Let’s put it this way… If I tell you that I’m going to pay you the market rate for something in the future, how much is that worth to you? Note that I’m not asking you to tell me what that rate IS in the future, but rather, how much are you willing to pay for my promise to actually PAY the market rate? Basically, your answer should be ZERO. If you are not willing to pay for that privilege (and I’m presumably not willing to pay you for the right to pay a market rate to you), then it doesn’t matter what market rates are in the future. The bond is worth par at next reset because on that date it will pay the market rate. No more (no premium) and no less (no discount).
But is it possible to express this as cash flows discounted by forward rates? Also, what about the value in between payments?
Yes, it is possible to express this as cash flows discounted by forward rates, but the forward rates you use would just cancel out of the equation and you would be left with par (try this at home if you like — but if I promise to pay you 1+r in the future, and you discount that future payment by (1+r), I think we can all agree that r doesn’t matter anymore). The value in between payments is pretty easy becauase we already know what the coupon rate on the bond is. Assume this is a three month LIBOR floating rate note that reset last month at 5%. So we know we are receiving 5% in interest for the next two months – discount that at today’s rate and you have an answer. Again… forward rates are a non-issue in this valuation.
But are they going to be discounted by the same forward rates we used to value a similar fixed rate bond? If so, the argument you presented doesn’t seem to hold…