# Cap and floor... Discount by 1+R?

Under option chapter, expirarion value of cap is discounted by 1+one year rate

while under cap-floor chapter, periodic payment doesn’t have the discount.

why?

Are they valuing them at the same time?

Yes, in the option chapter, it use bionomial and just straight forward in cap-floor chapter, So let me ask this way. If in time0 I buy a cap at 3%, interest rate in time0=4%, time1=5% time2=6%, than I will recieve (5%-3%)*NP, at time1 , right?

No; you’ll receive (4% - 3%) × NP at time 1. The floating rate is set at the beginning of the period, not at the end.

Thank you! so can I say the cap is like swap, rather than FRA?

Along the same lines, why does the “Interest Rate Derivatives” chapter seem to not discount the amounts back one period? Is it assumed that the LIBOR rate started one period before so that, for example, the 7.7% rate was established at t=0?

Suppose that a cap has a rate of 8% and a notional amount of 100MM. Settles quarterly, reference rate is 3 month LIBOR. 3 month LIBOR for the next 4 months is as shown, calculate each quarter’s payoff.

Quarter 3 Month LIBOR

1 7.7%

2 8%

3 8.4%

4 8.6%

Quarter 3 payoff = 1,000000((.084-.08)/4) = 100,000

Quarter 4 payoff = 1,000,000((.086-.08)/4) = 150,000

it makes sense as @S2000magician explained that we got paid off at the end of Q3 by 100,000.

But the bionomial part is still confusing… anyone?

Hey Steve, it seems I found the answer. On nots p72, professor’s note: Cap and floors pay in arrears: payoff occurs one period after expiration. The basic of caps and floors are discussed in the next topic.

Options (derivatives in general) pay at maturity not at expiration so no discounting here. FRA, however, pays at expiration of the contract so you need to discount payoff from maturity date to expiration date.