Guys, This has been the most daunting. Lets say ,Sam goes long on FRA for 60 days maturity based on 90 days LIBOR. Contract Rate is 6%. 0) Is the payoff known at start of contract (because we refer to starting period LIBOR for next period payoff?) 1) So at the expiration- What does the long get if the LIBOR at expiration is above contract rate? Is it the present value ? 2) Is the payroff at expiration or payoff is date of expiry of 90 days? {(Notional Amt)(Floating LIBOR(90/360)- Fix)}/(1+ Floating LIBOR(90/360)) What is to be done when its an interest rate option? 1)Do we also take present value at expiration here? 2) Is the payoff known at start of contract (because we refer to starting period LIBOR for next period payoff?) Pls enlighten me !
I think you have the formula wrong… Principal * (Expiry Rate - FRA Rate)(360/t) / (1+Expiry(360/t)) Easier to see the formula when its a image. http://en.wikipedia.org/wiki/Forward_rate_agreement
You use the value of the Libor at expiration of the FRA, because that will be the beginning rate to be used fr your underlying. Having said that, when your FRA expires, you compare the fra rate to the libor. Let’s say libor90 rise, so the long profit as he can borrow at lower rate than market for the next 90 days. 1. you calculate the saving in interest: value of the libor at expiration of the fra * 90/360 * notional 2. This interest saving is settled right away, at expiration of the fra, while the actual interest on your underlying will be due in 90 days, at maturity of the loan. That’s why you have to discount the interest saving calculated over the maturity of the underlying, 90 days. Personnally i use these 2 steps as i find it easier than the formula For interest rate option, the settlment is done not at expiration of the option, but at maturity of the underlying (or the next reset date of for caplet in the case of cap). So no need to discount, the interest saving calculated is your payoff = settlement amount
Formula: Notional Principal * ((Ref rate-Forward Rate)*(Days/360))/(1+(Ref rate*(Days/360)) The payment is made at expiration or settlement and is based on the LIBOR rate specified in the contract. Most problems tell you the end rate. If the Ref rate is above the forward rate the long receives a payment. If the Ref rate is below the forward rate the short receives a payment (the numerator will be negative). In either case they receive/pay the present value of the interest because the settlement time and the LIBOR rate the FRA is based on are two different times. So they have to discount the payment by the timing difference essentially, otherwise it would just be the difference in the Ref rate and the forward rate. Hope that helps!
Thanks MB45 and Miss*Yiota. Here is my understanding. For FRA,discount the savings. Ans (Savings/Discount) For interest Rate options, dont discount the savings: Ans (Savings) Can you pls confirm if this understanding is correct. Also, speaking of similar problem,lets say there is swap with fixed payer paying : 5 % and Floating Rate Payer paying based on LIBOR at the beginning of quarter. If the initial quarter LIBOR is 3% The long will get (Notional Amt){(LIBOR(Days/360)- FIXED)} Can you pls confirm this too?
your understanding for FRA and options is correct. For swaps, you can’t have a swaps with the 2 legs payer as in your example. Anyway just keep in mind that for a plain vanilla swap, there is no exchange of notional and the interest on the 2 legs are NETTED. So you calculate what you’ll receive (fix or float leg) and calculate also what you’ll pay. Then you calculate the difference of the 2, that give you your payoff Note that for cross currency swaps, you DONT net the 2 legs at all
Dontknow1987: You are correct on the FRA portion. The Plain vanilla swap you are referring to in the second paragraph needs revision. Don’t look at from a long or short perspective because that will just confuse you more. Plus the equation is not exactly right. Net fixed rate payment= (Swap fixed rate- LIBORt-1)*(#days/360)*(Notional principal) If number is negative fixed payer receives the difference If number is positive fixed payer owes the difference *Net interest is paid by the one who owes it*