Question

PROBLEM №3

In 270 days, a US-based company expects to borrow $ 15,000,000 for a period of 90 days at 90-day Libor set in 270 days. The company is concerned that rates may increase.

At time 0, this company enters a 9 × 12 FRA, an instrument that expires in 270 days and is based on 90-day Libor. The company will receive floating (long position).

At time 0:

90 -day Libor in USD (Lh) is 1.7%.

270 -day Libor in USD (Lh) is 2.1%.

360 -day Libor in USD (Lh) is 2.5%.

After 90 days:

90-day Libor in USD (Lh) is 1.62%.

180-day Libor in USD (Lh) is 1.9%.

270 -day Libor in USD (Lh) is 2.05%.

360 -day Libor in USD (Lh) is 2.5%.

After 270 days:

90-day Libor in USD (Lh) is 1.75%.

270 -day Libor in USD (Lh) is 2.2%.

360 -day Libor in USD (Lh) is 2.6%.

What is a price of this FRA at time 0?

What will be the payment paid or received to settle this contract? Further, please specify what party will make a payment and when?

What will be a value of an existing 9×12 FRA to the short and to the long parties 90 days from initiation of that contract?

In 270 days, a US-based company expects to borrow $ 15,000,000 for a period of 90 days at 90-day Libor set in 270 days. The company is concerned that rates may increase.

At time 0, this company enters a 9 × 12 FRA, an instrument that expires in 270 days and is based on 90-day Libor. The company will receive floating (long position).

At time 0:

90 -day Libor in USD (Lh) is 1.7%.

270 -day Libor in USD (Lh) is 2.1%.

360 -day Libor in USD (Lh) is 2.5%.

After 90 days:

90-day Libor in USD (Lh) is 1.62%.

180-day Libor in USD (Lh) is 1.9%.

270 -day Libor in USD (Lh) is 2.05%.

360 -day Libor in USD (Lh) is 2.5%.

After 270 days:

90-day Libor in USD (Lh) is 1.75%.

270 -day Libor in USD (Lh) is 2.2%.

360 -day Libor in USD (Lh) is 2.6%.

What is a price of this FRA at time 0?

What will be the payment paid or received to settle this contract? Further, please specify what party will make a payment and when?

What will be a value of an existing 9×12 FRA to the short and to the long parties 90 days from initiation of that contract?

thats all is provided

Answer 1

Here, the company plans to borrow $15,000,000 after 270 days for 90 days and also expects that the interest rate will be increased after 270 days. So it plans to take long position(Buy) forward rate agreement so that it will have to pay only fix interest rate.

Current Rate of LIBOR for 90 Days or Forward Rate for Contract = 1.70%

After 270 days, the Rate of LIBOR for 90 days = 1.75%

PARTY WHICH WILL MAKE THE PAYMENT AND AMOUNT OF PAYMENT=

In this case, interest rate has been increased, so the company will receive the settlement amount which can be calculated by following formula which describes discounted amount based on interest rate differential.

$\frac{Borrowing Amount*[(Reference Rate-Forward Rate)*(FRA Periods in Days/360)])}{1+Reference Rate(FRA Period in Days/360)}$

$\frac{15000000*[(0.0175-0.017)*(90/360)]}{1+[0.0175*(90/360)]}$

= $ 1,86,683.2607

So, the company will receive $1,86,683.2607 from the seller of the contract at the date of initiation of the period i.e. 270 days from time 0.

VALUE OF THE CONTRACT AT TIME 0 =

At time 0, the value will be discounted amount of $1,86,683.2607 i.e. calculated as below

$\frac{186683.2607}{1+[0.021*(270/360)]}$

= $1,83,788.5904

So, at time 0 the value the company receive is $1,83,788.5904

Here, the discount rate is used 2.1% prevailing at this date because for 270 days, the amount can be borrowed at this rate only at this time.

VALUE OF THE CONTRACT AFTER 90 DAYS FROM THE INITIATION OF THE CONTRACT =

In the case of FRA, settlement is done on the date of initiation of the contract, in this case, 270 days from now. So, after finding amount based on interest differential, we discount it with the period of contract and reference discount rate. If we don't discount it, we will get the value of the contract at maturity date i.e. in out case, 90 days from the initiation of the contract.

= 15000000*[(0.0175-0.017)*(90/360)

= $1,87,500

Thus, the company will receive $1,87,500 on the 90th day from the initiation of the contract. The value is the same for both to the short and to the long parties.