Question

Suppose that 6-month and 9-month LIBOR are 7% and 9% with continuous compounding. RST Inc. enters into a FRA to receive the forward market rate and pay 12% measured with quarterly compounding, on a notional principal of $1 million for 3 months beginning after 6 months from now.

(a) Is RST a FRA buyer or seller?

(b) What is value of this FRA to RST

Answer 1

Ans a)

Here RST received a Fixed Forward Rate of 12%. In FRA those who receive Fixed Rate are Buyers.

Ans: RST a FRA buyer

Ans b)

6-month LIBOR = 7% = 0.07

Effective Days = 6 Month = 180 Days

Effective Interest Rate for Period I6 = 0.07 * ( 180/360) = 0.035

9-month LIBOR = 9% = 0.09

Effective Days = 6 Month = 270 Days

Effective  Interest Rate for the Period    I9 =   0.09  *  ( 270/360)   = 0.0675

Now Effective Interest Rate for  3 months beginning after 6 months from now = 6I9

As Per FRA Principle :

( 1 + I6) * ( 1 + 6I9) = ( 1 + I9)

( 1+ 0.035) *  ( 1 + 6I9) = ( 1 + 0.0675)

1 + 6I9 = 1.0314

6I9 = 0.0314

Now this 6I9 is interest rate for 90 Days

Annual Interest Rate will be = 6I9 * ( 360/90) = 0.0314 * ( 360/90) = 0.1256 = 12.56%

Now

Value of FRA to RST =

Here FRA settled on After 09 Months But we are Valuing Today

So

Discount Factor = 1 / (1+ I9 ) = 1 / (1+ 0.0675) = 0.93677

Amount = $1 million = 1000,000

Value of FRA to RST

= - 58.28

value of this FRA to RST - 58.28 (Ans)