An FRA entered into some time ago ensures that a company will receive 4% (with s

Question

An FRA entered into some time ago ensures that a company will receive 4% (with semi-annual compounding "s.a") on $100 million for six months starting in one year. The forward LIBOR rate for the period is 5% (s.a.) and the 1.5 year rate is 4.5% with continuous compounding. If the 6-month interest rate in one year turns out to be 5.5% (s.a.), what is the payoff from the FRA? -$0.75M = $100M times (0.04 - 0.055) times 0.5 What is the amount at which the transaction could be settled in one year? (i.e. value at time = 1.0) -$0.73M = (-$0.75M)/(1.0275)

Explanation / Answer

Amount of settlement = notional amount * { (FRA rate - reference rate) * (days/basis) / ( 1+ (reference rate * (days / basis)) }

where notional amount is $ 100 million

FRA rate is 4% = 0.04

reference rate is 5.5 %= 0.055

days/ basis = 180 /360 = 0.5

here in the above example the numerator is calculate in first part and denominator is calculated in the secound part

lets see by putting the values in the formula

Amount of settlement = $100 M { (0.04 - 0.055) * (180/360) / (1+ ( 0.055 * (180/360)) }

= - $ 0.75 M / ( 1+ (0.055 * 0.5) )

= - $ 0.75 M / ( 1.0275) = - $ 0.7299 M or - $ 0.73 M

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