Question

A bank can borrow or lend at LIBOR. Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that can be locked in for the period between six months and nine months using an FRA is 9%. What arbitrage opportunities are open to the bank? All rates are continuously compounded.

Answer 1

1. T0: I borrow $100 for 9mo, I get the 6% rate, which makes me 100*e^(.06*.75) = 104.60 so loss of 4.60

2. T0: I lend $100 for 6 months at 5%, where i receive 100*e^(.05*.5) = 102.53 so profit of 2.53

3. T0: I buy a 6mo/9mo FRA at 9% to lend $100 for 3months after 6 months

4. T6: Lend $100 for 3 months at 9% (because I’m guaranteed to receive 9% on it because of my FRA)

Interest I need to receive on the loan is 100*e^(0.09*.25) = 102.28 so profit of 2.28

So I pay $4.60 from Borrowing $100, and I receive 2.53+2.28 = 4.81 Therefore I make a guaranteed $0.21 as a result of the arbitrage opportunity.

T0= Today
T6= after 6 months

e = 2.71828