Consider that all swaps involve yearly payments on both the fixed-leg and the floating-leg where the latter is associated with the Libor 12-month. The payoffs on the FRAs also depend on the realizations of the Libor 12-month. As a swap market-maker your Bloomberg terminal provides you the following information:

T	Spot Rates	Zero-coupon
0.5	0.05	0.975
1	0.05	0.951
1.5	0.055	0.921
2	0.055	0.896
2.5	0.06	0.861
3	0.06	0.835

You also observe that FS(0,1,3) = 7.5%, which is not a rate consistent with the absence of arbitrage.

a) Find F(0,2,3) and knowing that F(0,1,2) = 0.062, then use these forward rates to determine what should be the rate FS(0,1,3) that is consistent with the absence of arbitrage.

b) Given your answer in a), briefly explain the positions to be taken to exploit this arbitrage opportunity for a notional amount of $100.

Note of notation:

Note of notation:

FS(t, T_a, T_B) : Forward start swap applied between T_a and T_B, observed at time t=0

F(t,T_a,T_B): Forward rate at time t between T_a and T_B