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Given 3MLibor vs 12MLibor USD basis swap the 3M Libor is exchanged at 12MLibor+1%. How to calculate the cash flow

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Cashflow at time $T_i$ $$CF_{T_i} = Not \times cov(T_{i-1},T_i) \times ( L(T_{i-1},T_i) + spread)$$ where $L(T_{i-1},T_i)$ is the Libor fixed at time $T_{i-1}$ and $cov(T_{i-1},T_i)$ is the coverage or daycount fraction for period $[T_{i-1},T_i]$ (which depends on the specified convention eg Act/360).

The present value of this cashflow is $$ PV(t) = DF(t,T_i) \times Not \times cov(T_{i-1},T_i) \times ( L(t,T_{i-1},T_i) + spread) $$
where $L(t,T_{i-1},T_i) = E^{T_i}_t[L(T_{i-1},T_i)]$ is the forward Libor and $DF(t,T_i)$ is the discount factor.

Present value of one leg is the sum of cashflow pvs $$ Leg(t) = \sum_i DF(t,T_i) \times Not \times cov(T_{i-1},T_i) \times ( L(t,T_{i-1},T_i) + spread)$$

Finally, present value of the swap is the difference between the two legs pvs.

PS: I neglected the delay between fixing and settlement (usually a few days).

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I assume, you have the same notional for both legs, so in both cases is just the (Index + Spread) * Notional. Note that in this case, you only have a spread in the 12M leg. Until some notional payments are made, it's just interests cashflows.

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  • $\begingroup$ Yes, the notional is same so if we ignore the notational, the cash flow for one leg is 3M Libor rate and the cash flow for the other leg is 12M libor rate + 1%. Is this correct? $\endgroup$ – user13524 Nov 11 '14 at 19:35
  • $\begingroup$ Exactly, there you go. $\endgroup$ – MattR Nov 11 '14 at 20:44

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