Cash Flow and Present Value for a Floating-Rate Basis Swap

Summary

The document explains how to calculate periodic cash flows and present values for a USD cross-currency basis swap involving three-month and twelve-month LIBOR legs. For each period, it multiplies notional by the accrual fraction and the applicable LIBOR fixing plus any spread. Present value uses the payment-date discount factor and the forward LIBOR rate for that accrual period; summing these values gives each leg’s value, and the swap value is the difference between the two legs.

A second response notes that, under equal notionals, the legs consist of the index rate plus the applicable spread, with the spread on the twelve-month leg in the described setup. The calculation assumes interest-only cash flows until principal exchanges occur. It omits the delay between fixing and settlement and depends on the specified day-count convention and discount factors.

Key ideas

• A floating coupon equals notional times its accrual fraction times the fixing plus spread.
• Present value discounts each projected coupon using the payment-date discount factor.
• The value of a leg is the sum of its discounted projected cash flows.
• The swap value is the difference between the two leg values.
• The example neglects the usual delay between fixing and settlement.

Tags

# How to calculate cash flow for XC swap


# How to calculate cash flow for XC swap












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

## Answer by AFK (score 1)

https://quant.stackexchange.com/a/18806

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).

## Answer by MattR (score 0)

https://quant.stackexchange.com/a/15416

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.