Why does a plain vanilla interest rate swap have zero value at inception?

Question

AcadiFi · Accepted Answer

A plain vanilla interest rate swap is structured so that the present value of the fixed leg equals the present value of the expected floating leg at time zero. The swap rate C is chosen such that sum of C times discount factors equals 1 minus the final discount factor, which makes the contract worth zero to both counterparties.

Imagine Meridian Capital enters a 4-year annual-pay swap with Orchard Bank. Using spot rates of 2.10%, 2.45%, 2.80%, and 3.05%, the discount factors are roughly 0.9794, 0.9527, 0.9205, and 0.8860. The fair swap rate solves C times (0.9794+0.9527+0.9205+0.8860) = 1 - 0.8860, giving C ≈ 3.03%. At this rate the PV of each leg matches, so no upfront payment changes hands.

Dealers earn money through the bid-ask spread, not the mid-market rate. A market maker might quote 3.01% bid, 3.05% offer, capturing a 4 bp spread over the trade's duration. They also earn credit valuation adjustment charges on uncollateralized trades and funding valuation adjustments on the balance sheet cost of hedging.

After inception, the swap's value moves with rates. If 6 months later the 3.5-year swap rate drops to 2.70%, the fixed receiver gains because they keep receiving 3.03% on a now below-market contract.

Why does a plain vanilla interest rate swap have zero value at inception?

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