pricing a swap
Building a swap spread from the dealer's costs, working through one quarter with live SOFR, and a calculator to try your own numbers.
concept note · live ratesa swap's spread is a cost stack
The spread on a swap isn't pulled from thin air. The dealer builds it up from what the hedge costs to hold, then subtracts anything the hedge earns. If you understand the stack, you understand why two clients get different prices for the same stock.
When a carrier gives you a phone for a monthly fee, the fee covers the handset's cost, the carrier's financing of it, and a margin, minus anything it earns back. A swap works the same way. The dealer buys the stock (the handset), finances it, and charges you rate + spread each period until you hand it back.
building the spread for a long swap
Illustrative ranges for a liquid name. They move with the client, the stock and the dealer's balance sheet.
| Component | Why it exists | Illustrative |
|---|---|---|
| Dealer funding over the reference rate | the dealer can't borrow at SOFR itself; it pays a bit more | +10 to +30bp |
| Balance sheet and capital | the hedge shares use capacity that regulators charge for | +10 to +30bp |
| Execution costs, spread over the term | commissions, market impact, HK stamp duty of 0.1% on each side | +5 to +20bp a year on a 1-year trade; far more on a 1-month one |
| Securities lending income | the dealer can lend out the shares it holds as a hedge | −0 to −15bp |
| Client and relationship | a big, steady client gets a tighter spread | ± |
| Typical all-in | ≈ 45bp used on this site |
The execution line explains something counter-intuitive: stamp duty is a one-off cost, so a short-dated swap has to recover it over fewer days and needs a much wider annualised spread.
and for a short swap
The dealer now has to borrow the stock to short it as a hedge. It receives cash from the short sale and earns interest on it, but pays a borrow fee. So the client on a short swap receives rate − spread − borrow fee. For an easy-to-borrow name the fee is a few basis points. For a crowded short it can be several percent, which is why the same quote of "SOFR − 30bp" can mean very different things by name.
A swap is economically a forward, reset each period. r is the reference rate, s the spread, q the dividend yield. Raise the funding (r + s) and the forward rises; raise the dividends and it falls.
worked example: one quarter of a usd swap
The 90-day SOFR average stands in for the compounded SOFR a swap resetting last quarter would have paid.
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the tradelong US$10,000,000 total return swap · 91-day period · SOFR + 45bp · 2% dividend yield · stock rises 3%
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equity leg10,000,000 × 3%+$300,000
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dividends passed through10,000,000 × 2% × 91/365+$49,863
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funding leg−10,000,000 × (compounded SOFR ≈ 3.646% + 0.45%) × 91/360−$103,542
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net payment to you+$246,321
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break-eventhe stock has to rise 0.54% in 91 days just to cover funding net of dividends.
try it: one period of a swap
Pre-filled with today's SOFR. Switch to HKD to load one-month HIBOR and ACT/365. Try setting the stock move to zero to see what carry alone costs, or switch to short and compare.
The same arithmetic as the worked example. Borrow fees on shorts aren't included; subtract them from the spread.
valuing a swap after you've traded it
At each reset the swap is worth roughly zero: the equity leg settles, and the notional is re-struck at the current price. Between resets its value is the accrued equity move + accrued dividends − accrued funding.
There's one more piece, and it's the one that matters if you exit early. If your spread is locked for a term and the market spread has changed, your contract is off-market. Its value is that spread difference over the remaining life:
Example: N = $10m, locked at 60bp, the market now quotes 40bp, 9 months left. ≈ 10,000,000 × (−0.20%) × 0.75 ≈ −$15,000. The long is overpaying, so the lock is worth about $15k to the dealer, and that's what an early exit negotiation is about. Many prime-broker swaps can be terminated at any time without this charge; it bites only when the spread is term-locked.
- Spread = dealer funding + balance sheet + execution − lending income, give or take the relationship.
- Longs pay rate + spread; shorts receive rate − spread − borrow fee.
- One period: equity move + dividends − (rate + spread) × days/basis.
- A term-locked spread that's now off-market has a value, and it's what an early unwind is priced on.