Why does a swap that started at zero end up worth millions?

A swap is worth approximately nothing on the day it's signed. A day later it isn't, and by year three it can be one of the largest numbers on a balance sheet. Understanding why is what separates knowing the mechanics from understanding the risk.

The value is the gap between your rate and today's rate

You are paying 4.00% fixed on $10,000,000 for five years. A year passes and the market swap rate for the remaining four years is now 5.00%. Anyone entering the same trade today pays 5.00%. You pay 4.00%. You are advantaged by 1.00% of $10,000,000 = $100,000 per year for four remaining years.

Those four future advantages have to be discounted back to today. At around 5%, the four-year annuity factor is roughly 3.55, so:

Value ≈ $100,000 × 3.55 ≈ $355,000 in your favour.

The counterparty's position is the exact mirror: −$355,000. A swap is zero-sum to the penny between the two sides.

If instead the market rate had fallen to 3.00%, the sign flips and the same swap is worth roughly −$355,000 to you. Nothing about the contract changed. The world moved.

The rule of thumb

A swap's value moves like a bond's does — the longer the remaining life, the harder it swings:

These are rounded illustrations, not quotes. The shape is the lesson: duration is the multiplier, and a thirty-year swap is a violently sensitive instrument to a rate move that looks small in a headline.

Why this is not a paper number

Here is the part that matters. Under modern collateral practice, that mark-to-market is funded in cash, usually daily. The side that is $355,000 underwater posts $355,000 of variation margin — real money, moved, now.

So a contract with a zero purchase price generates genuine cash demands as rates move. A hedge that is working perfectly in economic terms can still create a liquidity problem, because the hedge's losses are settled in cash today while the offsetting gain on the underlying loan arrives slowly over years. Institutions have been forced to sell assets to meet collateral calls on hedges that were, in the end, correct.

That mismatch — economically hedged, operationally short of cash — is one of the most important ideas in derivatives, and it recurs in every remaining lesson of this course.

In the data

Repricing a swap needs a discount curve, and the US Treasury curve is the usual public proxy for it. Six points of it are below, on the latest day.

The Treasury publishes the curve at fourteen fixed maturities, from one month to thirty years. A cash flow that does not land exactly on one of them has to be valued at a rate read off the line between its neighbours, and how you draw that line moves the resulting mark. Two desks reading identical yields can carry the same swap at different values without either having made an error.

The Treasury curve is also not the swap curve. Dealers value a dollar swap off the SOFR curve, and the gap between a swap rate and the Treasury yield of the same maturity, the swap spread, is a traded number that has sat below zero at long maturities for most of the past decade. A ten-year swap marked off the Treasury curve differs from the dealer's mark by that spread times the annuity factor, which on $10,000,000 is a five- or six-figure difference rather than a rounding one. Overnight SOFR anchors the short end; treat the Treasury curve as a proxy to be corrected for the spread.

Try it now

1. A year of the US ten-year government yield is below. Read it as a yield, not a price: a reading of 4.6 means 4.6 per cent, and nothing trades in the series, so it shows no volume. Measure the twelve-month move in percentage points off it.

2. Using the table above, estimate the mark-to-market swing on a $10,000,000 ten-year swap over that period. Is it bigger or smaller than you expected?
3. Now ask the liquidity question: if that value moved against a holder who had to post it in cash, where would the cash come from? Write the answer as a question you'd ask a company's treasurer, not as a verdict.