The bull put spread

Sell a put below the price, buy a further one below that, and keep the difference.
The trade people reach for when they are mildly optimistic — and do not want punishing for being early.

What it is

Two legs. Same stock, same expiry.
You sell a put. That is the obligation, and the income.
You buy a cheaper put underneath it. That is the cap.
The difference between the two premiums is paid to you the moment you open the trade.

What you are actually agreeing to

You are paid to open it.
You keep the payment if the stock stays above the strike you sold.
The put you bought caps what you can lose — it is not there to make money, it is there to stop the loss running.
That cap is what turns an open-ended obligation into a number you can see before you enter.

The trade, written out

Everything above is the idea. This is the position — the lines you would actually send to a broker.

Order ticket

Leg	Action	Qty	Expiry	DTE	Strike	Delta	Price
1	Sell to open	-1	16 Oct 26	45	95 Put	+0.25 (25Δ)	$1.35
2	Buy to open	+1	16 Oct 26	45	90 Put	-0.10 (10Δ)	$0.41
Net	Credit	1 position	16 Oct 26	45	$5 wide	+0.15	$0.93

SELL -1 VERTICAL XYZ 16 OCT 26 90/95 PUT @ 0.93 CREDIT

Reading it back

One expiry. Both legs share it, which is what makes this a vertical.
Sell the 95 put. That is the income and the obligation.
Buy the 90 put. That is the cap, and what it costs.
The net is paid to you on the day you open — the ticket above shows it.

On delta, since it is written two ways

The model gives a put a negative delta.
Traders drop the sign and the decimal and say “25 delta”.
Same number. The ticket shows both so neither reader is lost.
Selling a put means you are long that delta — the minus signs cancel, which is why the net position is bullish.

The argument

Bull

makes the claim

This is my kind of trade. I don’t have to be right about direction — only about how far it won’t fall. The stock can rise, sit still, or drift down a little, and I still keep the lot.

Bear

doubts it

You are being paid rent, and rent is paid for a reason. That credit is what somebody thinks it is worth to be able to hand you the stock at 95. Collect it forty times, give it back twice, and you have gone backwards.

Ferret

settles it

Neither of you has said anything I can count. Which delta, which tenor, how wide, what minimum credit — and what closes it. Name those and I will go and measure. Until then you are both describing a mood.

The shape of it

The bull put spread on XYZ at $100 · 25% volatility · 4% rate · 45 days. Priced from the model, not written by hand.

	At expiry
Credit taken in	$93
Maximum profit	$93
Maximum loss	$-407
Breakeven	$94.07

The thick line is the payoff at expiry.
The faint lines are the same position with 45, 21 and 7 days left.
The gap between them is the trade.
At 45 days the line is a soft curve and almost nothing is decided. By 7 days it has hardened into the shape everyone recognises.
Nothing about the position changed. Only the time left did.

Where you actually enter

The chart above is the shape at expiry. It puts the bend right next to the money, which makes the trade look like it is already on the edge. It is not — here is the day you open it.

The same structure set up at 20Δ · 45 days · credit $78. The shaded band is the room between the stock and the strike you sold.

The same price, two different days

	On day one	At expiry
Stock at $94 (the strike you sold)	$-109	$78
Stock unchanged at $100	$0	$78

You enter at the dot, with the stock well above the strike you sold and the position worth nothing yet.
The shaded band is your room — how far the stock can fall before the strike is even reached.
At the short strike the two days disagree completely. At expiry that price is a full win. On day one it is a loss bigger than the whole credit.
That is not a quirk of the chart. It is the reason a stop set off the expiry picture fires when nothing has actually gone wrong yet.

Different ways to set it up

There is no such thing as the bull put spread. There is a family of them, and two dials decide which one you are holding.

How long you give it — the tenor.
How far out you sell — the delta.
Every panel below is the same $5-wide spread on the same $100 stock. Only those two things change.

Same delta, four tenors

Days	Short strike	Away from spot	Credit	Max loss	Risk : reward
7	97	+3.0%	$33	$-467	14.0 : 1
21	95	+5.0%	$51	$-449	8.8 : 1
45	94	+6.0%	$78	$-422	5.4 : 1
90	92	+8.0%	$91	$-409	4.5 : 1

20 delta is not a distance. At a week it puts the strike a few per cent below the stock; at three months the same 20 delta sits far further down.
Time is what buys the distance. The delta number does not move; the room underneath it does.
And the payoff is not close. Read the risk-to-reward column — the short-dated version is paying a fraction of the risk it carries.
Look at the panels: the short-dated one has almost no gap between its day-one line and its expiry line. There is no time left to be wrong in.

Same tenor, three deltas

Delta	Short strike	Away from spot	Credit	Max loss	Risk : reward
40Δ	99	+1.0%	$169	$-331	2.0 : 1
25Δ	95	+5.0%	$93	$-407	4.4 : 1
15Δ	92	+8.0%	$52	$-448	8.6 : 1

Selling closer to the money pays more and is hit more often. That part is obvious.
What is not obvious is the ratio. The further out you go, the worse the risk-to-reward gets, because the credit falls faster than the risk does.
A 15 delta strike is not a 15% chance of losing. It is a rough stand-in for finishing in the money, and it says nothing about what you lose when it happens.
Whether the extra room pays for the worse ratio is a question we can test. It is on the list.

Delta and tenor are two of the four numbers that turn a name into something testable. Width and minimum credit are the other two.

What the Greeks are doing

Four questions about the same position, and a fifth that barely applies here.
Every structure answers them differently, which is why this site never writes a general page about the Greeks.

Days left	Delta	Gamma	Theta / day	Vega	Rho
45	+15.0	-1.64	$+1.23	$-5.07	$+1.97
21	+14.4	-3.08	$+2.48	$-4.44	$+0.86
7	+6.3	-3.52	$+2.95	$-1.69	$+0.12

The position at entry — stock $100 · 25% volatility. Per contract, from the model.

Delta — which way you need the stock to go

The put you sold is the bigger of the two legs.
So the position leans bullish whether you meant it to or not.
The delta column above is roughly a share-count bet that the stock does not fall far.

Theta — what time does to you

Time is on your side here, which is the reason people sell these.
The number in the table is what one quiet day is worth.
It is not free income — see the next section.

Vega — what a change in fear does to you

You are short volatility. A jump in implied volatility widens the spread against you.
It can happen with the stock barely moving, which is what surprises people.
The position recovers if volatility falls back, and that is the difference between a mark and a loss.

Gamma — how fast your delta turns against you

Negative, and the closer to the short strike, the more negative.
It is the price of being paid theta, and the two cannot be separated.

Rho — what a change in interest rates does to you

Almost nothing at this tenor.
It is here because knowing when a number can be ignored is worth as much as knowing when it cannot.

Theta and gamma are one thing

This is the part that decides whether the strategy works, and it is almost never put plainly.

You cannot be paid theta without being short gamma. They are not two features of the trade. They are the rent and the risk on one lease.

The same position, three points in its life

Nothing about the position changes.
The stock sits still at $100 throughout.
Only the days left move.

Days left	Delta	Gamma	Theta / day	Vega	Rho
45	+15.0	-1.64	$+1.23	$-5.07	$+1.97
21	+14.4	-3.08	$+2.48	$-4.44	$+0.86
7	+6.3	-3.52	$+2.95	$-1.69	$+0.12

Now move the stock to $95.50

Same three dates. Same spread.
But now just above the strike you sold — which is where these trades are actually decided.

Days left	Delta	Gamma	Theta / day	Vega	Rho
45	+21.8	-1.18	$+0.67	$-3.31	$+2.78
21	+29.3	-2.90	$+1.94	$-3.80	$+1.70
7	+38.4	-9.25	$+6.81	$-4.05	$+0.72

Gamma goes from -1.18 to -9.25.
Theta goes from $+0.67 a day to $+6.81.
Both climb, and neither is available without the other.
Delta now moves roughly 8 times as far for every dollar the stock travels.

Which is what DTE actually sets

Days to expiry is not one dial among several.
It is the dial that moves both numbers at once, in the same direction.
Shorter tenor: more income per day, more violence per dollar.
Longer tenor: less of both.
There is no setting that hands you one without the other.

The trap

Every structure has one thing that catches people. On this one it is the stop.

A stop here is a percentage of what you staked — not of what you can lose.

You took in the credit on the ticket above.
You can lose the width less that credit.
A two hundred per cent stop means letting the spread run to three times the credit against you before you act.
It does not mean losing twice the trade.

Why it matters

Get it the wrong way round and the stop fires far too early, or far too late.
A working strategy becomes a losing one without a single rule appearing to change.
It is the most common way we see credit spreads mis-sized.

How this shows up in our tests — pending. No result has been published on this structure yet.