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The option seller's math cheat sheet
Here is every formula a covered-call or cash-secured-put seller needs, on one page. Each one is in plain words first, then worked out on the same made-up stock, so you can check your own numbers against it.
The short answer
Most seller math is subtraction and division. The numbers you'll use on almost every trade:
- Break-even = strike − premium (put) or share cost − premium (covered call).
- Max loss = break-even × 100, if the stock goes to zero.
- Premium per dollar = premium ÷ cash set aside.
- Contracts = account × cap ÷ (strike × 100), rounded down.
The rest of this page is the full list, worked on one example. Bookmark it, and check it before each trade in the wheel strategy.
Every formula, on one running example (an illustration, not a trade idea)
A made-up stock, XYZ, trades at $50. Implied volatility is 30%. With 30 days to expiry:
- The put: sell a $48 put for $0.80. Delta about 0.29.
- The covered call: own 100 shares bought at $50, sell a $53 call for $0.70. Delta about 0.28.
All prices are rough model numbers.
Premium and value
| Formula | In words | Example |
|---|---|---|
| Premium × 100 | One contract covers 100 shares | $0.80 × 100 = $80 |
| Call intrinsic | Stock − strike, if above zero | $50 − $53 = $0 |
| Put intrinsic | Strike − stock, if above zero | $48 − $50 = $0 |
| Extrinsic | Premium − intrinsic | $0.80 − $0 = $0.80 |
Out-of-the-money options are all extrinsic, which is the part a seller earns. See intrinsic vs extrinsic value for sellers.
Break-even, max loss and max gain
| Formula | In words | Put example | Call example |
|---|---|---|---|
| Break-even | Put: strike − premium. Call: share cost − premium | $48 − $0.80 = $47.20 | $50 − $0.70 = $49.30 |
| Max gain | Put: premium. Call: (strike − cost + premium) × 100 | $80 | ($3 + $0.70) × 100 = $370 |
| Max loss | Break-even × 100, stock at zero | $4,720 | $4,930 |
| Cushion | (Stock − break-even) ÷ stock | ($50 − $47.20) ÷ $50 = 5.6% | ($50 − $49.30) ÷ $50 = 1.4% |
The cushion is how far the stock can fall before you lose money. On a covered call it's just the premium. The rest of the fall is the stock's. Cushion explained for sellers goes further.
Yardsticks for comparing trades
| Formula | In words | Example |
|---|---|---|
| Premium ÷ cash | Pay per dollar promised (put) | $0.80 ÷ $48 = 1.7% for 30 days |
| Premium ÷ share value | Same for a covered call | $0.70 ÷ $50 = 1.4% for 30 days |
| Simple annualized | Period percent × 365 ÷ days | 1.7% × 365 ÷ 30 ≈ 20% |
| If called | Max gain ÷ share cost | $370 ÷ $5,000 = 7.4% if called at $53 |
These compare trades. They don't forecast anything. Annualizing option premium shows why the annualized line misleads.
Odds and movement
| Formula | In words | Example |
|---|---|---|
| Delta ≈ odds of ending in the money | Rough, from the model | $48 put ≈ 29%, model says about 32% |
| Odds of touching ≈ 2 × odds of ending in the money | Stock trades through the strike before expiry | About 60% or more |
| Expected move (1 SD) | Price × IV × √(days ÷ 365) | $50 × 0.30 × 0.287 ≈ ±$4.30 |
| Straddle move | At-the-money call + put | $1.80 + $1.65 = ±$3.45 |
The $48 strike sits inside the expected move. Expect it to be tested. See the expected move, explained and probability of assignment, explained.
Sizing and recovery
| Formula | In words | Example |
|---|---|---|
| Contracts | Account × cap ÷ (strike × 100), round down | $25,000 × 0.20 ÷ $4,800 = 1.04 → 1 |
| Loss at a test drop | (Strike − dropped price) × 100 − premium | Stock −30% to $35: $1,300 − $80 = $1,220 |
| Rise needed to recover | Loss ÷ (1 − loss) | −30% needs +43% |
After assignment and rolling
| Formula | In words | Example |
|---|---|---|
| Cost basis after put assignment | Strike − all premiums kept on this stock | $48 − $0.80 = $47.20 |
| Running basis after calls | Basis − each call premium kept | Sell a $49 call for $0.50: $47.20 − $0.50 = $46.70 |
| Net credit on a roll | New premium − cost to close the old one | $1.40 − $1.10 = $0.30 credit |
Your broker's tax basis may differ from this running number. Cost basis after assignment explains why.
Every outcome for the put
| XYZ at expiry | What happens | Shares | Premium | Total result |
|---|---|---|---|---|
| $55 | Put expires | — | +$80 | +$80 |
| $48 | Put usually expires; maybe assigned | $0 | +$80 | +$80 |
| $47.20 | Assigned at $48 | −$80 | +$80 | $0 (break-even) |
| $43 | Assigned at $48 | −$500 | +$80 | −$420 |
| $35 | Assigned at $48 | −$1,300 | +$80 | −$1,220 |
The math is simple. The hard part is accepting the bottom rows before you trade. That's a math example, not a promise.
Notice how lopsided it is. The best row pays $80. The $35 row costs $1,220, about fifteen times as much. Every formula above is a way of seeing that gap before you sell, rather than after. If you only memorise one line, make it the loss at a test drop: it's the number your account will actually feel when a trade goes wrong.
In plain words: before any trade, write four numbers: break-even, cushion, the loss if the stock falls 30%, and how many contracts your cap allows. If any of them makes you uneasy, the trade is too big or the stock is wrong.
Questions
What is the break-even on a short put?
The strike minus the premium. On a $48 put sold for $0.80, it's $47.20. Below that at expiry, you lose money once assigned.
How do I work out return if called on a covered call?
Add the strike minus your share cost to the premium, then divide by your share cost. For shares bought at $50 with a $53 call sold for $0.70, that's $3.70 on $50, or 7.4% if called. That's a ceiling, not an expected result.
How do I calculate the expected move?
Price × implied volatility × the square root of (days to expiry ÷ 365). Or add the at-the-money call and put prices. Both are rough and assume no view on direction.
Is there a quick way to check all of this?
Our cash-secured put calculator and covered call calculator run the main numbers for you. Check them against this page the first few times.
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