Debit versus credit vertical spreads: probability, expected value and strike selection
Build bull call and bull put spreads with real prices, compute break-even, approximate probability of profit and expected value, and see why the two are mirror images.
What you will learn
- How to price a debit and a credit vertical from the chain and derive maximum profit, maximum loss and break-even.
- How to approximate the probability of profit (POP) from the credit and the width.
- Why the market-implied expected value of any vertical is roughly zero before costs, and where an edge could come from.
- How width and strike choice change the trade's character.
Explanation
The payoff shapes of vertical spreads were introduced in the course Derivatives: Futures, Options, CFDs and Certificates. Here we go from shapes to decisions: which vertical, which width, which strikes, and what the numbers say about the odds.
A vertical spread is one long and one short option of the same type and expiry at different strikes: a debit spread if you pay net premium, a credit spread if you receive it. The width is the strike distance. For every vertical:
- Debit spread: maximum loss = debit paid; maximum profit = width - debit.
- Credit spread: maximum profit = credit received; maximum loss = width - credit.
Probability of profit
Options are priced so that, under the market's own probability distribution, expected payoff equals price. From that follows a widely used approximation:
POP (credit spread) is approximately 1 - credit / width
POP (debit spread) is approximately debit / width
Both ignore interest, fees and fat tails; treat them as a rough reading, not a measured probability.
Expected value
Expected value (EV) = POP x average win - (1 - POP) x average loss. With the approximate POP and the maximum profit and loss, EV is zero for every vertical: the market offers a fair bet before costs, and a slightly negative one after spread and commissions. An edge, if any, must come from a view the market does not share: IV above the volatility that will be realised, a direction more likely than delta implies, or management rules that cut losers early. None is guaranteed.
The mirror image
A bull call spread and a bull put spread with the same strikes and expiry are economically the same position: by put-call parity, the call spread's debit plus the put spread's credit equals the width (ignoring interest). Choose between them by liquidity and early-assignment risk (lesson 10).
Width and strike selection
- Wider spreads collect more credit and risk more; the credit-to-width ratio barely changes for the same short strike, so width is a sizing tool.
- A short strike near 0.30 delta gives a credit of roughly one third of the width; near 0.16 delta roughly one fifth. Lower delta: higher POP, smaller credit.
- Debit spreads bought in the money have POP near 50 percent and a profit-to-loss ratio near one; bought out of the money they are low-probability, high-payoff bets.
Worked example
Hypothetical example: stock at $100, 30 DTE, IV 25 percent, no dividends, interest ignored. Mid prices (rounded, model-based): 95 put 1.00, 100 put 2.90, 100 call 2.90, 105 call 1.10, 105 put 6.10.
Bull call spread 100/105 (debit): buy 100 call 2.90, sell 105 call 1.10. Debit 1.80 ($180). Max profit 5.00 - 1.80 = 3.20 ($320). Max loss $180. Break-even 101.80. POP approximately 1.80 / 5 = 36 percent. EV: 0.36 x 3.20 - 0.64 x 1.80 = 1.152 - 1.152 = 0.00.
Bull put spread 95/100 (credit): sell 100 put 2.90, buy 95 put 1.00. Credit 1.90 ($190). Max loss 5.00 - 1.90 = 3.10 ($310). Break-even 98.10. POP approximately 1 - 1.90 / 5 = 62 percent. EV: 0.62 x 1.90 - 0.38 x 3.10 = 1.178 - 1.178 = 0.00. Both fair before costs.
Costs: assume $0.65 commission per contract per side (4 x 0.65 = $2.60 per round trip) and fills 0.03 from mid per leg (0.03 x 100 x 2 legs x 2 sides = $12). Total about $14.60 per spread, turning zero EV into about -$14.60: 7.7 percent of the $190 maximum profit.
Mirror check: bull put spread 100/105: sell 105 put 6.10, buy 100 put 2.90, credit 3.20. Debit 1.80 plus credit 3.20 equals the width 5.00; same risk profile, same break-even 101.80.
Exclusions: taxes, interest and early assignment.
Common mistake
Practice activity
On paper: a stock trades at $80. You sell a 45-DTE bear call spread: sell the 85 call at 1.60, buy the 90 call at 0.60. Calculate credit, maximum loss, break-even, approximate POP and EV (using maximum profit and loss), then the EV with total costs of $12 per spread.
Show solution
Credit = 1.60 - 0.60 = 1.00 ($100). Width 5.00. Max loss = 5.00 - 1.00 = 4.00 ($400). Break-even = 85 + 1.00 = 86.00. POP approximately 1 - 1.00 / 5 = 80 percent.
EV = 0.80 x 100 - 0.20 x 400 = 80 - 80 = $0 before costs. With $12 costs: EV = about -$12 per spread.
Limitations: real trades are often closed early at partial profit or loss, which changes the arithmetic but not the conclusion that costs must be beaten by a genuine edge.
Key takeaways
- For any vertical: debit = max loss, width - debit = max profit; credit = max profit, width - credit = max loss.
- POP is approximately 1 - credit/width for credit spreads and debit/width for debit spreads; these are implied, not measured, probabilities.
- The market-implied EV of a vertical is zero before costs; costs make it negative, so any edge must be argued explicitly.
- Call and put spreads with the same strikes are mirror images; choose by liquidity and assignment considerations.
Next step
The next lesson combines a put credit spread and a call credit spread into an iron condor, and shows how to size and adjust it.
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