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Worked examples, in Risk & Portfolio Construction

Options Payoff Calculator: Worked Examples

These scenarios illustrate how the same directional view produces radically different payoff profiles across structures. All share the same parameters: 100 underlying, 20% annual volatility, 30 days to expiry, 5% rate. Net premium is the Black-Scholes cost; a negative premium means a credit received. Figures are per share; the tool reports dollars per position, so one 100-share contract is the per-share figure times 100 (a $2.49 premium is $249 per contract). Breakevens are where the expiry payoff crosses zero; max profit and loss are solved exactly from the piecewise-linear payoff, and an unbounded profit or loss is reported as unlimited.

4 examples. Published May 26, 2026. Updated Oct 5, 2026. By AI Fin Hub Research.

Worked examples

See the inputs and outcome together

Each scenario keeps the starting point, the outcome, and the actual lesson in one place so the page reads like a decision notebook, not a data dump.

  1. 1

    Long call: directional with capped loss

    Buying one at-the-money call. The simplest bullish bet: limited downside, large upside.

    Net premium $2.49 per share ($249 per contract) debit, delta 0.54, breakeven 102.49, max loss minus $2.49 per share, max profit unlimited.

    Structure

    Long 100 call

    Spot / vol / days

    100 / 20% / 30

    Risk-free rate

    5%

    The breakeven is the strike plus the premium, 100 plus 2.49, and the max loss is exactly the premium paid. Profit has no ceiling: at spot 140 it is already $37.51 per share, fifteen times the $2.49 you risk. That asymmetry, lose a little and win a lot, is the entire reason to own a call rather than the stock.

  2. 2

    Bull call spread: cheaper, capped both ways

    Buying the 100 call and selling the 105 call. A bullish view that trades away upside above 105 for a lower cost.

    Net premium $1.76 per share debit, delta 0.31, breakeven 101.76, max profit $3.24, max loss minus $1.76 per share.

    Structure

    Long 100 call, short 105 call

    Spot / vol / days

    100 / 20% / 30

    Risk-free rate

    5%

    Selling the 105 call cuts the cost from $2.49 to $1.76 and lowers the breakeven to 101.76, but caps profit at $3.24, the 5-point spread minus the net debit. The spread is the call made affordable by surrendering the tail; max profit and max loss now sum to the strike width.

  3. 3

    Long straddle: a pure volatility bet

    Buying the 100 call and the 100 put together. A direction-neutral position that profits from a large move either way.

    Net premium $4.58 per share debit, delta 0.08 (near zero), breakevens 95.42 and 104.58, max loss minus $4.58 per share, max profit unlimited.

    Structure

    Long 100 call, long 100 put

    Spot / vol / days

    100 / 20% / 30

    Risk-free rate

    5%

    The combined delta is near zero, confirming this is a volatility bet, not a directional one. The two breakevens sit roughly the premium away from the strike on each side, so the underlying must move more than about 4.6 percent in either direction just to break even.

  4. 4

    Cash-secured short put: income with tail risk

    Selling one 95 put to collect premium, willing to be assigned the stock at 95. The classic income trade.

    Net premium $0.50 per share credit, delta 0.16, breakeven 94.50, max profit $0.50, max loss the strike minus the premium: minus $94.50 per share if the stock falls to zero by expiration.

    Structure

    Short 95 put

    Spot / vol / days

    100 / 20% / 30

    Risk-free rate

    5%

    You collect a $0.50 credit (the negative premium) and keep it all if the stock stays above 95, but a short put carries the full downside of owning the stock from the strike down: the theoretical max loss is the strike minus the premium ($94.50), realized only if the stock falls to zero. The trade swaps a small, certain gain for a large, unlikely loss, the opposite asymmetry of the long call.

Patterns

A long call's breakeven is strike plus premium and its max loss is the premium; the upside is the asymmetry you pay for.
A vertical spread caps profit at the strike width minus net debit, lowering both cost and reward versus a single option.
A straddle's near-zero delta confirms it is a volatility bet; the underlying must move past either breakeven to profit.
A short put earns a small certain credit against a large tail loss, the inverse risk profile of a long call.

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Sources

  1. The Pricing of Options and Corporate Liabilities , Black, F. and Scholes, M., Journal of Political Economy (1973)
  2. Options, Futures, and Other Derivatives , Hull, J. C., Pearson (textbook)

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