Options Payoff Builder: 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. Breakevens are where the expiry payoff crosses zero; max profit and loss are read from the payoff grid spanning plus or minus 40% of spot, so a theoretically unlimited profit shows as the grid-edge value.
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
Long call: directional with capped loss
Buying one at-the-money call. The simplest bullish bet: limited downside, large upside.
Net premium $2.49 debit, delta 0.54, breakeven 102.49, max loss minus $2.49.
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 at the plus-40-percent grid edge (spot 140) is $37.51, 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
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 debit, delta 0.31, breakeven 101.76, max profit $3.24, max loss minus $1.76.
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
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 debit, delta 0.08 (near zero), breakevens 95.42 and 104.58, max loss minus $4.58.
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
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 credit, delta 0.16, breakeven 94.50, max profit $0.50, max loss the strike minus the premium: minus $94.50 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
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Sources & References
- The Pricing of Options and Corporate Liabilities — Black, F. and Scholes, M., Journal of Political Economy (1973)
- Options, Futures, and Other Derivatives — Hull, J. C., Pearson (textbook)
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