Tools › Investing › Options › Option Strategy Payoff › Example

Bull call spread: maximum profit, maximum loss and break-even at expiry

Tool	Option Strategy Payoff
Source	Illustrative position (no published example is reproduced). Payoff arithmetic in closed form; the Advanced values use the Black-Scholes model: Black, F., and Scholes, M. (1973), Journal of Political Economy, Vol. 81, No. 3, pp. 637–654.
Level	Undergraduate

Problem

A stock trades at 100. One call with strike 100 is bought for a premium of 4.35 and one call with strike 110 is sold for 1.10; each contract covers 100 shares. Find the net premium, the profit if the stock finishes at 108, the maximum profit, the maximum loss and the break-even stock price at expiry. In Advanced mode, with 60 days to expiry, 25 % volatility and a 4 % interest rate, find the model profit today, the position's sensitivities and the model probability of finishing above the break-even.

Inputs to Enter

Stock price now 100; contract size 100 shares
Leg 1: buy 1 call, strike 100, premium 4.35; leg 2: sell 1 call, strike 110, premium 1.10 (illustrative premiums, not quotes)
Advanced: 60 days to expiry, volatility 25 %, interest rate 4 %

Open the Option Strategy Payoff tool (loaded with this example)

Answers

Net premium −435 + 110 = −325 (325 paid)
Stock at 108: leg 1 gains 100 · (8 − 4.35) = 365, leg 2 gains 100 · (1.10 − 0) = 110, total 475
Totals at the prices that matter: −325 at 0 and at 100, 675 at 110, unchanged above 110
Maximum profit 675 at 110 or above; maximum loss 325 at 100 or below
Break-even 100 − (−325) · (110 − 100) / (675 − (−325)) = 103.25
Advanced: model value 325.28 against 325 paid (model profit 0.28); position sensitivities to the stock price 34.12 shares and 1.109, to one day −1.29, to one point of volatility 4.56; model probability of finishing above 103.25 = 38.16 %

Notes

The tool's default inputs are this case; press Submit. The numbers are the tool's own calculation, checked against an independent numpy / scipy grid search and finite differences (test_option_strategy_payoff.php). The premiums are Black-Scholes values rounded to 0.05, so the model profit is near zero by construction. The probability is a model output, not a forecast; the example describes the position and is not investment advice.