Long call, bullish target
Spot 100, target 120, 30% vol, 1% rate, 365 days, strikes 70–130 step 5.
- Best strike
- 90 call
- Premium
- 17.538
- Profit at 120
- 12.462
- Return
- 71.06%
Gamma Optimizer
Choose a long European call or put, then find the strike that maximizes return on premium if the underlier finishes at a price you have in mind.
The name is historical: this is not a gamma maximizer. It scans a listed strike grid and prices each vanilla of the type you selected with the same Black-Scholes formula as the vanilla option calculator. Long only. Figures are theoretical and for information only.
How the optimal option is chosen
You choose a long call or a long put. Each strike on the grid is then priced as that European vanilla with the site’s Black-Scholes formula (spot, strike, volatility, risk-free rate, and days ÷ 365). The option is assumed to expire with the underlier at your target. There is no path, no early exercise, and no second-order Greek in the ranking — only expiry payoff versus premium paid, scored as return on premium.
Call payoff = max(ST − K, 0)
Put payoff = max(K − ST, 0)
Return on premium = (payoff − premium) / premium
- ST — target price at expiry
- K — strike on the listed grid
- premium — Black-Scholes vanilla price, rounded to three decimals
Return on premium is payoff minus premium, per dollar of premium paid. That ranking usually sits closer to at-the-money than a deepest-in-the-money strike would. After Calculate, the heatmap shows that same yield for the selected call or put at nearby expiry spots so you can see how sensitive the pick is to the target.
Worked examples
These cases use the same Black-Scholes rounding and strike grid as the calculator. Type the inputs in and you should get the same strikes.
Long put, bearish target
Spot 100, target 80, same vol, rate, tenor, and 70–130 step-5 grid.
- Best strike
- 100 put
- Premium
- 11.373
- Profit at 80
- 8.627
- Return
- 75.86%
Short-dated long call
Spot 100, target 110, 30% vol, 1% rate, 90 days, strikes 90–120 step 1.
- Best strike
- 96 call
- Premium
- 8.173
- Profit at 110
- 5.827
- Return
- 71.3%
Related calculators on this site
Premiums here are the vanilla Black-Scholes values from the option calculator. Use a long call/put payoff chart if you already know the strike, or invert a market price into implied vol before you scan a grid.
Gamma Optimizer FAQ
Despite the name, it does not maximize gamma. You choose a long European vanilla call or put, and the tool finds the strike that maximizes return on premium if the underlier finishes at your target price. Premiums are the same Black-Scholes vanilla prices used on the option calculator.
Payoff at expiry is max(target minus strike, 0) for a call and max(strike minus target, 0) for a put. Return on premium is that payoff minus the Black-Scholes premium paid today, divided by the premium. The payoff is not discounted.
European vanilla calls and puts only, long only. Early exercise is not modelled, there is no dividend yield, and short option positions are not scanned.
Enter calendar days, the same convention as the other option tools (days divided by 365). You can instead pick an expiry or target date; the page converts that date into days from today. If both are set, the days field is used.
An evenly spaced listed-style chain. Set the strike step (for example 1 or 5) and optional minimum and maximum strikes. If you leave the bounds blank, the tool uses about 70% to 130% of spot, expanded so the target is included.
Rows are the same listed strikes the optimizer scanned. Columns are hypothetical expiry spots on that same grid, plus today’s spot and your typed target if they were missing. Color is return on premium for the call or put you selected; the scale is diverging around zero. The recommended strike is marked “Pick”, your target is the dashed column, and the starred cell is the strike that won.
Disclaimer: the contents of this website are for informational purposes only and do not constitute any investment recommendation. The visitor acts at his own risk.