How the path ledger separates option and hedge returns
The calculator uses aggregate position Greeks, not an option price forecast. Let S be the underlying price, D the option position delta in shares, G its gamma in shares per dollar, and T its signed daily theta in dollars. At each observation, Dᵢ = D₀ + G × (Sᵢ − S₀). The option value change is Dᵢ₋₁ × ΔS + ½G × ΔS² + T × elapsed days. Stock P&L is the shares held before the move times ΔS.
At a scheduled hedge, the new stock position is −Dᵢ. The initial hedge is opened before the first move; the final observation closes the stock instead of opening another hedge. Trading cost is absolute shares traded × (half the full stock spread + fee per share), plus the entered option entry and exit costs. Net P&L equals option P&L plus stock P&L minus costs. Theta is already part of option P&L.
A round trip can finish flat and still have hedge P&L
The default scenario is 100 → 102 → 100 → 102 → 100 over four quarter-day intervals. Initial delta is 50 shares, gamma is 10 shares/$, and theta is −$8/day. The full stock spread is $0.04, stock fees are zero, and total option costs are $2. These are invented inputs for calculation, not historical observations.
Hedging every interval holds −50, −70, −50, and −70 shares. Stock P&L is −$100 + $140 − $100 + $140 = $80. Option P&L is −$8 because price returns to its start while one calendar day passes. Initial, intermediate and final stock trades total 180 shares, costing $3.60. Net P&L is −$8 + $80 − $3.60 − $2 = $66.40.
Hedging every two intervals sees the price back at $100 each time. No intermediate stock adjustment is needed: stock P&L is zero and total turnover is 100 shares. Net P&L is −$8 − $2 − $2 = −$12. This path rewards frequent hedges. A smooth trend can reverse that comparison, because less frequent hedging leaves directional exposure. Raising spreads can also erase a gross gain.
Why a scanner score cannot identify future gamma profits
The scanner requests one provider-ordered page of up to 250 contracts within the chosen expiry range; it does not paginate the whole chain. Its 0 to 100 score weights gamma (30%), moneyness (15%), expiry (10%), volume (10%), open interest (10%), dollar spread (15%), and absolute delta near 0.5 (10%). These are uncalibrated ranking rules, not a probability of profit or a forecast.
Historical volatility is the sample standard deviation of daily log returns from the fetched 60-calendar-day window, annualized with √252. Identical duplicate dates are removed; invalid or conflicting closes stop the scan. Gaps between returned sessions are not filled, so incomplete history can distort this estimate. It uses the returned close, not a total-return series, and is not a fixed 30-day measure. An IV minus HV difference compares a forward-looking option input with past close-to-close movement. It does not establish that the option is cheap, and daily closes omit intraday moves used by a frequent hedge.
Only contracts with finite Greeks and valid, non-crossed positive bid/ask quotes are displayed. Data availability and delay depend on the provider. The displayed option price is a daily close, which can differ from the current quote. Verify timestamps, exact expiry, strike, option type and contract multiplier before copying inputs. Volume and open interest do not guarantee a fill at the displayed price.
Build the structure, then record the assumptions
- Use TradingView Options Strategy Builder to inspect the legs of a long-gamma structure. Record each leg's signed quantity, strike, expiry and multiplier.
- Cross-check available quotes and Greeks in the scanner or Pineify AI Stocks & Options Picker. Sum signed, multiplier-adjusted Greeks for the same underlying. Snapshot inputs do not recreate past option chains.
- Run several paths and cost assumptions. In Trading Journal, keep the scenario assumptions in notes and record actual hedge fills separately. This calculator does not send trades or automatically sync its ledger.
Where the approximation fails
Gamma and theta change as price, volatility and expiry change. This fixed-Greeks model ignores vega, jumps between observed prices, exercise and assignment, borrow availability and financing. It assumes immediate fills with fractional stock shares. A long option position can lose its premium; stock hedges can add losses and margin requirements. Use actual option marks and execution records to assess a traded strategy. Educational analysis only, not investment advice.
Sources checked October 21, 2026: OIC on gamma, OIC on theta, and Massive option chain snapshot fields. The equations and worked path above describe this calculator's explicit approximation.