// multi-utility computation suite · offline · instant · precise
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fin.black-scholes-delta-gamma Calculator
Calculates call and put delta, gamma, and all Greeks from Black-Scholes inputs. Gamma is highest for at-the-money options near expiry — the gamma risk of short options at expiry is the reason many traders close positions before the last week.
Inputs
S
Current price per share. Used in P/E ratios, options pricing, and market cap calculations.
K
The price at which an option can be exercised. Call options profit when the market price exceeds the strike; put options profit when it falls below.
T Years
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
R Pct
Return on a theoretically safe investment like a government T-bill. The baseline return everything else is compared against. Enter as a decimal (e.g. 0.05 for 5%).
Sigma Pct
Annualised standard deviation of returns, as a decimal (e.g. 0.2 for 20%). Higher volatility increases option value. Implied vol is derived from market prices.
Results
call delta Δ
The change (final minus initial) in the quantity.
put delta Δ
The change (final minus initial) in the quantity.
gamma Γ
Reference formula or conversion factor shown for context.
vega ν (per 1% vol)
Reference formula or conversion factor shown for context.
d1
Reference formula or conversion factor shown for context.
d2
Reference formula or conversion factor shown for context.