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fin.black-scholes-call-put Calculator
Calculates call and put prices with full Greeks using the complete Black-Scholes option pricing model. The Black-Scholes formula requires log-normal stock price distribution and no dividends — real options require adjustments for discrete dividends and early exercise (American options).
Inputs
S Price
Current price per share. Used in P/E ratios, options pricing, and market cap calculations.
K Strike
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 option price
Value of the right (not obligation) to BUY the underlying at the strike price. Valuable when market price exceeds strike. Loses value as expiration approaches with no movement (time decay).
put option price
Value of the right (not obligation) to SELL the underlying at the strike price. Valuable when market price falls below strike. Used for hedging or speculation on price declines.
call delta
The change (final minus initial) in the quantity.
d1
Reference formula or conversion factor shown for context.
d2
Reference formula or conversion factor shown for context.
Black-Scholes 1973
Theoretical option fair value under the Black-Scholes model (assumes constant volatility, no dividends). Market prices may differ due to volatility skew and real-world frictions.