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fin.black-scholes-option Calculator
Calculates Black-Scholes call and put option prices from spot price, strike, time to expiry, volatility, and risk-free rate. The Black-Scholes model won the 1997 Nobel Prize — it's the foundational pricing model for all vanilla options.
Inputs
Stock Price
Current price per share. Used in P/E ratios, options pricing, and market cap calculations.
Strike Price
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.
Time Years
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Risk Free 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%).
Volatility 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.
d1
Reference formula or conversion factor shown for context.
d2
Reference formula or conversion factor shown for context.
delta (call)
The change (final minus initial) in the quantity.
put-call parity
Reference formula or conversion factor shown for context.