Calculates Black-Scholes implied volatility from an observed option market price using the Newton-Raphson iterative method. Implied volatility is forward-looking market consensus on uncertainty — the VIX is the 30-day implied volatility of S&P 500 options.
Inputs
Market Price Usd
Current trading price. For bonds, rises when interest rates fall and drops when rates rise.
S Usd
Current price per share. Used in P/E ratios, options pricing, and market cap calculations.
K Usd
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%).
Results
implied volatility IV (%)
The market's expected future volatility backed out from the option price. High implied vol means the market anticipates large price swings. Spikes ahead of earnings or major events.
Black-Scholes theoretical price ($)
Theoretical option fair value under the Black-Scholes model (assumes constant volatility, no dividends). Market prices may differ due to volatility skew and real-world frictions.
delta Δ
The change (final minus initial) in the quantity.
theta Θ ($ per day)
Reference formula or conversion factor shown for context.
Newton-Raphson IV solve | σ_{n+1} = σ_n − (BS(σ)−P_mkt)/vega
pH of the solution. Below 7: acidic. 7: neutral. Above 7: basic (alkaline).
IV interpretation
Qualitative summary of what the computed numbers mean in practical terms.