Implied Volatility (Black-Scholes)
Computes the implied volatility of a European call option by inverting the Black-Scholes formula via bisection: given the market price, it finds the volatility the model would need to reach it. It's the volatility the market is actually pricing in, the number behind the volatility smile and the VIX. Unlike the other Greeks, it has no closed form and requires a numerical solution. Enter the spot price, the strike, the interest rate, the term and the market price of the call.
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Implied Volatility (Black-Scholes)
Computes the implied volatility of a European call option by inverting the Black-Scholes formula via bisection: given the market price, it finds the volatility the model would need to reach it. It's the volatility the market is actually pricing in, the number behind the volatility smile and the VIX. Unlike the other Greeks, it has no closed form and requires a numerical solution. Enter the spot price, the strike, the interest rate, the term and the market price of the call.
The one variable the market won't tell you
In Black-Scholes, every ingredient is observable but one. You know the spot price, the strike, the rate and the term. Future volatility, though, nobody knows. But there's a trick: the option's market price already embeds the volatility expectation of every participant. Inverting the formula to extract that volatility is what we call implied volatility.
Unlike the other Greeks, it has no closed form. You have to numerically search for the volatility value that makes Black-Scholes reproduce exactly the observed price. This tool does it by bisection, narrowing the interval until it pins the answer. Implied volatility is the raw material of the volatility smile and what the VIX index measures for the whole market.
Enter the spot price, the strike, the interest rate, the term and the market price of the call. The tool returns the implied volatility as a percentage. The price entered must be between the intrinsic value and the asset price, otherwise no volatility can justify it in the model, and the tool will warn you.
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Black-Scholes-Merton Call (Dividends)
Computes the price of a European call option with the Black-Scholes-Merton model, the extension that incorporates a continuous dividend yield q. The premium is S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2), and the dividend lowers the call's value, because part of the asset's return leaks to whoever holds the stock. It's the standard model for options on dividend-paying stocks and on indices. Enter the spot price, the strike, the interest rate, the dividend yield, the term and the volatility.
Call Dual Delta
Computes the dual delta of a call option: the premium's sensitivity to the strike price, that is, dC/dK. While ordinary delta measures the reaction to the underlying's price, dual delta measures how much the option would change if the strike were slightly different. For a call it equals −e^(−rT)·N(d2) and has a practical reading: in absolute terms it approximates the risk-neutral probability of the option finishing in the money. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Option Price (Heston Model)
Prices a European call under the Heston (1993) model, where the asset volatility is itself stochastic and mean-reverting — reproducing the volatility smile and skew that constant-vol Black-Scholes misses. The price comes out in semi-closed form by numerically integrating the characteristic function (Little Heston Trap formulation, Gauss-Legendre quadrature). Enter spot, strike, maturity, rate, dividend and the five model parameters: initial variance, kappa, theta, vol of vol and correlation.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.