📊 Options Pricing — Black-Scholes

What It Demonstrates

This simulator implements the Black-Scholes-Merton formula for European option pricing. It computes the theoretical price of call and put options and visualises how the price varies across a range of underlying asset prices. The payoff diagram overlays the intrinsic value at expiry against the current option price curve, revealing the time value component. Below, a Greeks chart shows how delta, gamma, theta and vega change with the spot price.

How to Use

• Toggle between Call and Put.
• Adjust the Spot Price S, Strike K, Time to Expiry T, Volatility σ, and Risk-free Rate r sliders.
• Watch the payoff diagram and Greeks update in real time.
• The vertical dashed line marks the current spot price; the white dashed line marks the strike.

Did You Know?

Fischer Black, Myron Scholes and Robert Merton published their options pricing model in 1973 — the same year the Chicago Board Options Exchange (CBOE) opened. Scholes and Merton received the Nobel Prize in Economics in 1997 for this work. The formula assumes constant volatility and log-normal returns, which doesn't hold in real markets — leading to the well-known volatility smile.