Black–Scholes model

A mathematical model for estimating the fair price of European options from the underlying asset price, strike price, volatility, time to expiration, and risk-free interest rate.

Black–Scholes equation: A partial differential equation describing how an option’s value changes with asset price and time. It expresses the model’s no-arbitrage pricing condition before boundary conditions specify an option.
Option (finance): A contract giving its holder the right, but not the obligation, to buy or sell an asset under specified terms. The model assigns a value to this kind of contingent contract.
Louis Bachelier: A French mathematician whose 1900 thesis modeled price fluctuations using Brownian motion. His early mathematical treatment of market randomness preceded modern option pricing.
Black–Scholes formula: Closed-form expressions for the prices of European calls and puts under Black–Scholes assumptions. This is the model’s direct calculation for standard European options.
Binomial options pricing model: A discrete-time method that prices options by modeling possible upward and downward asset-price moves. It can handle early exercise directly, unlike the basic European Black–Scholes formula.
Delta hedging: A strategy that offsets an option’s price sensitivity by trading its underlying asset. Continuous delta hedging is the model’s key step toward a riskless portfolio.
Strike price: The price at which an option holder may buy or sell the underlying asset. It sets the exercise payoff that the model discounts and averages.
Paul Samuelson: An American economist who helped introduce stochastic models of asset prices and option values. His work helped frame the financial problem the model later solved.
Options market: A financial market where standardized and customized contracts give rights to buy or sell assets. Traders use Black–Scholes prices and implied volatilities to quote and compare options.
Merton model: A structural credit-risk model that treats a firm’s equity as an option on its assets. It applies option-pricing logic to corporate default rather than standard traded options.

Linked from 11 pages