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In mathematical finance, the Black?Scholes equation is a partial differential equation (PDE) governing the price evolution of a European call or European put under the Black?Scholes model. Broadly speaking, the term may refer to a similar PDE that can be derived for a variety of options, or more generally, derivatives.

The Black-Scholes model, aka the Black-Scholes-Merton (BSM) model, is a differential equation widely used to price options contracts. The Black-Scholes model requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility.

What is the Black-Scholes Model For? The model is used to find the current value of a call option whose ultimate value depends on the price of the stock at the expiration date. Because the stock price keeps changing, the value of this call option will change too.

Overall: Intuitively, and roughly, the Black-Scholes-Merton formula subtracts K e ? r ( T ? t ) N ( d 2 ) Ke^{-r(T-t)}N(d_2) Ke?r(T?t)N(d2), the exercise price discounted back to present value times the probability that the option is above the strike price at maturity, from S 0 N ( d 1 ) S_0N(d_1) S0N(d1), the stock ...

Definition: Black-Scholes is a pricing model used to determine the fair price or theoretical value for a call or a put option based on six variables such as volatility, type of option, underlying stock price, time, strike price, and risk-free rate.

Limitations of the Black-Scholes Model Assumes constant values for the risk-free rate of return and volatility over the option duration. None of those will necessarily remain constant in the real world. Assumes continuous and costless trading?ignoring the impact of liquidity risk and brokerage charges.

Black's Model, also known as the Black 76 Model, is a versatile derivatives pricing model for valuing assets such as options on futures and capped variable rate debt securities. The model was developed by Fischer Black by elaborating on the earlier and more well-known Black-Scholes-Merton options pricing formula.