the Black-Scholes assumptions are

Black-Scholes formula

The Black-Scholes formula is a theoretical estimate of the price of European-style options, derived from the Black-Scholes equation.

The Black-Scholes model assumes constant volatility, meaning it does not account for changes in volatility over time.

The model also assumes no dividends are paid out during the life of the option, simplifying the calculation of the option's price.

Example

If an investor wants to price a European call option using the Black-Scholes formula, they would input the current stock price, strike price, time to expiration, risk-free rate, and constant volatility into the formula to get the theoretical price.

Remember this

Understanding the assumptions behind the Black-Scholes model is crucial for accurately interpreting its outputs and recognizing its limitations in real-world scenarios.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

Related concepts

the Black-Scholes formula prices

Black–Scholes equation governs derivative prices

Black–Scholes model

How can you predict the price of an option?

implied volatility tells you

Implied volatility (IV) = option price / Black–Scholes model

Write the Black-Scholes formula for a European call option: C = S·N(d₁) - K·e^(-rT)·N(d₂)

C = S·N(d₁) - K·e^(-rT)·N(d₂)

d₁ and d₂ are in Black-Scholes: d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T

d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T), d₂ = d₁ - σ√T

Volatility smile

Implied volatility varies with strike price, contradicting Black-Scholes

Educational content, not financial advice.

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