Black–Scholes equation governs derivative prices
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the Black-Scholes formula prices
Black–Scholes equation governs derivative prices
European call and put options are derivatives with a fixed maturity time, T, and their payoff depends on the stock's value at that time, denoted as S_T. The Black–Scholes equation helps in calculating the price of these options by considering factors like the stock's current price, the strike price, time to maturity, risk-free interest rate, and the stock's volatility.
Example
Consider a European call option with a strike price of 100, maturity of 1 year, current stock price of 95, risk-free rate of 5%, and volatility of 20%. The Black–Scholes equation can be used to calculate the option's price by inputting these values into the formula.
Remember this
Understanding the Black–Scholes equation is crucial for accurately pricing European call and put options, which are widely traded financial instruments.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Related concepts
Black–Scholes model
How can you predict the price of an option?
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)
the Black-Scholes assumptions are
Black-Scholes formula
implied volatility tells you
Implied volatility (IV) = option price / Black–Scholes model
Greeks (finance)
Greeks measure sensitivity of option prices to underlying parameters
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
Educational content, not financial advice.
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