Black-Scholes Model
The Black-Scholes model is a mathematical formula for pricing European-style options, considering factors like stock price, strike price, time to expiration, risk-free rate, and volatility.
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Definition
The Black-Scholes model is a mathematical formula for pricing European-style options, considering factors like stock price, strike price, time to expiration, risk-free rate, and volatility.
Use case
Used in derivatives workflows, analysis, and technical interviews.
Judgment check
Useful only when the assumptions and inputs behind the metric are understood.
Deep dive
How to think about Black-Scholes Model
Developed by Fischer Black, Myron Scholes, and Robert Merton (Nobel Prize 1997). The formula assumes log-normal price distribution, constant volatility, no dividends (though modifications exist), and efficient markets. While no model perfectly predicts prices, Black-Scholes provides a theoretical benchmark and is foundational for modern derivatives markets.
Example: For a call option: Stock = $100, Strike = $100, Time = 1 year, Risk-free rate = 5%, Volatility = 20%. Black-Scholes calculates fair value ≈ $10.45. If the market prices it at $12, the option may be overvalued or volatility expectations differ.