Options Pricing
What is Black-Scholes Model?
The foundational mathematical model for pricing European options.
š Complete Definition
The Black-Scholes-Merton model is the most famous option pricing formula, developed in 1973. It calculates theoretical option prices based on stock price, strike price, time to expiration, risk-free rate, and volatility. While it has limitations (assumes European options, constant volatility, no dividends), it remains the foundation of options pricing and Greeks calculation.
š Formula
C = SāN(dā) - Ke^(-rT)N(dā) P = Ke^(-rT)N(-dā) - SāN(-dā)
š” Examples
- āBlack-Scholes calculates the "fair value" of an option given inputs
- āImplied volatility is derived by solving Black-Scholes backwards from market prices
ā Frequently Asked Questions
Why is Black-Scholes important?
It provides the mathematical framework for pricing options and calculating Greeks. All brokers use Black-Scholes or variants to price options and display Greeks.
š Related Terms
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