BLACK SCHOLES MODEL

Summary

The Black-Scholes Model is a mathematical formula developed by Fischer Black, Myron Scholes, and Robert Merton that calculates the theoretical price of European-style options (which can only be exercised at expiration). The model uses five key inputs: the current stock price, the strike price, time to expiration, risk-free interest rate, and the stock's volatility. It assumes constant volatility, no dividends, and that markets are efficient with no transaction costs. The model produces a fair value estimate that helps traders determine if an option is overpriced or underpriced in the market.

Usage Context

Essential for understanding derivatives pricing, risk management, and options trading strategies. Fundamental concept in financial engineering and quantitative finance courses.

Common Confusions

• Thinking it works for American options (which can be exercised early)
• Confusing theoretical fair value with actual market price
• Not understanding that volatility must be estimated/assumed
• Believing the model accounts for dividends (standard version doesn't)
• Assuming the calculated price is what you'll actually pay in the market