Black-Scholes Model Explained: The Math Behind Options Pricing

Ryan O'Connell, CFA, FRM · Beginner ·📄 Research Papers Explained ·1mo ago

About this lesson

In this video, I break down the Black-Scholes model, the Nobel Prize-winning formula that revolutionized options pricing. You'll learn what the formula is actually doing, why bell curves appear in the equation, and what d1 and d2 represent. I walk through each input — stock price, strike price, time to expiration, risk-free rate, and volatility — and show how they combine to produce a theoretical call option price. I also run through a complete numerical example so you can see the calculation from start to finish. Plus, I cover the key assumptions behind the model and why real-world traders adjust for things like volatility smiles and fat tails. Whether you're studying for a finance exam or trying to understand how options are priced on Wall Street, this video gives you the intuition behind Black-Scholes. 🎓 *This Video Is Part of My Full Options Trading Course:* Go deeper with step-by-step lessons, paper trading practice, and downloadable resources. 👉 https://ryano.finance/options-course Chapters 0:00 - Introduction to the Black Scholes Model 0:47 - The Pricing Problem Before 1973 1:33 - Call Option Payoffs 2:15 - The Black-Scholes Formula 3:10 - Understanding d1 and d2 4:00 - The Normal Distribution in Black-Scholes 7:36 - Worked Example with Real Numbers 9:16 - Assumptions & Limitations *Seeking Alpha Deals:* 💰 *Get $50 OFF Alpha Picks:* https://ryano.finance/alpha-picks 📈 *Get $159 OFF Seeking Alpha Premium and Alpha Picks Bundle:* https://ryano.finance/seeking-alpha-bundle 🔥 *Get $30 OFF Seeking Alpha Premium:* https://ryano.finance/seeking-alpha 🎓 *Get 25% Off CFA Courses (Featuring My Videos!) — Use code RYAN25 here:* 👉 https://ryano.finance/cfa 🎓 *Ivy League Certificate Programs by Wall Street Prep — Save $300 with code RYANOC* 1. Columbia & Wall Street Prep AI for Business & Finance: https://ryano.finance/columbia-ai 2. Wharton & Wall Street Prep Real Estate Investing & Analysis: https://ryano.finance/wharton-real-estate 3. Wharton & Wall Street

Original Description

In this video, I break down the Black-Scholes model, the Nobel Prize-winning formula that revolutionized options pricing. You'll learn what the formula is actually doing, why bell curves appear in the equation, and what d1 and d2 represent. I walk through each input — stock price, strike price, time to expiration, risk-free rate, and volatility — and show how they combine to produce a theoretical call option price. I also run through a complete numerical example so you can see the calculation from start to finish. Plus, I cover the key assumptions behind the model and why real-world traders adjust for things like volatility smiles and fat tails. Whether you're studying for a finance exam or trying to understand how options are priced on Wall Street, this video gives you the intuition behind Black-Scholes. 🎓 *This Video Is Part of My Full Options Trading Course:* Go deeper with step-by-step lessons, paper trading practice, and downloadable resources. 👉 https://ryano.finance/options-course Chapters 0:00 - Introduction to the Black Scholes Model 0:47 - The Pricing Problem Before 1973 1:33 - Call Option Payoffs 2:15 - The Black-Scholes Formula 3:10 - Understanding d1 and d2 4:00 - The Normal Distribution in Black-Scholes 7:36 - Worked Example with Real Numbers 9:16 - Assumptions & Limitations *Seeking Alpha Deals:* 💰 *Get $50 OFF Alpha Picks:* https://ryano.finance/alpha-picks 📈 *Get $159 OFF Seeking Alpha Premium and Alpha Picks Bundle:* https://ryano.finance/seeking-alpha-bundle 🔥 *Get $30 OFF Seeking Alpha Premium:* https://ryano.finance/seeking-alpha 🎓 *Get 25% Off CFA Courses (Featuring My Videos!) — Use code RYAN25 here:* 👉 https://ryano.finance/cfa 🎓 *Ivy League Certificate Programs by Wall Street Prep — Save $300 with code RYANOC* 1. Columbia & Wall Street Prep AI for Business & Finance: https://ryano.finance/columbia-ai 2. Wharton & Wall Street Prep Real Estate Investing & Analysis: https://ryano.finance/wharton-real-estate 3. Wharton & Wall Street
Watch on YouTube ↗ (saves to browser)
Sign in to unlock AI tutor explanation · ⚡30

Related Reads

Chapters (8)

Introduction to the Black Scholes Model
0:47 The Pricing Problem Before 1973
1:33 Call Option Payoffs
2:15 The Black-Scholes Formula
3:10 Understanding d1 and d2
4:00 The Normal Distribution in Black-Scholes
7:36 Worked Example with Real Numbers
9:16 Assumptions & Limitations
Up next
Think Like an Entrepreneur | AP Business Topic 1.4
Jacob Clifford
Watch →