Black-Scholes Option Pricing Model – Concept & Inputs

1. Introduction

In 1973, Fisher Black and Myron Scholes published a formula that changed the world of finance. Before this, option pricing was a guess. The Black-Scholes-Merton (BSM) model provided a scientific way to calculate the Fair Value of a European call/put option.

2. Key Inputs (The Determinants)

The BSM model uses 5 variables to output one price (Premium):

1. Spot Price (S): Current price of the stock.
2. Strike Price (K): Agreed price.
3. Time to Maturity (t): Time left in years.
4. Risk-free Rate (r): Gov bond yield.
5. Volatility (σ): Standard deviation of stock returns.

Note on Volatility: This is the most special input. High volatility means the stock swings wildly. In options, Wild Swings = Good, because your loss is limited to Premium but profit is unlimited. So, higher volatility = higher option price.

3. Critical Assumptions

The model is based on strict theoretical assumptions (which often don't hold in real life):

1. European Style: Options can only be exercised at expiry.
2. No Dividends: The stock pays no dividend during the life of option.
3. Constant Volatility: The risk (sigma) remains constant. (This is the biggest flaw).
4. Efficient Markets: Information travels instantly.
5. No Transaction Costs: No brokerage or taxes.

4. The Formula (Simplified Concept)

C = S × N(d1) - K × e^(-rt) × N(d2)

• Don't panic. You usually don't need to calculate this manually in basic exams.
• Intuition:
  • Part 1 (S × N(d1)): Expected Benefit from buying earnings.
  • Part 2 (K × e^(-rt)): Present Value of the Strike Price you have to pay.
  • Result: Benefit - Cost = Premium.

5. Exam Notes: Writing the Answer

Question: "Explain the assumptions of Black-Scholes Model." (10 Marks)

Answering Structure:

1. Introduction: "Developed in 1973... Nobel Prize winning model...".
2. Assumptions: This is the main part. List 5 assumptions clearly (European, No Dividend, Constant Volatility, etc.).
3. Input Variables: List the 5 inputs.
4. Criticism: Mention that "Constant Volatility" is unrealistic because real markets have changing volatility.

6. Quiz Time! 🎯

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