Binomial Option Pricing Model – Stepwise Approach

1. Introduction

The Black-Scholes model uses complex calculus. The Binomial Model uses simple algebra and a "Tree" diagram. It is easier to visualize. It assumes that in the next period, the stock price can only go to two possible levels: Up or Down.

2. The Step-by-Step Logic

1. Start: Current Price = 100.
2. Movement: In 1 year, Stock can either go up to 120 (Up State) or down to 90 (Down State).
3. Option Value: Calculate the option value at both end points (at 120 and 90).
4. Backward Induction: Work backwards to find the value today.

3. Risk Neutral Valuation

The model assumes investors are "Risk Neutral". It creates a Risk Free Hedge Portfolio combining Stock and Loan to replicate the option.

• Key Concept: We calculate a "Probability of Rise" (p) not based on gut feeling, but mathematically based on interest rates.

4. Diagram: The Binomial Tree

5. Exam Notes: Writing the Answer

Question: "Explain the logic of Binomial Option Pricing Model." (5 Marks)

Answering Structure:

1. Name: "Binomial" means "Two Names" or two possibilities.
2. Assumption: Price follows a "Random Walk" but can only take two values in next step (Up/Down).
3. Advantage: Unlike BSM, Binomial model can be used for American Options (because you can check for early exercise at each node).

6. Quiz Time! 🎯