Module 5:
Options Pricing Using the Black–Scholes–Merton Model
1. Module Overview
This module introduces the Black–Scholes–Merton (BSM) model, one of the most widely used methods for pricing options. The focus is on understanding the intuition behind the model, its key inputs, and how it determines fair option value.
2. Learning Objectives
By the end of this module, you will be able to:
- Understand the purpose of the Black–Scholes–Merton model
- Identify the key inputs that affect option prices
- Explain how each variable influences option value
- Interpret pricing outcomes in real-world contexts
3. Core Concept
3.1 What Is the Black–Scholes–Merton Model
The Black–Scholes–Merton model is a mathematical framework used to estimate the fair price of European-style options.
Key idea:
The value of an option depends on the probability of future price movements and the time value of money.
4. Key Inputs of the Model
The model uses five main variables:
| Input | Meaning |
|---|---|
| Current Price | Price of the underlying asset today |
| Strike Price | Price at which the option can be exercised |
| Time to Maturity | Time remaining until expiration |
| Volatility | How much the asset price is expected to fluctuate |
| Risk-Free Rate | Interest rate used for discounting |
5. Intuition Behind Pricing
Think of option pricing as balancing two things:
Higher chance of profit → Higher option value
Lower risk / uncertainty → Lower option value
6. How Each Input Affects Option Price
6.1 Underlying Price
- Higher price → Call option becomes more valuable
- Lower price → Put option becomes more valuable
6.2 Strike Price
- Higher strike → Call option less valuable
- Lower strike → Call option more valuable
6.3 Time to Maturity
More Time → More Uncertainty → Higher Option Value
- Options gain value with more time (time value)
6.4 Volatility
Higher Volatility → Higher Option Value
- More price movement = higher chance of profit
6.5 Risk-Free Rate
- Higher interest rates → Call options more valuable
- Lower interest rates → Put options more valuable
7. Simple Conceptual Diagram
Inputs (Price, Time, Volatility, Rate)
↓
Black-Scholes Model
↓
Fair Option Price