Fintech Reach

Module 4:
Options Pricing Using Binomial Trees

1. Module Overview

This module introduces the binomial tree model, a simple and intuitive method for pricing options. It shows how option values are derived step by step using possible future price movements.

2. Learning Objectives

By the end of this module, you will be able to:

Understand the logic behind binomial pricing
Construct a one-step and two-step binomial tree
Calculate option values using backward induction
Apply the model to basic call and put options

3. Core Concept

3.1 What Is a Binomial Tree

A binomial tree models how an asset price can move over time.

At each step, the price can:

Go up
Go down

4. Simple Price Tree (1-Step)

Up (S × u)
/
S —-
\
Down (S × d)

Where:

S = current price
u = up factor
d = down factor

5. Option Payoff at Maturity

At the end of the tree:

Call option payoff:
= max(0, Price – Strike)
Put option payoff:
= max(0, Strike – Price)

6. Pricing Logic (Backward Induction)

The key idea:

Start from the future → move backward to today

Steps:

Calculate option values at final nodes
Work backward step by step
Discount expected value to present

7. Two-Step Binomial Tree (Visual)

            S×u×u
          /
     S×u
    /     \
S           S×u×d
    \     /
     S×d
          \
           S×d×d

Meaning:

More steps = more realistic pricing
Captures multiple possible outcomes

8. Step-by-Step Example

Given:

Current price = 100
Up factor (u) = 1.2 → price becomes 120
Down factor (d) = 0.8 → price becomes 80
Strike price = 100

Step 1: Final Payoffs (Call Option)

If price = 120 → payoff = 20
If price = 80 → payoff = 0

Step 2: Work Backward

Calculate expected value
Discount to present value

Result:
This gives the fair value of the option today.

Module 4: Options Pricing Using Binomial Trees