Options are often introduced using formulas, but their logic is easier to understand through scenarios. The binomial option model does exactly that. Instead of assuming continuous price movements, it breaks time into small steps and asks a simple question at each step: what can the price do next?

This step-by-step reasoning makes the binomial option model one of the most intuitive tools in derivatives, and that is why exams test it so frequently.

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What the Binomial Option Model Is

The binomial option model is a method used to value options by modelling possible future movements in the price of the underlying asset.

At each step, the asset price can move in only two directions:

• up
• down

By repeating this process over multiple periods, the model builds a price tree that shows all possible paths the asset price can take.

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Why the Model Is Called “Binomial”

The term binomial comes from the fact that each step has two possible outcomes.

From today’s price, the asset either increases by a certain factor or decreases by another factor. Over time, these up and down movements create a tree-like structure.

This structure allows analysts to see how option payoffs evolve backward from expiration to today.

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How Option Values Are Determined

The binomial model works by backward induction.

First, the option’s payoff is calculated at expiration for every possible price outcome.
Then, those payoffs are moved backward through the tree to determine the option’s value today.

At each step, the option value is based on the expected value of future payoffs, adjusted for risk and discounted at the risk-free rate.

Exams often focus on this backward-looking logic rather than the mechanics.

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Risk-Neutral Valuation

A key idea behind the binomial option model is risk-neutral valuation.

Instead of using actual probabilities, the model uses risk-neutral probabilities. These probabilities ensure that the expected return on the underlying asset equals the risk-free rate.

This approach simplifies valuation and aligns the model with no-arbitrage principles.

Understanding why risk-neutral probabilities are used is more important than memorising formulas.

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Valuing Call and Put Options

The binomial model can be used to price both call and put options.

At each node in the tree:

• the intrinsic value of the option is known
• the continuation value is calculated

For European options, the higher of these values is taken only at expiration.
For American options, early exercise is allowed, so the model compares intrinsic value and continuation value at every step.

This flexibility makes the binomial model especially useful.

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Why the Binomial Model Is Important for American Options

Unlike the Black–Scholes model, the binomial model can easily handle early exercise.

Because the option value is checked at every node, the model naturally captures situations where exercising early is optimal.

Exams frequently test this advantage of the binomial model.

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Binomial Model Versus Black–Scholes

This comparison appears often.

The binomial model is discrete and flexible.
The Black–Scholes model is continuous and formula-based.

As the number of steps in the binomial model increases, its value converges toward the Black–Scholes value for European options.

Understanding this relationship helps answer conceptual exam questions.

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Assumptions Behind the Model

The binomial option model assumes:

• no arbitrage
• frictionless markets
• constant risk-free rate
• known up and down movements

While simplified, these assumptions allow the model to focus on core option logic.

Exams may test whether candidates recognise these assumptions and their limitations.

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Common Exam Confusions

Students often confuse real-world probabilities with risk-neutral probabilities.
Another common mistake is forgetting to check for early exercise in American options.

Some candidates also assume the binomial model is inferior because it is simpler. In reality, its flexibility is its strength.

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Final Thought

The binomial option model builds option value one step at a time. By modelling price movements explicitly and valuing options through backward induction, it offers clear intuition into how options work. For exam preparation, focus on tree logic, risk-neutral valuation, and early exercise decisions. Once these ideas are clear, binomial option questions become logical rather than intimidating.