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TL;DR

A discrete-time option pricing model where the stock moves up by factor u or down by factor d each period. The risk-neutral probability is \( p = \frac{e^{r\Delta t} - d}{u - d} \). Option prices are computed by backward induction.

By Valenke Exam Prep Team·Last updated 2026-06-03

Binomial Tree Model

A discrete-time option pricing model where the stock moves up by factor u or down by factor d each period. The risk-neutral probability is \( p = \frac{e^{r\Delta t} - d}{u - d} \). Option prices are computed by backward induction.

Why it matters for interviews

The binomial tree provides intuition for continuous-time pricing (it converges to Black-Scholes). It handles American options, dividends, and path dependence. Its simplicity makes it a favorite interview topic for testing understanding of risk-neutral pricing.

Definition and Mathematical Foundation

A discrete-time option pricing model where the stock moves up by factor u or down by factor d each period. The risk-neutral probability is \( p = \frac{e^{r\Delta t} - d}{u - d} \). Option prices are computed by backward induction.

Application in Quantitative Finance

The binomial tree provides intuition for continuous-time pricing (it converges to Black-Scholes). It handles American options, dividends, and path dependence. Its simplicity makes it a favorite interview topic for testing understanding of risk-neutral pricing.

Related Concepts

Backward Induction

Related Terms

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Frequently Asked Questions

How does the binomial tree converge to Black-Scholes?▼
Using the CRR parameterization \( u = e^{\sigma\sqrt{\Delta t}} \), \( d = 1/u \), as the number of steps \( n \to \infty \), the binomial price converges to the Black-Scholes price. This follows from the CLT applied to the binomial log-returns.
How does the binomial tree handle American options?▼
At each node, compare the continuation value (discounted expected future value) with the immediate exercise value. The option value is the maximum of the two. This naturally handles early exercise.
What are the Cox-Ross-Rubinstein parameters?▼
\( u = e^{\sigma\sqrt{\Delta t}} \), \( d = e^{-\sigma\sqrt{\Delta t}} = 1/u \), \( p = \frac{e^{r\Delta t} - d}{u - d} \). These choices ensure the tree recombines and matches the first two moments of the continuous-time distribution.