Jarrow-Rudd Model Formulas

This page explains formulas used in Jarrow-Rudd binomial option pricing model.

For similar pages for other models see Cox-Ross-Rubinstein, Leisen-Reimer.

For implementation of these formulas in Excel see Jarrow-Rudd Model in Excel.

Binomial Tree Probabilities

Like other binomial option pricing models, Jarrow-Rudd binomial trees are defined by up and down move sizes and probabilities.

The main characteristic of Jarrow-Rudd model is that up and down moves have equal probabilities: 50% each. The model is sometimes called the equal probability model.

p = 0.5

Binomial Tree Up Move

With probabilities fixed, all the inputs which describe price movement – volatility σ, risk-free interest rate r and yield q – are reflected in up and down move sizes.

Jarrow-Rudd up move formula is:

Jarrow-Rudd up move multiplier

... where Δt is the duration of one step in years, calculated as the option's time to expiration t divided by the model's number of steps n:

Binomial step duration

Binomial Tree Down Move

The formula for down move is very similar:

Jarrow-Rudd down move multiplier

The only difference is a minus sign before the last part.

Calculating Binomial Trees

Other than these formulas, the rest of the model is the same as Cox-Ross-Rubinstein and other binomial option pricing models.

Up and down move multipliers u and d are used the generate the underlying price tree, starting from the currenct underlying price S and ending at option expiration. From each node in the tree, price can go either up (S · u) or down (S · d) to one of two nodes in the next step.

Underlying prices at expiration (the last step in the tree) are then used to calculate option payoffs at expiration, which form the last step in the option price tree.

Then the rest of the option price tree is calculated backwards, eventually reaching its first node, which is the current option price.

The entire logic and formulas are explained here:

How Binomial Trees Work

For Excel implementation see:

Jarrow-Rudd Model in Excel

By remaining on this website or using its content, you confirm that you have read and agree with the Terms of Use Agreement.

We are not liable for any damages resulting from using this website. Any information may be inaccurate or incomplete. See full Limitation of Liability.

Content may include affiliate links, which means we may earn commission if you buy on the linked website. See full Affiliate and Referral Disclosure.

We use cookies and similar technology to improve user experience and analyze traffic. See full Cookie Policy.

See also Privacy Policy on how we collect and handle user data.

© 2022 Macroption