Expanding an Equation in a Multinomial Option Pricing Solution

Summary

The question concerns a worked example for pricing calls and puts with a multinomial tree and risk-neutral probabilities. The learner asks where certain highlighted equations in the book’s solution come from, contrasting that approach with a replicating-portfolio method. The sole response suggests that the equations follow by expanding the third term on the left-hand side and simplifying.

This is a narrow algebraic clarification rather than a full treatment of multinomial pricing. The document does not include the tree, the highlighted expressions, the expansion itself, or numerical evidence, so readers cannot independently follow the calculation from this exchange alone. Its useful point is the suggested operation: expand the indicated term, then collect and simplify expressions. The risk-neutral framework and call and put valuation provide the context, but the detailed derivation must be obtained from the original example.

Key ideas

• The question asks how equations in a multinomial tree pricing example are obtained.
• The proposed step is to expand the third term on the left-hand side.
• Simplifying after expansion is said to produce the displayed equations.
• The document omits the original expressions, so it does not provide a verifiable derivation.

Tags

# Calculating the price of a call and put using multinomial trees and risk-neutral probabilities


# Calculating the price of a call and put using multinomial trees and risk-neutral probabilities












I am self-studying for an actuarial exam and I encountered this example. The books shows one method of solving using a replicating portfolio, and then shows this solution involving risk-neutral probabilities.

My question is - I do not understand where the equations highlighted in red come from.

## Answer by Mark Joshi (score 2)

https://quant.stackexchange.com/a/22863

I think they have expanded the third term on the LHS and simplified.

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