Pricing an American Option with a Step-Up Share Notional

Summary

This document poses a pricing question about an equity call whose share notional increases at scheduled intervals during its life. The contract is described as Bermudan at first, with an initial period when exercise is unavailable, and American thereafter. The central implementation issue is how to represent the growing number of underlying shares in a binomial tree while retaining the known strike and early exercise feature.

One suggested decomposition is to value each scheduled notional increase as a forward-starting option, with a delayed start and an appropriate discounting treatment. The document does not provide an answer, a tree construction, or valuation results, so the decomposition remains an open proposal rather than a demonstrated method. A practical valuation would need to specify precisely how the strike applies to each added share tranche, whether each tranche can be exercised independently, and the exercise and settlement rules. Those contract details determine whether separate option values can reproduce the payoff of a single step-up contract.

Key ideas

• The contract increases its underlying share notional at scheduled dates.
• A binomial valuation must represent both the changing notional and the applicable exercise rights.
• The question proposes valuing later increases as forward-starting option tranches.
• The document leaves the pricing method unresolved and supplies no numerical evidence.
• Strike allocation and tranche exercise terms are needed to define the payoff fully.

Tags

# How to price an option with a "step up" feature using binomial tree?


# How to price an option with a "step up" feature using binomial tree?












I have a call option with expiry in two years. In my case the option is bermudan style with first 9 months w/o ability to exercise (i.e. European) and after exercise at any time (i.e. American), but I believe this may not matter and will accept answer for purely american options. This option starts with let's say 100 shares as underlying, and then every quarter the "notional" increases by say 20 shares. So Q1 = 120, Q2 = 140 ... etc. How can I implement this in a binomial tree? Should I price each of the increases as a forward starting option? I.e. value the first increase as 21 month option with 6 month lock-out period and discount? Any other ideas? I know the strike at inception of the option.

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