Not every exotic enlarges the state space with a running average or extremum. Compound, chooser, and forward-start options are path-independent at the level of the underlying — their complexity sits in nested or deferred optionality: the right to buy a call, the right to pick call vs put later, or a vanilla whose strike is fixed only when the contract starts. Equity-linked notes, employee stock options with vesting, and deferred-premium hedges all use these templates. Under GBM the standard attack is reduction to one or two Black–Scholes prices (or a bivariate normal for compounds), not a two-factor PDE — which is why this note sits after Asians and lookbacks in the curriculum.
Learning objectives. By the end of this note you should be able to:
- write payoffs for compound options (call-on-call, put-on-put, …) and identify the two expiry dates;
- state the Geske compound-call structure and when a tree or Monte Carlo is simpler;
- price a simple chooser via the Rubinstein put–call decomposition;
- value an ATM forward-start option as a deferred vanilla with rescaled spot;
- explain why forward-start options are sensitive to forward-smile dynamics in production.
In this lesson
- Compound options — option on an option
- Geske's compound call-on-call
- Simple chooser options
- Forward-start options
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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