How does a compound option work, and how are they priced?

Question

AcadiFi · Accepted Answer

A compound option is an option whose underlying is itself another option. Four basic types: 1. Call-on-Call (CoC): right to buy a call at K1 expiring at T1, where that call has its own strike K2 on the underlying S expiring at T2 (T2 > T1). 2. Put-on-Call: right to sell a call. 3. Call-on-Put: right to buy a put. 4. Put-on-Put: right to sell a put. Use case: Redstone Bidco is preparing a contingent takeover of a target firm. They want to hedge the target's share price only if the board approves the bid (uncertain in 3 months). Buying a vanilla call now wastes premium if the bid fails. Instead, they buy a 3-month call-on-call: if the bid is approved at T1, they exercise (paying K1) and receive a 9-month call on target equity with strike K2. If the bid fails, they let the compound expire and save premium. Pricing (Geske, 1979): value depends on two correlated random variables: S at T1 (to decide exercise) and S at T2 (to pay off vanilla call). Use bivariate normal CDF and a critical stock price S* at T1 where vanilla call value = K1. Key properties: - Compound options are cheaper than direct vanilla options because buyer takes on extra sequential decision risk. - Vega of compound = non-trivial; can be higher than vanilla because compound is more convex in vol. - Can be used to decompose real options: investment-timing problems often modeled as compound options. ```mermaid graph LR A[Today] --> B[T1 Pay K1] B --> C[Vanilla call
strike K2] C --> D[T2 Pay K2] D --> E[Receive asset] ``` CFA exam tip: you won't need Geske formula - just understand conceptual mapping to real options and cost structure.

How does a compound option work, and how are they priced?

Master Level II with our CFA Course

Related Questions

Practice Questions