Chooser and Compound Options
Chooser and Compound Options
Chooser options and compound options add an additional layer of optionality to standard options. Chooser options allow the holder to decide whether the option becomes a call or put at a specified date. Compound options are options on options, providing the right to buy or sell another option. Both structures help manage uncertainty about market direction or timing.
Definition and Key Concepts
Chooser Options
Chooser option (as-you-like-it option): An option where the holder chooses whether it becomes a call or put at a specified decision date before final expiry.
Key parameters:
- Strike price (K)
- Choice date (T₁)
- Expiration date (T₂)
- Choice date < Expiration date
Payoff at choice date: Holder selects: max(Call value, Put value)
Compound Options
Compound option: An option that gives the right to buy or sell another option.
| Type | Description |
|---|---|
| Call on call | Right to buy a call option |
| Call on put | Right to buy a put option |
| Put on call | Right to sell a call option |
| Put on put | Right to sell a put option |
Key parameters:
- Compound strike (premium to buy underlying option)
- Compound expiry (when compound decision is made)
- Underlying option strike (K)
- Underlying option expiry (T)
Comparison to Vanilla Options
| Feature | Vanilla | Chooser | Compound |
|---|---|---|---|
| Direction | Fixed | Chosen later | Fixed (on underlying option) |
| Optionality layers | 1 | 1.5 | 2 |
| Premium | Base | Higher | Lower (for same exposure) |
| Flexibility | Low | High | High |
How It Works in Practice
Chooser Option Mechanics
Example: Equity chooser option
- Underlying: Stock at $100
- Strike: $100
- Choice date: 1 month
- Expiration: 3 months
- Implied volatility: 20%
At choice date (1 month):
| Stock Price | Call Value | Put Value | Choice |
|---|---|---|---|
| $110 | $12.50 | $2.00 | Call |
| $100 | $5.00 | $5.00 | Either |
| $90 | $1.50 | $11.00 | Put |
Holder always gets the more valuable option.
Chooser Pricing
Simple chooser (same strike/expiry for call and put): Using put-call parity, at choice date T₁: Chooser value = Call(T₂) + Put(T₂) - min(Call, Put)
Pricing formula: Chooser ≈ Call(K, T₂) + e^(-d(T₂-T₁)) × Put(K × e^(r-d)(T₂-T₁), T₁)
Where:
- d = dividend yield
- r = risk-free rate
The chooser is worth more than a single call or put, but less than a straddle.
Compound Option Mechanics
Example: Call on call
- Underlying stock: $100
- Underlying call strike: $105
- Underlying call expiry: 6 months
- Compound strike: $5 (premium to pay)
- Compound expiry: 3 months
At compound expiry (3 months):
| Stock Price | 6M Call Value | Exercise Compound? | Net Position |
|---|---|---|---|
| $95 | $3.00 | No (pay $5 for $3 option) | No position |
| $100 | $5.50 | Yes (pay $5 for $5.50 option) | Long call |
| $110 | $10.00 | Yes (pay $5 for $10 option) | Long call |
If stock rallies, exercise compound and hold underlying call.
Worked Example
Hedging Uncertain M&A with Chooser
Situation:
- Company awaiting regulatory decision on acquisition
- If approved: Need to hedge currency exposure (buy EUR)
- If rejected: Stock may decline (need downside protection)
- Decision date: 2 months
- Final hedge needed for: 6 months
Traditional approach: Buy both EUR call options and stock put options Total cost: $1.2 million
Chooser approach:
- Chooser with choice date at 2 months
- Single strike structure
- Becomes EUR call if deal approved
- Becomes stock put if deal rejected
- Cost: $800,000
Savings: $400,000 (33%)
Outcome analysis:
| Regulatory Decision | Chooser Selection | Hedge Result |
|---|---|---|
| Approved | EUR call | Currency risk covered |
| Rejected | Stock put | Downside protected |
| Delayed | Defer choice if possible | Flexibility maintained |
Compound Option for Project Finance
Situation:
- Real estate developer considering land purchase
- Land option expires in 6 months
- If purchased, will need construction financing
- Financing rates uncertain
Structure: Call on interest rate cap
- Compound expiry: 6 months (land decision)
- Underlying cap strike: 6%
- Underlying cap tenor: 3 years
- Compound premium: $50,000
- Underlying cap premium if exercised: $200,000
Scenarios:
| Land Decision | Compound Exercise? | Total Cost |
|---|---|---|
| Don't buy land | No | $50,000 (compound premium only) |
| Buy land, rates low | Maybe | $50,000 + $200,000 if want cap |
| Buy land, rates high | Yes | $50,000 + $200,000 (locked in cap) |
Benefit: Limits commitment until project is certain.
Greeks of Chooser Options
Delta evolution:
| Time Period | Delta Behavior |
|---|---|
| Far from choice date | Approximately straddle delta |
| Near choice date, stock up | Converges to call delta |
| Near choice date, stock down | Converges to put delta |
| At choice date | Jumps to chosen option delta |
Vega:
- Before choice: Higher than single option (two outcomes possible)
- After choice: Standard option vega
Greeks of Compound Options
Call on call:
- Delta: Lower than underlying call (only fraction of exposure)
- Gamma: Can be very high near compound expiry
- Vega: Sensitive to both underlying vol and vol of underlying option
Risks, Limitations, and Tradeoffs
Chooser Option Risks
| Risk | Description |
|---|---|
| Choice timing | Must decide on specified date |
| Premium cost | More expensive than single option |
| Complexity | Greeks change as choice date approaches |
| Basis risk | May not perfectly match exposure |
Compound Option Risks
| Risk | Description |
|---|---|
| Two-stage commitment | Pay twice (compound + underlying) |
| Model sensitivity | Requires volatility of volatility assumptions |
| Liquidity | Less liquid than vanilla options |
| Basis risk | Underlying option may not match needs |
Common Pitfalls
| Pitfall | Description | Prevention |
|---|---|---|
| Overpaying for optionality | Premium exceeds flexibility value | Compare to alternatives |
| Wrong choice date | Doesn't align with information arrival | Match to decision timing |
| Ignoring exercise decision | Letting compound expire without analysis | Monitor near expiry |
| Delta hedging errors | Discontinuous delta at choice date | Prepare for transition |
Applications
Chooser Option Uses
| Application | Rationale |
|---|---|
| Event uncertainty | Direction unknown until event occurs |
| M&A hedging | Deal approval creates different exposures |
| Currency hedging | Trade direction unknown |
| Volatility trading | Bet on move, not direction |
Compound Option Uses
| Application | Rationale |
|---|---|
| Project contingent hedging | Hedge only if project proceeds |
| Staged investment | Limit early commitment |
| Insurance on insurance | Reinsurance structures |
| Real options | Sequential investment decisions |
Pricing Considerations
Chooser Pricing Factors
| Factor | Impact |
|---|---|
| Time to choice | Longer → higher price (more uncertainty) |
| Volatility | Higher → higher price |
| Strike vs. spot | ATM choosers most valuable |
| Interest rates/dividends | Affect call vs. put relative value |
Compound Pricing Factors
| Factor | Impact |
|---|---|
| Compound strike | Higher → lower compound price |
| Time between expiries | Longer → higher compound price |
| Volatility | Complex (affects both layers) |
| Correlation | Of underlying to option value |
Checklist and Next Steps
Pre-trade checklist:
- Define choice date/compound expiry
- Specify underlying option parameters
- Compare to alternative structures
- Calculate breakeven scenarios
- Assess premium vs. optionality value
- Document exercise procedures
Execution checklist:
- Confirm ISDA documentation
- Verify choice/exercise notification process
- Set up calendar reminders for key dates
- Plan decision framework
- Prepare for delta hedge changes
Risk management checklist:
- Monitor distance to choice/compound expiry
- Track Greek evolution
- Prepare exercise decision analysis
- Plan post-exercise hedging
- Report position to risk management
Related articles:
- For Asian options, see Asian and Lookback Option Structures
- For convertibles, see Convertible Bonds as Embedded Options