Correlation Trading and Basket Options
Correlation Trading and Basket Options
Correlation trading involves taking positions that profit from changes in how assets move together. Basket options, dispersion trades, and correlation swaps allow investors to express views on correlation without directional exposure to the underlying assets. Understanding correlation dynamics is essential for pricing exotic products and managing portfolio risk.
Definition and Key Concepts
Correlation Basics
Correlation (ρ): Statistical measure of how two assets move together, ranging from -1 to +1.
| Correlation | Meaning |
|---|---|
| +1.0 | Perfect positive (move together) |
| +0.5 | Moderate positive |
| 0.0 | Uncorrelated |
| -0.5 | Moderate negative |
| -1.0 | Perfect negative (move opposite) |
Implied vs. Realized Correlation
| Type | Definition | Source |
|---|---|---|
| Implied correlation | Market expectation from option prices | Basket option vs. singles |
| Realized correlation | Actual historical correlation | Past returns |
| Correlation risk premium | Implied - Realized | Traded in dispersion |
Key Instruments
| Instrument | Correlation View | Mechanics |
|---|---|---|
| Basket option | Long correlation | Pays on basket performance |
| Dispersion trade | Short correlation | Long singles, short basket |
| Correlation swap | Direct correlation bet | Pays realized vs. strike |
| Worst-of option | Short correlation | Highest payout when correlation low |
How It Works in Practice
Basket Option Valuation
Basket call pricing depends on correlation:
Example:
- 2 stocks, each $100
- Individual volatility: 30%
- Strike: $100 (ATM basket)
- Tenor: 1 year
Basket volatility by correlation:
| Correlation | Basket Vol | Basket Call Value |
|---|---|---|
| 1.0 | 30% | $12.00 |
| 0.5 | 26% | $10.40 |
| 0.0 | 21% | $8.50 |
| -0.5 | 15% | $6.00 |
Higher correlation → Higher basket volatility → Higher basket option price
Extracting Implied Correlation
From option prices:
Given:
- Basket option price (observable)
- Individual option prices (observable)
- Individual volatilities (from singles)
Solve for correlation that makes: Basket vol = √(Σwᵢ²σᵢ² + 2ΣΣwᵢwⱼσᵢσⱼρᵢⱼ)
Match theoretical basket option price to market price.
Dispersion Trade Mechanics
Classic dispersion:
- Long: Straddles on each basket component
- Short: Straddle on basket index
Example:
- Index: S&P 500
- Components: Long straddles on 500 stocks (weighted)
- Hedge: Short S&P 500 index straddle
Profit/loss:
- If realized correlation < implied: Singles outperform index → Profit
- If realized correlation > implied: Index outperforms singles → Loss
Worked Example
Dispersion Trade on S&P 500
Setup:
- Index: S&P 500 at 5,000
- Implied index vol: 16%
- Average implied single-stock vol: 28%
- Implied correlation: (16/28)² ≈ 0.33
Historical realized correlation: 0.28
Trade:
- Sell S&P 500 3-month straddle: Receive $300
- Buy component straddles (vega-weighted): Pay $280
- Net premium: Receive $20
Scenario 1: Correlation drops to 0.20 Stocks move independently, singles volatility realizes.
- Singles P/L: +$150 (stocks move, straddles profit)
- Index P/L: -$80 (index moves less due to diversification)
- Net: +$70
Scenario 2: Correlation spikes to 0.50 Everything moves together (crisis).
- Singles P/L: +$100 (stocks move)
- Index P/L: -$200 (index moves more than implied)
- Net: -$100
Correlation Swap
Terms:
- Underlying: 10 tech stocks
- Notional: $10,000 per correlation point
- Strike: 40% (0.40)
- Tenor: 6 months
Payoff: Payoff = Notional × (Realized Correlation - Strike)
Calculation of realized correlation: Use pairwise correlations of daily returns over observation period.
Outcome scenarios:
| Realized Correlation | Payoff Calculation | P/L |
|---|---|---|
| 0.55 | $10,000 × (55 - 40) | +$150,000 |
| 0.40 | $10,000 × (40 - 40) | $0 |
| 0.25 | $10,000 × (25 - 40) | -$150,000 |
Worst-of Correlation Sensitivity
3-stock worst-of digital note:
- Pays 15% if all stocks above 80% barrier
- Pays 0% if any stock below barrier
Probability of all above barrier:
| Correlation | P(All > 80%) | Note Value |
|---|---|---|
| 0.8 | 75% | High |
| 0.5 | 60% | Medium |
| 0.2 | 45% | Low |
Seller of worst-of is implicitly long correlation.
Risks, Limitations, and Tradeoffs
Correlation Risks
| Risk | Description |
|---|---|
| Regime change | Correlation structure shifts permanently |
| Crisis correlation | All correlations spike toward 1 in crashes |
| Mean reversion | Correlation tends to revert to long-term average |
| Model risk | Correlation is difficult to model accurately |
Dispersion Trade Risks
| Risk | Description |
|---|---|
| Correlation spike | Losses if correlation increases |
| Execution cost | Bid-ask on many options |
| Rebalancing | Need to adjust weights as prices move |
| Liquidity | Single-stock options may be illiquid |
Crisis Correlation Pattern
Typical behavior:
| Market Condition | Correlation Level |
|---|---|
| Bull market | 0.25-0.40 |
| Normal | 0.30-0.50 |
| Correction | 0.50-0.70 |
| Crisis | 0.70-0.95 |
Dispersion trades lose money in crises when needed least.
Common Pitfalls
| Pitfall | Description | Prevention |
|---|---|---|
| Ignoring crisis risk | Dispersion blow-up in crashes | Size conservatively |
| Stale correlations | Using outdated historical data | Update regularly |
| Wrong pairing | Comparing unrelated assets | Ensure economic linkage |
| Execution slippage | Bid-ask erodes edge | Trade liquid instruments |
| Model overfit | Assuming past correlations persist | Use robust estimates |
Applications
Use Cases
| Application | Correlation View | Strategy |
|---|---|---|
| Relative value | Mean reversion expected | Dispersion trade |
| Diversification bet | Low correlation expected | Long singles, short basket |
| Crisis protection | High correlation expected | Long correlation swap |
| Yield enhancement | Willing to sell correlation | Worst-of products |
Market Participants
| Participant | Typical Position | Rationale |
|---|---|---|
| Dispersion traders | Short correlation | Extract premium |
| Structured product desks | Long correlation | Hedge worst-of |
| Macro hedge funds | Both | Express views |
| Index volatility sellers | Short correlation | Collect premium |
Checklist and Next Steps
Pre-trade checklist:
- Calculate implied correlation from option prices
- Estimate historical realized correlation
- Assess correlation risk premium
- Size position for correlation spike scenario
- Plan execution across multiple instruments
- Document correlation assumptions
Dispersion trade checklist:
- Select basket and components
- Verify liquidity in single-stock options
- Calculate vega weights for hedge
- Set up monitoring for correlation changes
- Plan rebalancing schedule
- Define exit criteria
Risk management checklist:
- Stress test for correlation = 1 scenario
- Monitor realized correlation daily
- Track P/L attribution to correlation
- Set position limits
- Report to risk committee
Related articles:
- For basket notes, see Structured Notes Linked to Equity Baskets
- For dispersion trades, see Dispersion Trades Using Options