Vega Hedging for Volatility Surfaces
Vega Hedging for Volatility Surfaces
Vega hedging manages exposure to implied volatility changes across the entire volatility surface—not just parallel shifts but also term structure changes and smile movements. Sophisticated vega hedging requires decomposing exposure into buckets by strike and tenor, then constructing hedges that match the risk profile.
Definition and Key Concepts
Vega Defined
Vega measures option price sensitivity to implied volatility:
Flat vega: Total portfolio sensitivity to a 1% parallel shift in the entire volatility surface.
Bucketed vega: Sensitivity by tenor and/or strike segments.
| Bucket Type | Description |
|---|---|
| Tenor buckets | 1M, 3M, 6M, 1Y, 2Y vega |
| Strike buckets | 90%, 95%, ATM, 105%, 110% vega |
| Combined | 3M ATM, 1Y 90% put, etc. |
The Volatility Surface
The surface has three dimensions:
| Dimension | Description | Risk |
|---|---|---|
| Level | Overall IV across surface | Parallel shift |
| Term structure | IV by expiration | Calendar risk |
| Smile/skew | IV by strike | Strike risk |
Vega Profile Components
Volga (vomma): Sensitivity of vega to volatility changes Vanna: Sensitivity of vega to spot changes
These second-order Greeks affect hedge stability.
How It Works in Practice
Vega Bucketing
Example portfolio vega by tenor:
| Tenor | Vega ($) | % of Total |
|---|---|---|
| 1 month | +$150,000 | 25% |
| 3 month | +$200,000 | 33% |
| 6 month | -$50,000 | -8% |
| 1 year | +$100,000 | 17% |
| 2 year | +$200,000 | 33% |
| Total | +$600,000 | 100% |
This portfolio benefits from IV rising, especially in 3M and 2Y tenors.
Example portfolio vega by strike:
| Strike (% of spot) | Vega ($) |
|---|---|
| 90% (OTM puts) | +$100,000 |
| 95% | +$50,000 |
| 100% (ATM) | +$300,000 |
| 105% | +$100,000 |
| 110% (OTM calls) | +$50,000 |
| Total | +$600,000 |
Hedging Strategies
Flat hedge: Buy/sell ATM options to neutralize total vega.
Bucket hedge: Match vega in each tenor/strike bucket independently.
Principal component hedge: Hedge the first 2-3 principal components of surface movement.
| Strategy | Complexity | Accuracy | Cost |
|---|---|---|---|
| Flat hedge | Low | Low | Low |
| Bucket hedge | High | High | High |
| PC hedge | Medium | Medium | Medium |
Hedge Instrument Selection
| Hedge Need | Typical Instrument |
|---|---|
| Short-term vega | 1M ATM straddle |
| Long-term vega | 1Y+ ATM options |
| Skew exposure | Risk reversal (OTM put vs. OTM call) |
| Smile wings | Butterfly spread |
| Term structure | Calendar spread |
Worked Example
Portfolio: Complex book of equity options across strikes and tenors.
Vega exposure (before hedge):
| Tenor | 90% | 95% | ATM | 105% | 110% | Row Total |
|---|---|---|---|---|---|---|
| 1M | +$30K | +$20K | +$50K | +$30K | +$20K | +$150K |
| 3M | +$40K | +$30K | +$80K | +$30K | +$20K | +$200K |
| 6M | -$10K | -$10K | -$20K | -$5K | -$5K | -$50K |
| 1Y | +$20K | +$15K | +$40K | +$15K | +$10K | +$100K |
| Total | +$80K | +$55K | +$150K | +$70K | +$45K | +$400K |
Hedge construction:
Step 1: Neutralize total vega Sell 3M ATM straddles: -$200,000 vega Sell 1Y ATM options: -$100,000 vega Net: +$400K - $300K = +$100K remaining
Step 2: Address skew exposure Portfolio is long OTM put vega (+$80K at 90%) Sell 3M 90% puts: -$50K vega Remaining skew: +$30K
Step 3: Address term structure Long 1M, short 6M → Enter 1M/6M calendar spread
Post-hedge vega:
| Tenor | Net Vega | Status |
|---|---|---|
| 1M | +$30K | Within tolerance |
| 3M | +$20K | Within tolerance |
| 6M | -$10K | Within tolerance |
| 1Y | -$10K | Within tolerance |
| Total | +$30K | Acceptable residual |
Hedge Ratio Calculation
For 3M ATM straddle hedge:
- Target: Reduce 3M vega by $200K
- 3M ATM straddle vega: $5,000 per straddle
- Contracts needed: $200K / $5K = 40 straddles (sell)
Hedge cost: Selling straddles generates premium but exposes to gamma risk.
VaR Analysis
Pre-hedge vega VaR (95%, 1-day): = Total vega × Expected IV move × Confidence = $400,000 × 1.5% × 1.65 = $9,900
Post-hedge vega VaR: = $30,000 × 1.5% × 1.65 = $743
VaR reduction: 92%
Risks, Limitations, and Tradeoffs
Term Structure Risk
Even with total vega hedged, term structure moves create P/L:
| Scenario | Effect |
|---|---|
| Curve steepens | Long front, short back = loss |
| Curve flattens | Long front, short back = gain |
| Parallel shift | Hedged (no P/L) |
Smile Risk
Skew and smile changes are difficult to hedge perfectly:
| Movement | Risk |
|---|---|
| Skew steepens | Long OTM put vega gains |
| Wings expand | Long butterfly vega gains |
| Smile twists | Complex P/L pattern |
Second-Order Effects
| Greek | Description | Impact |
|---|---|---|
| Volga | Vega convexity | Hedge ratio changes with IV |
| Vanna | Vega-delta cross | Spot moves affect vega |
| Charm | Delta-time cross | Greeks shift approaching expiry |
Hedge Costs
| Cost Type | Magnitude |
|---|---|
| Bid-ask spread | 0.5-2% of option value |
| Gamma pickup | Short options = short gamma |
| Theta | Long options = theta decay |
| Margin | Collateral requirements |
Common Pitfalls
| Pitfall | Description | Prevention |
|---|---|---|
| Bucket mismatch | Hedge tenor differs from exposure | Match tenors closely |
| Ignoring skew | Hedging only ATM vega | Include OTM buckets |
| Over-hedging | Transaction costs exceed risk reduction | Set tolerance bands |
| Static hedge | Not adjusting as surface moves | Dynamic rebalancing |
Advanced Techniques
Principal Component Hedging
The first three principal components typically explain 95%+ of surface variation:
| PC | Description | Typical Variance |
|---|---|---|
| PC1 | Parallel shift | 70-80% |
| PC2 | Term structure tilt | 10-15% |
| PC3 | Curvature/smile | 5-10% |
Hedge by matching exposure to PC1, PC2, PC3 rather than every bucket.
Variance Swap Hedging
Variance swaps provide pure vega exposure without gamma:
| Feature | Options | Variance Swap |
|---|---|---|
| Gamma | Yes | No |
| Theta | Yes | Minimal |
| Vega | Yes | Yes |
| Smile exposure | Yes | Weighted average |
Checklist and Next Steps
Vega assessment checklist:
- Calculate total portfolio vega
- Break down by tenor buckets
- Break down by strike buckets
- Identify largest exposures
- Assess term structure tilt
- Evaluate skew exposure
- Calculate vega VaR
Hedge implementation checklist:
- Select hedge instruments by bucket
- Calculate hedge ratios
- Evaluate hedge costs
- Execute hedges
- Verify post-hedge vega profile
- Set rebalancing thresholds
- Monitor residual vega
Related articles:
- For gamma trading, see Gamma Scalping and Volatility Trading
- For portfolio hedging, see Using Options to Hedge Equity Portfolios