Topic 24 – Hedging Intuition

1. Basic idea of hedging

Hedging = trade something liquid to offset risk in something less liquid or more complex.

Very simple picture:

• You hold a derivative with PV = $V$.
• It depends on some risk factor $S$ (spot, forward, curve bucket).
• For small changes: $$\Delta V \approx \Delta \cdot \Delta S$$ where $\Delta = \partial V / \partial S$ is delta.

If you short Δ units of S:

• Portfolio = long derivative + short Δ·S.
• For small dS, the P&L from derivative and hedge cancels ≈ flat.

This is local risk-neutralisation, not magic.

2. Delta hedging in practice

In theory (Black–Scholes):

• Continuous re-hedging, no spreads, no constraints → riskless.

In reality:

• You hedge discretely (daily/hourly).
• There are jumps, gaps, and illiquidity.
• There is basis: you often hedge with a related, not identical, instrument.

So delta hedging:

• Works locally (small moves between hedge times).
• Leaves gamma risk (curvature) and gap risk.

Power / commodities flavour:

• You hedge options on spot/loads with forwards and spreads, not spot.
• You often hedge at hub vs exposure at zone → basis risk.
• Many positions are in assets (plants, storage) where “delta” is nonlinear in state.

3. Vega hedging (volatility risk)

Vega = $\partial V / \partial \sigma$: sensitivity to volatility / implied vol.

• Long vega:
  • Option value increases when implied vol goes up.
• Vega hedge:
  • Add positions in liquid vanilla options to flatten vega in certain buckets:
    • e.g. “ATM 1Y vega flat”, “short 3M wing vega”.

In reality:

• Vol surface moves non-uniformly (smile, term structure).
• You are long vega in some strikes/tenors and short in others.
• Vega hedging is always approximate.

4. What breaks hedging in the real world

Key failure modes:

1. Discrete hedging & gamma
   • You do not hedge continuously.
   • Big moves between hedges → P&L from gamma.
   • Large gaps (weekends, events) can overwhelm delta hedges.
2. Model error in Greeks
   • Greeks depend on the model (GBM vs mean-reverting, smile, jumps).
   • If model is wrong, hedges target the wrong sensitivities.
3. Smile / surface dynamics
   • Vega hedge at one strike/tenor doesn’t protect against skew/term changes.
   • For power/gas, vol surfaces can move in very idiosyncratic ways.
4. Basis and proxy hedging
   • Hedge with correlated but not identical instrument:
     • Hub vs zone,
     • Nearby tenor vs far tenor,
     • Gas vs power (spark).
   • Correlation < 1 → residual basis risk.
5. Liquidity and costs
   • Spreads, market impact, position limits.
   • Continuous hedging is too expensive; you accept residual risk.

5. Power / commodities specifics

• Hedging often done in forward space:
  • Hedge optional loads with strips of forwards (Cal, Winter, Summer).
• Hedge shape and spreads:
  • Base vs peak, winter vs summer, hub vs zone, power vs gas.
• Optional assets (plants, storage, swing):
  • “Delta” depends on expected future prices and constraints.
  • Effective exposure changes as inventories/dispatch decisions change.

Interview line:

“Delta and vega hedging are local: they neutralise first-order sensitivity to small moves under a specific model. On a power/commodities book, we mostly hedge in forwards and spreads, and many positions are optional assets like plants and storage, so gamma, basis, and model risk are central. Hedging reduces risk, but discrete hedging, wrong Greeks, and surface/basis effects mean it never removes it completely.”