Delta and Gamma Hedging
Find the shares and traded options that make an options book delta-neutral, gamma-neutral or vega-neutral, and see how the hedge changes the gain or loss on a spot move.
Learning focus: shares can only fix delta, so each other Greek to be neutralized needs a traded option, chosen first, with shares trading last to clear the delta those options add.
Used for options priced by Black–Scholes–Merton (positions and hedge options entered as a call or put).
| Line | Quantity traded | Delta | Gamma | Vega |
|---|---|---|---|---|
| Book | 0.00 | −5,000.00 | −8,000.00 | |
| Option 1 trade | 400.00 | 240.00 | 200.00 | 800.00 |
| Option 2 trade | 6,000.00 | 3,000.00 | 4,800.00 | 7,200.00 |
| Shares trade | −3,240.00 | −3,240.00 | 0.00 | 0.00 |
| After the hedge | 0.00 | 0.00 | 0.00 |
Options are traded first to clear gamma (and vega); their own delta is then cleared with shares, which leave gamma and vega unchanged. Negative quantities are sales or written options.
Both lines use the delta–gamma(–vega) estimate for an immediate move, so a delta-only hedge leaves a curve of ½Γ·ΔS² and a gamma-neutral hedge is flat.