Delta Neutral - Theory

Theory

The existence of a delta neutral portfolio was shown as part of the original proof of the Black–Scholes model, the first comprehensive model to produce correct prices for some classes of options. See Black-Scholes: Derivation.

From the Taylor expansion of the value of an option, we get the change in the value of an option, for a change in the value of the underlier :

where (delta) and (gamma); see The Greeks.

For any small change in the underlier, we can ignore the second-order term and use the quantity to determine how much of the underlier to buy or sell to create a hedged portfolio. However, when the change in the value of the underlier is not small, the second-order term, cannot be ignored: see Convexity (finance).

In practice, maintaining a delta neutral portfolio requires continuous recalculation of the position's Greeks and rebalancing of the underlier's position. Typically, this rebalancing is performed daily or weekly.