Mathematical Interpretation
Delta measures the sensitivity of the value of an option to changes in the price of the underlying stock assuming all other variables remain unchanged.
Mathematically, delta is represented as partial derivative of the option's fair value with respect to the price of the underlying security.
Delta is clearly a function of S, however Delta is also a function of Strike Price and time to expiry.
Therefore, if a position is delta neutral (or, instantaneously delta-hedged) its instantaneous change in value, for an infinitesimal change in the value of the underlying security, will be zero; see Hedge (finance). Since delta measures the exposure of a derivative to changes in the value of the underlying, a portfolio that is delta neutral is effectively hedged. That is, its overall value will not change for small changes in the price of its underlying instrument.
Read more about this topic: Delta Neutral
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