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
Famous quotes containing the word mathematical:
“It is by a mathematical point only that we are wise, as the sailor or the fugitive slave keeps the polestar in his eye; but that is sufficient guidance for all our life. We may not arrive at our port within a calculable period, but we would preserve the true course.”
—Henry David Thoreau (1817–1862)