Where does delta collide?

The Dirac delta, written δ(x), is not an ordinary function but a distribution, an idealised unit impulse that is zero everywhere except at a single point yet integrates to one, so that integrating it against a function returns that function's value at that point. Dirac's 1927 The physical interpretation of the quantum dynamics introduced it as a convenient notation for a quantity concentrated at one point, a use later made rigorous as a distribution. The referent is a linear functional that samples a function at a point, defined by how it behaves under an integral rather than by a value at each x, and it shares only its Greek letter with a finite change, a river's deposit, or a hedge ratio.[1]

Unit

Not a measured quantity; a distribution defined by its action under an integral

Recovery means

Not applicable

Measured by

Characterised by its sifting property, that integrating it against a function returns the function's value at a point

In geography and sedimentology a delta is the low-lying landform built where a river enters a standing body of water, such as a sea or a lake, and drops the sediment it carries as its flow slows and spreads: the deposit is often roughly triangular, and it is crossed by branching distributary channels. Galloway's 1975 Process framework for describing the morphologic and stratigraphic evolution of deltaic depositional systems classified deltas by whether the river, the waves, or the tides dominate the reworking of that sediment. The referent is a depositional landform of sand, silt, and clay at a river mouth, mapped in the field, and it is not a symbol for change, an idealised impulse, or a measure of option risk.[2]

Unit

A depositional landform of river sediment at a river mouth

Recovery means

Not applicable

Measured by

Mapped by field survey, cores, and remote sensing of its channels, and classified by the balance of river, wave, and tidal energy

In finance the delta of an option is one of the Greeks: the sensitivity of the option's price to a small change in the price of the underlying asset, that is, the partial derivative of the option's value with respect to the underlying. Black and Scholes's 1973 The pricing of options and corporate liabilities derived the option value from which this derivative follows, and Hull's 2018 Options, Futures, and Other Derivatives sets out delta and the other Greeks and how a position is delta-hedged to neutralise that first-order exposure. The referent is a hedge ratio, a dimensionless number between minus one and one for a plain option, and it is not a symbol for change in general, an idealised impulse, or a landform, even though it too is a rate of change.[3][4]

Unit

The change in an option's price per unit change in the underlying, a dimensionless ratio

Recovery means

Not applicable

Measured by

Computed from an option-pricing model as the partial derivative of price with respect to the underlying, and read off as a hedge ratio