Where does gamma collide?

The function that extends the factorial to real and complex arguments, written with the capital Greek letter Γ, so that for a positive whole number n its value equals the factorial of n minus one. Euler introduced it around 1730 in De progressionibus transcendentibus seu quarum termini generales algebraice dari nequeunt as an integral that interpolates the factorial between whole numbers, and Legendre later fixed the name and the symbol Γ in his 1811 Exercices de calcul intégral. The referent is a continuous mathematical object, a smooth curve passing through the factorial values, and it has nothing to do with radiation given off by a nucleus or a trader's measure of how an option reacts to price.[1][2]

Unit

A value of the function Γ(z) for a real or complex argument z

Recovery means

Not applicable

Measured by

Computed from its integral definition or from series and continued-fraction approximations

The most penetrating form of radiation given off by a radioactive nucleus: a high-energy electromagnetic photon, more energetic than an X-ray, that carries no electric charge and passes through matter far more readily than an alpha or beta particle. Villard reported this undeviated, highly penetrating radiation from radium in 1900, and Rutherford named it the gamma ray in his 1903 The magnetic and electric deviation of the easily absorbed rays from radium, completing the alpha, beta, and gamma naming of the three emissions. The referent is a physical photon released in nuclear decay, scaled by its energy, and it is unrelated to a factorial-extending function or a sensitivity carried in an options book.[3][4]

Unit

A single high-energy photon emitted by a nucleus, scaled by its energy

Recovery means

Not applicable

Measured by

Detected and its energy resolved by scintillation or semiconductor detectors in gamma-ray spectroscopy

In options trading, the rate at which an option's delta changes as the price of the underlying asset moves: it is the second derivative of the option's value with respect to that price, so it measures the curvature of the pricing relationship. Black and Scholes derived the pricing model that yields these sensitivities in their 1973 The Pricing of Options and Corporate Liabilities, and the second-order term later took the name gamma in the trading vocabulary known as the Greeks. The referent is a number attached to a position in a financial contract, describing how quickly its hedge ratio shifts, and it bears no relation to radiation from a nucleus or the factorial function of mathematics.[5]

Unit

The change in an option's delta per unit change in the underlying price

Recovery means

Not applicable

Measured by

Computed as the second partial derivative of the option value, for example from the Black-Scholes formula