Glossary

Characteristic Function

The characteristic function of a random variable \(x\) is the Fourier transform of \(P^x\), where \(P^x\) is the distrubution measure of \(x\)

(79)\[\begin{equation} \Phi_{x,u} = {\mathbb E}\left[e^{i u x_t}\right] = \int e^{i u x} P^x\left(dx\right) \end{equation}\]

Hurst Exponent

The Hurst exponent is a measure of the long-term memory of time series. The Hurst exponent is a measure of the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction.

Check this study on the Hurst exponent with OHLC data.

Moneyness

Monenyness is used in the context of option pricing and it is defined as

(80)\[\begin{equation} \ln\frac{K}{F} \end{equation}\]

where \(K\) is the strike and \(F\) is the Forward price. A positive value implies strikes above the forward, which means put options are in the money and call options are out of the money.