Greeks

 Delta

\Delta = \frac{\partial V}{\partial S}

Delta,\Delta , measures the rate of change of the theoretical option value with respect to changes in the underlying asset’s price. Delta is the first derivative of the value V of the option with respect to the underlying instrument’s price S.

Vega

\nu=\frac{\partial V}{\partial \sigma}

Vega measures sensitivity to volatility. Vega is the derivative of the option value with respect to the volatility of the underlying asset.

Theta

\Theta = -\frac{\partial V}{\partial \tau}

Theta,\Theta , measures the sensitivity of the value of the derivative to the passage of time (see Option time value): the “time decay.”

Rho

\rho = \frac{\partial V}{\partial r}

Rho,\rho , measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate (for the relevant outstanding term).

Lambda

\lambda = \frac{\partial V}{\partial S}\times\frac{S}{V}

Lambda,\lambda , omega,\Omega , or elasticity is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing.

Psi

{\displaystyle \psi ={\frac {\partial V}{\partial q}}}

Psi (Ψ) is the total change in option value over the total change in the underlying assets dividend rate, if the asset pays dividends.

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