# Technical Glossary

glossary of technical terms we use in the formula pages on this site as well as in the paper itself

# Technical Glossary

Term Explanation
$x,y$ token amounts (in native quantities) in two-asset case
$\Delta x, \Delta y$ virtual token balances in case of concentrated liquidity
$x = (x_0, x_1, \ldots, x_N)$ token amounts (in native quantities) in multi-asset case
$f(x,y)$ characteristic function in two-asset case
$f(x) = f(x_0, x_1, \ldots, x_N)$ characteristic function in multi-asset case
$\lambda$ scaling parameter
$k, k^*, \bar k$ indifference curve or hypersurface parameter ($k=f(x)$)
$y_k(x)$ indifference curve with parameter $k$
$\varphi(x,x'), \varphi(\Delta x)$ fee function
$\pi(\xi)$ price response function (PRF) in two-asset case
$\pi_i(\xi)$ PRF against numeraire asset 0 in multi-asset case
$\pi_{ij}(\xi)$ cross-asset PRF in multi asset case
$\xi$ normalized price ratio; sometimes the price itself
$\nu(\xi)$ normalized portfolio value ratio; sometimes the value itself
$\mu(K), \mu_{\mathrm{cash}}$ strike density function
$\Lambda(\xi)$ Divergence Loss, aka Impermanent Loss
$\alpha$ asset skew or asset weight parameter in multi-asset model
$\eta(\alpha)$ convenience parameter equivalent to $\alpha$ in multi asset model
$\tau(\alpha)$ exponential growth time scale depending on asset weight (0.5 for constant product)
$\rho(\alpha)$ the growth rate equivalent to tau
$\chi$ curve shape parameter, eg in the stable swap model
$\Theta$ time decay / infinitesimal option premium (Black Scholes)
$\Delta$ hedge ratio (Black Scholes)
$\Delta_{\mathrm{cash}}$ hedge amount in cash terms (Black Scholes)
$\Gamma$ payoff convexity; change in $\Delta$ when price changes (Black Scholes)
$\Gamma_{\mathrm{cash}}$ $\Gamma$ denominated in cash terms
$d_+, d_-$ coefficients used in the Black Scholes call and put pricing formulas
$\nu_\alpha(\xi)$ the power law payoff function $\xi^\alpha$; closely related to $\nu(\xi)$
$C_K(\xi)$ the final payoff of a call $max(\xi-K, 0)$
$\partial_i$ the partial derivative with respect to the i-the component
$\partial_\xi, \partial_t$ the partial derivative with respect to $\xi, t$
$df$ differential of f, ie $\sum \partial_i f df$