The AMM Book | 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 $\sum \partial_i f df$