The AMM Book | Technical Glossary

Term	Explanation
$x, y$	token amounts (in native quantities) in two-asset case
$Δ x, Δ y$	virtual token balances in case of concentrated liquidity
$x = (x_{0}, x_{1}, \dots, x_{N})$	token amounts (in native quantities) in multi-asset case
$f (x, y)$	characteristic function in two-asset case
$f (x) = f (x_{0}, x_{1}, \dots, x_{N})$	characteristic function in multi-asset case
$λ$	scaling parameter
$k, k^{*}, \bar{k}$	indifference curve or hypersurface parameter ( $k = f (x)$ )
$y_{k} (x)$	indifference curve with parameter $k$
$φ (x, x^{'}), φ (Δ x)$	fee function
$π (ξ)$	price response function (PRF) in two-asset case
$π_{i} (ξ)$	PRF against numeraire asset 0 in multi-asset case
$π_{i j} (ξ)$	cross-asset PRF in multi asset case
$ξ$	normalized price ratio; sometimes the price itself
$ν (ξ)$	normalized portfolio value ratio; sometimes the value itself
$μ (K), μ_{c a s h}$	strike density function
$Λ (ξ)$	Divergence Loss, aka Impermanent Loss
$α$	asset skew or asset weight parameter in multi-asset model
$η (α)$	convenience parameter equivalent to $α$ in multi asset model
$τ (α)$	exponential growth time scale depending on asset weight (0.5 for constant product)
$ρ (α)$	the growth rate equivalent to tau
$χ$	curve shape parameter, eg in the stable swap model
$Θ$	time decay / infinitesimal option premium (Black Scholes)
$Δ$	hedge ratio (Black Scholes)
$Δ_{c a s h}$	hedge amount in cash terms (Black Scholes)
$Γ$	payoff convexity; change in $Δ$ when price changes (Black Scholes)
$Γ_{c a s h}$	$Γ$ denominated in cash terms
$d_{+}, d_{-}$	coefficients used in the Black Scholes call and put pricing formulas
$ν_{α} (ξ)$	the power law payoff function $ξ^{α}$ ; closely related to $ν (ξ)$
$C_{K} (ξ)$	the final payoff of a call $m a x (ξ - K, 0)$
$\partial_{i}$	the partial derivative with respect to the i-the component
$\partial_{ξ}, \partial_{t}$	the partial derivative with respect to $ξ, t$
$d f$	differential of f, ie $\sum \partial_{i} f d f$