| Term | Explanation |
|---|---|
| x,yx,y | token amounts (in native quantities) in two-asset case |
| Δx,ΔyΔx,Δy | virtual token balances in case of concentrated liquidity |
| x=(x0,x1,…,xN)x=(x0,x1,…,xN) | token amounts (in native quantities) in multi-asset case |
| f(x,y)f(x,y) | characteristic function in two-asset case |
| f(x)=f(x0,x1,…,xN)f(x)=f(x0,x1,…,xN) | characteristic function in multi-asset case |
| λλ | scaling parameter |
| k,k∗,ˉkk,k∗,¯k | indifference curve or hypersurface parameter (k=f(x)k=f(x)) |
| yk(x)yk(x) | indifference curve with parameter kk |
| φ(x,x′),φ(Δx) | fee function |
| π(ξ) | price response function (PRF) in two-asset case |
| πi(ξ) | PRF against numeraire asset 0 in multi-asset case |
| πij(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),μcash | 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) |
| Δcash | hedge amount in cash terms (Black Scholes) |
| Γ | payoff convexity; change in Δ when price changes (Black Scholes) |
| Γcash | Γ denominated in cash terms |
| d+,d− | coefficients used in the Black Scholes call and put pricing formulas |
| να(ξ) | the power law payoff function ξα; closely related to ν(ξ) |
| CK(ξ) | the final payoff of a call max(ξ−K,0) |
| ∂i | the partial derivative with respect to the i-the component |
| ∂ξ,∂t | the partial derivative with respect to ξ,t |
| df | differential of f, ie ∑∂ifdf |
Technical Glossary
glossary of technical terms we use in the formula pages on this site as well as in the paper itself
Technical Glossary
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