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 $\sum \partial_i f df$ |

# 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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