OptionMath

Git Source

State Variables

ALPHA

SD59x18 internal constant ALPHA = SD59x18.wrap(-6.37309208e18);

LAMBDA

SD59x18 internal constant LAMBDA = SD59x18.wrap(-0.61228883e18);

S1

SD59x18 internal constant S1 = SD59x18.wrap(-0.11105481e18);

S2

SD59x18 internal constant S2 = SD59x18.wrap(0.44334159e18);

SQRT_2PI

int256 internal constant SQRT_2PI = 2_506628274631000502;

MIN_INPUT_PRICE

UD60x18 internal constant MIN_INPUT_PRICE = UD60x18.wrap(1e1);

MAX_INPUT_PRICE

UD60x18 internal constant MAX_INPUT_PRICE = UD60x18.wrap(1e34);

Functions

helperNormal

Helper function to evaluate used to compute the normal CDF approximation

function helperNormal(SD59x18 x) internal pure returns (SD59x18 result);

Parameters

Returns

normalCdf

Approximation of the normal CDF

The approximation implemented is based on the paper 'Accurate RMM-Based Approximations for the CDF of the Normal Distribution' by Haim Shore

function normalCdf(SD59x18 x) internal pure returns (SD59x18 result);

Parameters

Returns

normalPdf

Normal Distribution Probability Density Function.

Equal to Z(x) = (1 / σ√2π)e^( (-(x - µ)^2) / 2σ^2 ). Only computes pdf of a distribution with µ = 0 and σ = 1.

function normalPdf(SD59x18 x) internal pure returns (SD59x18 z);

Parameters

Returns

relu

Implementation of the ReLu function f(x)=(x)^+ to compute call / put payoffs

function relu(SD59x18 x) internal pure returns (UD60x18);

Parameters

Returns

d1d2

Returns the terms d1 and d2 from the Black-Scholes formula that are used to compute the price of a call / put option.

function d1d2(UD60x18 spot, UD60x18 strike, UD60x18 timeToMaturity, UD60x18 volAnnualized, UD60x18 riskFreeRate)
    internal
    pure
    returns (SD59x18 d1, SD59x18 d2);

Parameters

Returns

optionDelta

Calculate option delta

function optionDelta(
    UD60x18 spot,
    UD60x18 strike,
    UD60x18 timeToMaturity,
    UD60x18 volAnnualized,
    UD60x18 riskFreeRate,
    bool isCall
) internal pure returns (SD59x18);

Parameters

Returns

blackScholesPrice

Calculate the price of an option using the Black-Scholes model

this implementation assumes zero interest

function blackScholesPrice(
    UD60x18 spot,
    UD60x18 strike,
    UD60x18 timeToMaturity,
    UD60x18 volAnnualized,
    UD60x18 riskFreeRate,
    bool isCall
) internal pure returns (UD60x18);

Parameters

Returns

is8AMUTC

Returns true if the maturity time is 8AM UTC

function is8AMUTC(uint256 maturity) internal pure returns (bool);

Parameters

Returns

isFriday

Returns true if the maturity day is Friday

function isFriday(uint256 maturity) internal pure returns (bool);

Parameters

Returns

isLastFriday

Returns true if the maturity day is the last Friday of the month

function isLastFriday(uint256 maturity) internal pure returns (bool);

Parameters

Returns

calculateTimeToMaturity

Calculates the time to maturity in seconds

function calculateTimeToMaturity(uint256 maturity) internal view returns (uint256);

Parameters

Returns

calculateStrikeInterval

Calculates the strike interval for strike

function calculateStrikeInterval(UD60x18 strike) internal pure returns (UD60x18);

Parameters

Returns

roundToStrikeInterval

Rounds strike using the calculated strike interval

function roundToStrikeInterval(UD60x18 strike) internal pure returns (UD60x18);

Parameters

Returns

scaleDecimals

Converts a number with inputDecimals, to a number with given amount of decimals

function scaleDecimals(uint256 value, uint8 inputDecimals, uint8 targetDecimals) internal pure returns (uint256);

Parameters

Returns

scaleDecimals

Converts a number with inputDecimals, to a number with given amount of decimals

function scaleDecimals(int256 value, uint8 inputDecimals, uint8 targetDecimals) internal pure returns (int256);

Parameters

Returns

fromTokenDecimals

Converts a number with decimals, to a UD60x18 type

function fromTokenDecimals(uint256 value, uint8 decimals) internal pure returns (UD60x18);

Parameters

Returns

toTokenDecimals

Converts a UD60x18 number with decimals, to it's uint256 type scaled down.

function toTokenDecimals(UD60x18 value, uint8 decimals) internal pure returns (uint256);

Parameters

Returns

truncate

Truncates a UD60x18 number down to the correct precision.

function truncate(UD60x18 value, uint8 decimals) internal pure returns (UD60x18);

Parameters

Returns

log10Floor

Performs a naive log10 calculation on input returning the floor of the result

function log10Floor(uint256 input) internal pure returns (uint256 count);

computeCLevel

Calculates the C-level given a utilisation value and time since last trade value (duration). (https://www.desmos.com/calculator/0uzv50t7jy)

function computeCLevel(
    UD60x18 utilisation,
    UD60x18 duration,
    UD60x18 alpha,
    UD60x18 minCLevel,
    UD60x18 maxCLevel,
    UD60x18 decayRate
) internal pure returns (UD60x18);

Parameters

Returns

computeCLevelGeoMean

Calculates the geo-mean C-level given a utilisation before and after collateral is utilised.

function computeCLevelGeoMean(
    UD60x18 utilisationBefore,
    UD60x18 utilisationAfter,
    UD60x18 duration,
    UD60x18 alpha,
    UD60x18 minCLevel,
    UD60x18 maxCLevel,
    UD60x18 decayRate
) internal pure returns (UD60x18 cLevel);

Parameters

Returns

Errors

OptionMath__NonPositiveVol

error OptionMath__NonPositiveVol();

OptionMath__OutOfBoundsPrice

error OptionMath__OutOfBoundsPrice(UD60x18 min, UD60x18 max, UD60x18 price);

OptionMath__Underflow

error OptionMath__Underflow();

OptionMath__UtilisationOutOfBounds

error OptionMath__UtilisationOutOfBounds();

Structs

BlackScholesPriceVarsInternal

struct BlackScholesPriceVarsInternal {
    int256 discountFactor;
    int256 timeScaledVol;
    int256 timeScaledVar;
    int256 timeScaledRiskFreeRate;
}