OptionMathExternal

Functions

optionDelta

Calculate option delta

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

Parameters

Name	Type	Description
`spot`	`UD60x18`	Spot price
`strike`	`UD60x18`	Strike price
`timeToMaturity`	`UD60x18`	Duration of option contract (in years)
`volAnnualized`	`UD60x18`	Annualized volatility
`riskFreeRate`	`UD60x18`
`isCall`	`bool`	whether to price "call" or "put" option

Returns

Name	Type	Description
`<none>`	`SD59x18`	price Option delta

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
) public pure returns (UD60x18);

Parameters

Name	Type	Description
`spot`	`UD60x18`	Spot price (18 decimals)
`strike`	`UD60x18`	Strike price (18 decimals)
`timeToMaturity`	`UD60x18`	Duration of option contract (in years) (18 decimals)
`volAnnualized`	`UD60x18`	Annualized volatility (18 decimals)
`riskFreeRate`	`UD60x18`	The risk-free rate (18 decimals)
`isCall`	`bool`	whether to price "call" or "put" option

Returns

Name	Type	Description
`<none>`	`UD60x18`	price The Black-Scholes option price (18 decimals)

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
) public pure returns (UD60x18);

Parameters

Name	Type	Description
`utilisation`	`UD60x18`	The utilisation after some collateral is utilised
`duration`	`UD60x18`	The time since last trade (hours)
`alpha`	`UD60x18`	(needs to be filled in)
`minCLevel`	`UD60x18`	The minimum C-level
`maxCLevel`	`UD60x18`	The maximum C-level
`decayRate`	`UD60x18`	The decay rate of the C-level back down to minimum level (decay/hour)

Returns

Name	Type	Description
`<none>`	`UD60x18`	The C-level corresponding to the post-utilisation value.

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
) public pure returns (UD60x18 cLevel);

Parameters

Name	Type	Description
`utilisationBefore`	`UD60x18`	The utilisation before some collateral is utilised.
`utilisationAfter`	`UD60x18`	The utilisation after some collateral is utilised
`duration`	`UD60x18`	The time since last trade (hours)
`alpha`	`UD60x18`	(needs to be filled in)
`minCLevel`	`UD60x18`	The minimum C-level
`maxCLevel`	`UD60x18`	The maximum C-level
`decayRate`	`UD60x18`	The decay rate of the C-level back down to minimum level (decay/hour)

Returns

Name	Type	Description
`cLevel`	`UD60x18`	The C-level corresponding to the geo-mean of the utilisation value before and after collateral is utilised.