# BeyondPricer.sol

## Beyond Pricer

### General Overview

The Beyond Pricer contains logic for Rysk's option pricing. It prices the options using the Black-Scholes model and applies slippage, a spread, and fees to the Black-Scholes quote based on the state of the protocol. https://rysk.notion.site/Mk1-Options-Pricing-Model-1165471865f644e99a590707a08f3572

### Function by function

`quoteOptionPrice(Types.OptionSeries memory _optionSeries, uint256 _amount, bool isSell, int256 netDhvExposure)`

**Access Controlled**

`quoteOptionPrice(Types.OptionSeries memory _optionSeries, uint256 _amount, bool isSell, int256 netDhvExposure)`

**Access Controlled**This is the entry point of thhe contract for obtaining a quote (denominated in the strike asset) of an order, as well as the total delta exposure of the options in the order and fees applied to the order. The function first obtains an IV and forward value to price the option at from our Volatility Feed contract, the forward price is passed to the black scholes equation then returns a "vanilla" Black-Scholes quote for the option series using that IV, the price is then discounted by the forward.

A slippage multiplier value is obtained from the internal function `_getslippageMultiplier()`

which the vanilla price is multiplied by. This function is explained below. A spread premium is then added to the final order amount if the order is a buy order (meaning the DHV is selling those options). This is obtained from the internal function `_getSpreadValue()`

.

`getSlippageMultiplier(int256 _amount, int256 _optionDelta, int256 _netDhvExposure, bool _isSell)`

**Access Controlled**

`getSlippageMultiplier(int256 _amount, int256 _optionDelta, int256 _netDhvExposure, bool _isSell)`

**Access Controlled**This function returns a value that can be above or below 1, which is applied as a factor to the vanilla BS price. Slippage serves a couple of purposes; firstly, it disincentivises traders to buy or sell options that the DHV is already heavily exposed to, mitigating and spreading out our risk. It also allows governance to set discreet coefficients for the base of the exponential function for different option delta values. As an example, far OTM options earn the DHV a much smaller premium but require similar collateral requirements to the ATM equivalent option. It is undesirable for the DHV to sell many of these options and so we can set the slippage function to be much more severe on the wings.

The slippage function takes the form `(1 + g)^ -x`

, where g is the slippageGradient after it has been modified by the delta band multipliers and x is the net exposure to the particular option series. X is positive if the DHV is net long on that series and negative if it is net short.

`slippageGradient`

is a gov controlled variable that determines how steep the exponential function is. It will be set to a small number, for example 0.01e18, and then modified before being plugged into the equation. The modification is obtained by taking the delta value of the option and dividing it by `deltaBandWidth`

and looking up a factor to multiply `slippageGradient`

in the `callSlippageGradientMultipliers`

or `putSlippageGradientMultipliers`

array in the resulting index.

To ensure the slippage function is applied fairly as `x`

changes within the transaction, the function is integrated between the bounds of the `x`

value at the start of the tx and the `x`

value as a result of the tx to fund the area under the curve, which is then divided by the amount of options being sold.

`getSpreadValue(Types.OptionSeries memory _optionSeries, uint256 _amount, int256 _optionDelta, int256 _netDhvExposure, uint256 _underlyingPrice)`

**Access Controlled**

`getSpreadValue(Types.OptionSeries memory _optionSeries, uint256 _amount, int256 _optionDelta, int256 _netDhvExposure, uint256 _underlyingPrice)`

**Access Controlled**The spread function is only applied to options the DHV sells and reflects the cost of the collateral required to back the short option, as well as delta hedging costs incurred by the DHV as a result of the delta exposure of the tx.

The cost of collateral postion of the spread is calculated as `c * (1 + r)^t -c`

where c is the collateral requirements of the short options, t is the duration of the option in years, and r the collateral lending rate (governance settable variable). It is only applied to contracts that result in a net short position for the DHV. For example, if the DHV is long 10 contracts of this particular series and someone is requesting to purchase 30 of the same series from the DHV, the `collateralLendingPremium`

is only calculated from the 20 options that the DHV would be net short.

The `deltaHedgingPremium`

part of the spread is calculated as `d * (1 * r)^t -d`

where d is the dollar delta of the position, t is option duration in years, and r is the long or short delta borrow rate (gov settable variables used to reflect the cost of borrowing delta exposure in other markets). The spread is calculated based on the whole position and so is added to the final total quote for the position, not applied to each contract individually.

Last updated