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# Partial Collateralization Parameters

## PenaltyRatio

Value
• penaltyRatio: 0.05 (5%)
Meaning/Justification
• When a user is liquidated, they buy back their option with their locked collateral. The remaining collateral is then slashed - the slashed amount (as a percentage) is given by penaltyRatio.
• Example: Alice has $1000 in locked collateral and is liquidated on an option worth$300. She buys back the option for $300, leaving$700 in remaining collateral. This is then slashed by 5% ($35) and she walks away with$665.

## LiquidatorFeeRatio

Value
• LiquidatorFeeRatio: 10%
Meaning/Justification
• This parameter is the percentage of slashed funds (see penaltyRatio) that is given to liquidators (the caller of the liquidation function).
• Since liquidators only have to pay gas to liquidate a trader, their share of the slashed collateral should not be too large.
• That said, it should be enough to encourage fast liquidations and offset gas costs.

## SMFeeRatio

Value
• SMFeeRatio: 0%
Meaning/Justification
• This parameter is the percentage of slashed funds (see penaltyRatio) that is given to the security module (SM).
• The security module is responsible for ensuring solvent traders are able to close their positions at settlement (as well as insurance for other shortfall events). LPs in the SM should therefore be entitled to a portion of the slashed collateral.
AMM receives the bulk of slashed collateral:
• Implicit in LiquidatorFeeRatio and SMFeeRatio is the fact that the AMM will receive 100 - LiquidatorFeeRatio - SMFeeRatio = 90%.
• Example: Say there's a liquidation with $220 in slashed collateral. This will be split between the liquidator, SM and AMM in a 10:0:90 split. That is, the liquidator will receive$22, the SM $0 and the AMM the remaining$198.

Value
• MinLiquidation Fee: $20 Meaning/Justification • There is a minimum penalty that a trader incurs when they are liquidated and it is given by MinLiquidationFee. • This is to ensure that the liquidator always receives a sufficient reward to make up for their gas costs. ## minStaticQuoteCollateral Value • minStaticQuoteCollateral:$400 USD
Meaning/Justification
• When a user partially collateralizes either a short call or short put, they have to deposit collateral (in this case, denominated in USD). minStaticQuoteCollateral represents the minimum amount of the quote asset that must be deposited to open a short.

## minStaticBaseCollateral

Values
• minStaticBaseCollateral (ETH): 0.5 ETH
Meaning/Justification
• As for minStaticQuoteCollateral, this parameter represents the minimum amount of the base asset that can be deposited to open a short call.

## shockVol

Values:
• $T_{A}=4$
weeks (ETH)
• $T_{B} = 8$
weeks (ETH)
• ETH:
$\texttt{ShockVolA} =300$
• ETH:
$\texttt{ShockVolB}=180$
• if time to expiry
$(t) < T_{A}$
,
$\texttt{ShockVol} = \texttt{ShockVolA}$
• if
$T_{A}
,
$\texttt{ShockVol} = \texttt{ShockVolA} - \frac{\texttt{ShockVolA} -\texttt{ShockVolB}}{T_{A}-T_{B}}\times (t-T_{A})$
• else if
$t > T_{B}$
,
$\texttt{ShockVol} = \texttt{ShockVolB}$
Meaning/Justification
• To compute the minimum collateral required for a user’s partially collateralized short, a time dependent shock volatility is used in the Black Scholes pricing formula.
• The shock volatility should be exceptionally rare and increasing as expiration approaches. This means shorter dated expiries have a larger shock (since they're naturally more volatile) and vice versa.

## call(put)SpotPriceShock

Values
• callSpotPriceShock: 120% (ETH)
• putSpotPriceShock: 80% (ETH)
Meaning/Justification
• A shock (up or down depending if call or put) to the spot price is used to compute the minimum collateral required for a user's short.
• Based on historical data, rapid shocks of 20-25% to the spot price are exceptionally rare. This gives a large buffer time for underwater shorts to be liquidated.