MinterAmm is an Automated Market Maker or "AMM" designed specifically for trading options for ERC20 tokens. It exposes functions for buying and selling bToken as well as selling wToken[^1]. Each MinterAmm trades one of the two types of option Series: Puts or Calls. All option premiums will be in units of the AMM's collateral token, which for a Call AMM will be equal to the underlying token (e.g. a WBTC Call AMM's collateral token is WBTC), and for a Put AMM be equal to USDC (e.g. a WBTC Put AMM's collateral token is USDC). It uses the collateral token added by liquidity providers to mint bTokens and wTokens, keeping the wTokens for itself and selling the bTokens to traders. The AMM exposes functions for providing and withdrawing liquidity in the AMM pool. It is often useful to know the total value of all the option tokens and collateral token that comprise a pool, and there is a function for that as well.MinterAmm, the quoted premium includes consists of the component from the onchain Black-Scholes approximation formula, as well as a price impact component. It is not possible to guarantee an exact option token price, because the price depends on the reserves of bToken and wToken held by the AMM, and those reserves might change if another transaction which affects the reserve amounts gets mined before the original trader's transaction gets mined. This is also true for when an LP withdraws their liquidity from the AMM and sets sellTokens = true, which will sell the wTokens owed to trader back to AMM in return for collateral token. This is why all of these functions take some slippage function argument, either collateralMinimum when selling option tokens, or collateralMaximum when buying option tokens.bTokens, buying 'bTokens', and selling wTokens.bTokenBuy, bTokenSell, or wTokenSell unexpected behavior can occur. So to preclude this from happening we gate these function calls with the minTradeSize modifierupdateImplementation and transferOwnership exist so that the owners can update the contracts in the event of a critical vulnerability that puts user's funds at risk.ERC20 token whose price determines the (glossary.md#moneyness) of the Series this AMM trades. For example, both WBTC Call option series and WBTC Put option series share WBTC as their underlying token, because the price of WBTC determines whether the Series is in or out of the money. If this AMM trades Calls then this will be the same token as the collateralToken.ERC20 token used to denominate the strike price of the Series this AMM trades. This will almost always be USDC, but in the future could be different when SIREN denominates prices in something other than USDC. If this AMM trades Puts then this will be the same token as the collateralToken​ERC20 token this AMM uses for collateral. This is the token used to denominate all option prices (a.k.a. premiums) in the MinterAmm, as well as the liquidity provided by LPs​SeriesController associated with this MinterAmm. The MinterAmm uses the SeriesController to interact with the Series it trades.ERC1155Controller associated with this MinterAmm. The MinterAmm uses the ERC1155Controller to interact with the the option tokens of the Series it trades.MinterAmm takes when it executes a trade.0.4, multiplied by the square root of the number of seconds in a year (i.e. implied_volatility * 0.4 * Math.sqrt(365 * 24 * 60 * 60))includeUnclaimed exists only as a way to save on gas when calculating total pool value on chain; if the caller knows all option tokens have been claimed (which will be true if claimAllExpiredTokens has just been called), it can pass false for includeUnclaimed and skip calculating their value.includeUnclaimedtrue if the value of expired of unclaimed wToken should be included in the total pool calculation, and false if it should not be includedseriesIdbToken and wToken available to the AMM for the given seriesId. The AMM uses these balances as inputs into its bonding curve equation to compute the premiums for buying and selling option tokens.bToken and wToken held by the AMM, but additionally those option tokens that could be minted using the AMM's collateral token. The amounts returned will likely be slightly less than the full bToken and wToken amounts owned by the AMM, because the amounts returned must satisfy the ratio of the wToken and bToken prices computed by the onchain Black-Scholes approximation formula. See the documentation section on [protocol math](TODO point to this) for the motivation behind calculating virtual reserve balances in this manner.seriesIdbTokenVirtualBalancebToken available on the AMMwTokenVirtualBalancewToken available on the AMMseriesId denominated in the priceToken. The returned values always use 8 decimal places. For example, if the Series' underlying == WBTC and price == USDC, then this function will return 4500000000000 ($45_000 in human readable units).seriesIdbToken as a percentage of collateral locked by 1 option token, multiplied by a scaling factor of 1e18. For instance, if the price of 1 bToken is 0.1 * 1e18, and the bToken's Series has a strike price of $35,000, then the price of 1 bToken in units of USDC is $3,500.0.5 * 1e18 and be thought treated logically as simply 0.5.calcPrice uses a Black-Scholes approximation formula for pricing bTokens. See the section [protocol math](TODO link to this) for more details on the approximation formula.wToken is always 1e18 - price_of_btoken, so in the above scenario, the price of the wToken would be $35,000 - $3,500 = $31,500.strikecurrentPricebTokenAmount of bTokens on the given seriesId in units of collateral token. The premium has two components: the price returned by the Black-Scholes approximation formula, and the added cost of price impact.seriesIdbTokenAmountbToken the caller wants to receive in return for paying the premiumbTokenAmount of bTokens on the given seriesId in units of collateral token. The premium has two components: the price returned by the Black-Scholes approximation formula, and the price impact.seriesIdbTokenAmountbToken the caller wants to sell to the AMMwTokenAmount of wTokens on the given seriesId in units of collateral token. The premium has two components: the price returned by the Black-Scholes approximation formula, and the price impact.seriesIdwTokenAmountwToken the caller wants to sell to the AMMbTokens and wTokens held by the AMM. This function is useful for offchain clients to calculate the total collateral token available to the AMM. The offchain clients can use this to calculate the collateral owed to LPs when The LPs withdraw their LP Token​bTokens and wTokens held by the AMM on the LP's behalf. This function is useful for offchain clients to calculate value of the option tokens owed to the holder of lpTokenAmount of LP Token.lpTokenAmount is equal to 10% of the total supply of LP Token, then the return value of MinterAmm.getOptionTokensSaleValue will be equal to the premiums for selling 10% of the bTokens and wTokens held by the AMM. See MinterAmm.bTokenGetCollateralOut and MinterAmm.wTokenGetCollateralOut for how to calculate the premiums when selling bTokens and wTokens.lpTokenAmountlpTokenMinimum argument to specify the minimum acceptable amount of LP Token the caller will receive, and any lower than this will cause the function call to revert.lpTokenMinimumcollateraAmount of collateral tokenlpTokenAmount of their LP Token and in exchange receives their pro-rata share of the AMM's tokens. For example, if lpTokenAmount is equal to 10% of the total supply of LP Tokens, then the caller will receive 10% of the AMM's collateral token as well as 10% of each of the option tokens the AMM holds. If sellTokens is set to true, then the caller will receive only collateral token, because all of LP's option tokens will be sold to the AMM in exchange for collateral token. However, because of price impact the value of the collateral token the LP receives may be less than 10% of the AMM's total value.collateralMinimum argument to specify the minimum acceptable amount of collateral token the caller will receive, and any lower than this will cause the function call to revert.lpTokenAmountsellTokenstrue if the caller wishes to sell their option tokens to the AMM and only receive collateral token, and false if they wish to receive less collateral token but receive their pro-rata share of the AMM's option tokens which they can sell at a later timecollateralMinimumMinterAmm.claimExpiredTokens​bTokens and wTokens held by the AMM. If the Series is out of the money then all bTokens will be worthless, and the wTokens will be claimed for the collateral value locked when minting them. If the Series is in the money then both the bTokens and wTokens will have some non-zero value.seriesIdbTokenAmount of bToken from the AMM, but will revert if the premium calculated by the AMM exceeds collateralMaximum. The return value is the premium (in units of collateral token) the caller pays. Prior to calling this function, the caller must approve the AMM for the collateralMaximum amount. See MinterAmm.bTokenGetCollateralIn for how the AMM calculates the premium.seriesIdbTokenAmountbToken the caller wishes to purchasecollateralMaximumbToken. The actual premium can exceed this value due to slippage​bTokenAmount of bToken to the AMM, but will revert if the premium calculated by the AMM goes below collateralMinimum. The return value is the premium (in units of collateral token) the caller receives. Prior to calling this function, the caller must approve the AMM for the bTokenAmount. See MinterAmm.bTokenGetCollateralOut for how the AMM calculates the premium.seriesIdbTokenAmountbToken the caller wishes to purchasecollateralMinimumbToken, The actual premium can go below this value due to slippage​wTokenAmount of wToken to the AMM, but will revert if the premium calculated by the AMM goes below collateralMinimum. The return value is the premium (in units of collateral token) the caller receives. Prior to calling this function, the caller must approve the AMM for the wTokenAmount. See MinterAmm.wTokenGetCollateralOut for how the AMM calculates the premium.seriesIdwTokenAmountwToken the caller wishes to purchasecollateralMinimumwToken, The actual premium can go below this value due to slippage​MinterAmm.calcPrice for how it is used._volatilityFactor0.4 * implied_vol * sqrt(num_seconds_in_year)MinterAmm's logic contract. The SIREN protocol's contracts use the EIP-1822 standard for implementing upgradeable contracts. This allows us to update vulnerable contracts and keep users' option tokens safe. When the SIREN protocol has reached a certain level of stability, we can remove these safety guards and ensure no one on the Siren team can swap out the smart contract functionality._newImplementationMinterAmm's function implementationsnewOwner address. See the onlyOwner modifier for the permissions granted to the protocol admin.newOwnerwToken because of a technical blocker in the SIREN protocol's Black-Scholes approximation algorithm. The algorithm over-prices bToken's and underprices wToken's, and so if the AMM were to sell wToken's then through arbitrage the AMM would quickly be drained of all wToken's. For that reason, we cannot add functionality for selling wToken's to the AMM