2a:null 2b:["$","title",null,{"children":"Auctions / Float Protocol | Float Protocol | Observable"}] 30:T833,md`

Float Protocol › Auctions

# Auctions Each period (set to ${bind( Tangle({ format: x => (x / SECONDS_IN_AN_HOUR).toFixed(2) }), viewof auctionPeriod )} hours) we calculate the FLOAT time-weighted average price, ${tex`\bar{m}_\star^{FLOAT}`}. If it differs from the FLOAT Target Price, ${tex`t_\star`}, we do either an expansion or contraction of FLOAT supply. If the price of FLOAT is away from its Target Price, we want to change the supply by minting (expansion) or buying up and burning FLOAT (contraction).

${dot`digraph { buyer1 -> FP; buyer2 -> FP; buyerN -> FP}`} Forward Auction (Expansion)

${dot`digraph { seller1 -> FP; seller2 -> FP; seller3 -> FP }`} Reverse Auction (Contraction)

In order to modify this supply we'd like the following properties: 1. **Predictable valuation** - if you participate in a sale, you should have certainty over the current price at any point. 2. **Instant clearing** - if a transaction goes through you should instantly receive/use your token, you shouldn't have to submit another transaction to fill / clear. 3. **Capital Efficient** - We don't want to be minting any more supply than necessary to adjust the price. 4. **Defined Completion** - The auction should be completed in a reasonable amount of time. ### Basket Tracking In addition, we track the Basket Factor, ${tex`b`}, which denotes the ratio of the value stored in the basket, ${tex`b_\star^{ETH}`} accounting for the desired Basket Target Factor (version 1 will have ${tex`b_t = 100\%`}) and the desired market cap. ${tex.block`b = \frac{b_\star^{ETH}}{\Sigma^{FLOAT} \times t_\star'} \times b_t`} `31:T102e,md`## Stabilisation Cases As a decentralised system, we rely on external actors to prevent the Protocol's market price from shifting from the target. These "Keepers" are incentivised by arbitrage opportunities to participate in Auctions. All Dutch Auctions start from a "fools trade" - a trade in which, given correct oracle values, it would never make sense to make, but would be incredibly favourable to the Protocol. As the Dutch Auctions progress the protocol will give out less efficient offers at each relative block number (step ${tex`s`}) in our auction of ${tex`N = 150`} blocks. As such we can define efficiency, ${tex`E`}, as how close we are to the start. ${tex.block`E = 1 - \frac{s}{N}`} Each Dutch Auction aims to remove or add a certain amount of FLOAT from the market which would cause the necessary price correction. We call this value ${tex`\Delta`}. ${tex.block`\Delta = \overbrace{ \frac{\bar{m}_\Xi^{FLOAT} \times \Sigma^{FLOAT}}{t_\Xi'} }^\text{Targeted Supply} - \overbrace{ \Sigma^{FLOAT} }^\text{Current Supply}`} Another commonly used value is our price delta in ETH ${tex`\delta_\Xi = |t_\Xi' - \bar{m}_\star^{FLOAT}|`} that represents our euclidean distance from the Target Price. In order to account for stale auction prices, we use a percentage factor ${tex`\alpha`} which provides a buffer zone around the starting price. Starting the price higher in an expansion, and lower in a contraction. This gives us to values for the market price: ${tex.block`\bar{m}_{+\Xi}^{FLOAT} = (1 + \alpha) \times \bar{m}_{\Xi}^{FLOAT}`} ${tex.block`\bar{m}_{-\Xi}^{FLOAT} = (1 - \alpha) \times \bar{m}_{\Xi}^{FLOAT}`} 1. **Up (Expansion) Case:** ${tex.block`\bar{m}_\star^{FLOAT} \ge t_\star \land b \ge 1`} Both the Basket and demand for FLOAT are on the rise. We want more FLOAT and we are in a well supported position. BANK holders will benefit most from this case. We sell ${tex`\Delta`} FLOAT for the pair ${tex`\langle \text{ETH}, \text{BANK}\rangle`}: ${tex.block`\langle t_\Xi' , \frac{\delta_{+\Xi}}{\bar{m}^{BANK}_\Xi} \times E \rangle`} ${tex.block`\langle t_\Xi', \frac{\bar{m}_{+\Xi}^{FLOAT} - t_\Xi' }{\bar{m}^{BANK}_\Xi} \rangle \Rightarrow \langle t_\Xi', 0 \rangle `} 2. **Re-stock (Expansion) Case:** ${tex.block`\bar{m}_\star^{FLOAT} \ge t_\star \land b \lt 1`} Demand for FLOAT is high, but the underlying Basket is not increasing at the same rate. The ETH goes towards resupplying the Basket. We sell ${tex`\Delta`} FLOAT for the pair ${tex`\langle \text{ETH}, \text{BANK}\rangle`}: ${tex.block`\langle \bar{m}_\Xi^{FLOAT} - \delta_\Xi \times (1 - E) , 0 \rangle`} ${tex.block`\langle \bar{m}_{+\Xi}^{FLOAT}, 0 \rangle \Rightarrow \langle t_\Xi', 0 \rangle `} 3. **Confidence (Contraction) Case:** ${tex.block`\bar{m}_\star^{FLOAT} \lt t_\star \land b \ge 1`} Demand for FLOAT is low, but the underlying Basket is well supported. This is one of the favourable cases as it allows us to resupply the Basket with no cost to BANK holders. We buy ${tex`\Delta`} FLOAT for the pair ${tex`\langle \text{ETH}, \text{BANK}\rangle`}: ${tex.block`\langle \bar{m}_\Xi^{FLOAT} + \delta_\Xi \times (1 - E) , 0 \rangle`} ${tex.block`\langle \bar{m}_{-\Xi}^{FLOAT}, 0 \rangle \Rightarrow \langle t_\Xi', 0 \rangle `} 4. **Down (Contraction) Case:** ${tex.block`\bar{m}_\star^{FLOAT} \lt t_\star \land b \lt 1`} Both the Basket and FLOAT have a reduced demand. We aim to resupply the Basket, and mint BANK to relieve the net pressure on the Basket. This balances our distribution between ETH and BANK by how far below the Basket we are. We buy ${tex`\Delta`} FLOAT for the pair ${tex`\langle \text{ETH}, \text{BANK}\rangle`}: ${tex.block`\langle b_f . ( \bar{m}_{-\Xi}^{FLOAT} + \delta_\Xi \times (1 - E) ), (1 - b_f) . ( \frac{\bar{m}_{-\Xi}^{FLOAT}}{\bar{m}^{BANK}_\Xi} + \frac{\delta_\Xi}{\bar{m}^{BANK}_\Xi} \times (1 - E) ) \rangle`} ${tex.block`\langle b_f \times \bar{m}_{-\Xi}^{FLOAT}, (1 - b_f) \times \frac{\bar{m}_{-\Xi}^{FLOAT}}{\bar{m}^{BANK}_\Xi} \rangle \Rightarrow \langle b_f \times t_\Xi', (1 - b_f) \times \frac{t_\Xi'}{\bar{m}^{BANK}_\Xi} \rangle `} `32:T820,html`

${swatches({ color, marginLeft: margin.left, columns: "80px" })} ${chart}

Step @ ${step}

${Math.abs(neededFloatDelta).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })} FLOAT was ${ neededFloatDelta > 0 ? "sold to" : "bought from" } the market at an average price of ${( avgEthPriceInUsd / ethereumUSDPrice ).toFixed(8)} ETH ($${avgEthPriceInUsd.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })}) and ${(avgBankPriceInUsd / bankMarketPrice).toFixed( 8 )} BANK ($${avgBankPriceInUsd.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })}) = $${( avgEthPriceInUsd + avgBankPriceInUsd ).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })}

Basket Factor: ${(startingBasketFactor * 100).toFixed( 2 )}% has moved to ${(finalBasketFactor * 100).toFixed(2)}%

${Math.abs(basketDeltaInEth).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })} ETH ($${Math.abs(basketDeltaInUsd).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })}) has been ${ expansion ? "added to" : "removed from" } the basket.

${Math.abs(bankDeltaInBank).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })} ($${Math.abs(bankDeltaInUsd).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })}) of BANK has been ${expansion ? "burned" : "minted"}.

Expected profit (given market price) $ ${( floatMarketPrice * neededFloatDelta - (basketDeltaInUsd + bankDeltaInUsd) ).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 })}

`33:T732,md`## Handling Adverse Conditions The model above makes some naive assumptions: 1. There is only one average clearing price. 2. The market price always equals the TWAP price 3. The ETH-USD price oracle is accurate ### Market Manipulation We use a ${ twapWindow / SECONDS_IN_AN_HOUR } hour sliding window TWAP price before the auction starts to calculate the necessary values. This is vital as it means we can remain flash-trade friendly, while reducing the ability for market manipulation to lead to unfavourable offers to the protocol. By using the average, any market manipulation will have to be sustained over ${ twap_period / SECONDS_IN_AN_HOUR } hours. Making it cost-prohibitive as arbitragers will be able to trade into the manipulation and turning impermanent loss permanent. ### Underlying Price Changes We rely on price data for BANK-ETH, FLOAT-ETH and ETH-USD. We fix these prices at the start of an auction, but what happens if these prices are stale? - Calculate Max / Average ETH price movements per block - Calculate the impact of the deviation from peg (in contraction, in expansion etc) ### Efficiency vs Perfect Stability We often have a choice between efficiency (giving more value to BANK holders) and perfectly correcting the market price to target price every time. In general, we lean on the side of efficiency as the market is likely to self-correct the last part of the price and we can run the auctions back-to-back (i.e. as soon as one auction is finished, we start the next). For this reason, we have hard limits on the price movement. - We will not mint more than 10% of the supply in a single auction. - We will not burn more than 10% of the supply in a single auction. This increases our resilience to change, as it gives a chance for the target price to update relative to the market conditions. `34:Tc9d,chart = { const isExpansion = stabilisationCase === "up" || stabilisationCase === "restock"; const label = isExpansion ? "Sale Price $ (↓)" : "Purchase Price $ (↑)"; const x = d3 .scaleLinear() .domain(d3.extent(data, d => d.step)) .range([margin.left, width - margin.right]); const y = d3 .scaleLinear() .domain([0, d3.max(series, d => d3.max(d, d => d[1]))]) .nice() .range([height - margin.bottom, margin.top]); const xAxis = g => g.attr("transform", `translate(0,${height - margin.bottom})`).call( d3 .axisBottom(x) .ticks(width / 80) .tickSizeOuter(0) ); const yAxis = g => g .attr("transform", `translate(${margin.left},0)`) .call(d3.axisLeft(y).ticks(height / 40)) .call(g => g.select(".domain").remove()) .call(g => g .selectAll(".title") .data([label]) .join("text") .attr("class", "title") .attr("x", -margin.left) .attr("y", 10) .attr("fill", "currentColor") .attr("text-anchor", "start") .text(label) ); const makerDaoCurve = d3 .line() .x(d => x(d.step)) .y(d => y(floatMarketPrice * 1.1 * Math.pow(0.997, d.step))); const area = d3 .area() .x(d => x(d.data.step)) .y0(d => y(d[0])) .y1(d => y(d[1])); const stacked = g => g.call(g => g .selectAll("path") .data(series) .join("path") .attr("fill", ({ key }) => color(key)) .attr("d", area) .append("title") .text(({ key }) => key) ); // const c = isExpansion // ? floatMarketPrice * (1 + buffer) // : floatMarketPrice * (1 - buffer); // const grad = (floatTargetPrice - c) / auctionLength; // const xPos = (floatMarketPrice - c) / grad; // console.log(grad); // const efficiency = // xPos + (auctionLength - xPos - 1) * (1 - auctionEfficiency); const bisect = d3.bisectCenter(d => d.step); const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]); svg .append("g") .selectAll("path") .data(series) .join("path") .attr("fill", ({ key }) => color(key)) .attr("d", area) .append("title") .text(({ key }) => key); // svg // .append('path') // .datum(data) // .attr('d', makerDaoCurve) // .attr("stroke", "black") // .attr('fill', 'none') // .attr('stroke-width', 2); svg.append("g").call(xAxis); svg.append("g").call(yAxis); svg .append("line") .attr("x1", x(step)) .attr("x2", x(step)) .attr("y1", margin.top) .attr("y2", height - margin.bottom) .attr("stroke", "black") .attr("stroke-dasharray", 4); svg .append("line") .attr("x1", margin.left) .attr("x2", width - margin.right) .attr("y1", y(floatTargetPrice)) .attr("y2", y(floatTargetPrice)) .attr("stroke", "black") .attr("stroke-dasharray", 4); svg .append("line") .attr("x1", margin.left) .attr("x2", width - margin.right) .attr("y1", y(floatMarketPrice)) .attr("y2", y(floatMarketPrice)) .attr("stroke", "black") .attr("stroke-dasharray", 4); return svg.node(); }35:[] 2e:{"id":"a517b30672f6a180","slug":"auctions","title":"Auctions / Float Protocol 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parameters.\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":63,"value":"html`${bind(Range([1000, 1e10], {\n step: 1000,\n transform: Math.log,\n width: \"60%\",\n label: html`Float Supply ${tex`\\Sigma^{FLOAT}`}`,\n}), viewof floatSupply)} The total quantity of FLOAT in circulation.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":193,"value":"html`${bind(Range([0, 2.5], {\n step: 0.001,\n width: \"50%\",\n label: html`Float Target Price ${tex`t`}`\n}), viewof floatTargetPrice)} The target price we want FLOAT to be.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":188,"value":"html`${bind(Range([0, 2.5], {\n step: 0.001,\n width: \"50%\",\n label: html`Float Market Price ${tex`m^{FLOAT}`}`\n}), viewof floatMarketPrice)} The current trading price of FLOAT in circulation, measured as ${tex`\\bar{m}_\\Xi^{FLOAT} \\times \\Xi_\\$`}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":183,"value":"html`${bind(\n Range([0, 1], {\n step: 1 / 150,\n width: \"50%\",\n label: html`Auction Efficiency`\n }),\n viewof auctionEfficiency\n)} How efficient an auction is.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":180,"value":"html`${bind(\n Range(\n [(floatTargetPrice * floatSupply) / 2, floatTargetPrice * floatSupply * 2],\n {\n step: 100,\n width: \"50%\",\n label: html`Value in Basket ${tex`b^{ETH}`}`\n }\n ),\n viewof valueInBasket\n)} The value of our underlying basket of cryptocurrencies in $.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":105,"value":"{\n const cases = {\n up: [1, \"Up Case\", \"Linear Forward Dutch Auction\"],\n restock: [2, \"Re-stock Case\", \"Linear Forward Dutch Auction\"],\n confidence: [3, \"Confidence Case\", \"Linear Reverse Dutch Auction\"],\n down: [4, \"Down Case\", \"Linear Reverse Dutch Auction\"]\n };\n const [number, title, auctionType] = cases[stabilisationCase];\n return md`### _${title} (${number})_ - ${auctionType}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":137,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"md`## Adding Liquidity Pool Interaction\n\nAs people buy/sell FLOAT from the auction, the price should adjust on the respective liquidity pools to account for this increased supply.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":392,"value":"html`${bind(Range([1e4, 1e7], {\n transform: Math.log,\n width: \"60%\",\n label: html`BANK Supply ${tex`\\Sigma^{BANK}`}`,\n}), viewof bankSupply)} The total quantity of BANK in circulation.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":403,"value":"html`${bind(Range([100, 500], {\n step: 10,\n width: \"50%\",\n label: html`Bank Market Price ${tex`m^{BANK}`}`\n}), viewof bankMarketPrice)} The current trading price of BANK in circulation, measured as ${tex`\\bar{m}_u^{BANK}`}.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":446,"value":"html`${bind(\n Range([0, 1], {\n step: 0.1,\n width: \"50%\",\n label: html`Liquid BANK quotient ${tex`Q^{BANK}`}`\n }),\n viewof bankLiquidityQuotient\n)} The proportion of BANK which is stored in liquidity pools`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":479,"value":"html`${bind(\n Range([0, 1], {\n step: 0.1,\n width: \"50%\",\n label: html`Liquid FLOAT quotient ${tex`Q^{FLOAT}`}`\n }),\n viewof floatLiquidityQuotient\n)} The proportion of FLOAT which is stored in liquidity pools`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2147,"value":"md`Next, we'll look at how the Target Price changes.\n\nNext`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"md`\n---\n## Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"md`### Appendix: Constants`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2055,"value":"DEBUG = false","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"SECONDS_IN_AN_HOUR = 60 * 60","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":253,"value":"FLOAT_INITIAL_PRICE = 1.618","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"md`### Appendix: Simplified Auction State`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"twap_period = twapWindow / twapGranularity","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":108,"value":"startingBasketFactor = valueInBasket / (floatSupply * floatTargetPrice);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":111,"value":"expansion = floatMarketPrice >= floatTargetPrice","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2070,"value":"step = Math.floor((1 - auctionEfficiency) * (auctionLength - 1))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":107,"value":"stabilisationCase = {\n let underlyingDemand = startingBasketFactor >= 1;\n if (underlyingDemand && expansion) return STABILISATION_CASE.UP;\n if (underlyingDemand && !expansion) return STABILISATION_CASE.CONFIDENCE;\n if (!underlyingDemand && expansion) return STABILISATION_CASE.RESTOCK;\n if (!underlyingDemand && !expansion) return STABILISATION_CASE.DOWN;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2073,"value":"neededFloatDelta = (floatMarketPrice / floatTargetPrice) * floatSupply -\n floatSupply","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2076,"value":"avgEthPriceInUsd = calculateEthDelta(\n stabilisationCase,\n floatMarketPrice,\n floatTargetPrice,\n startingBasketFactor,\n step\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2079,"value":"avgEthPriceInEth = avgEthPriceInUsd / ethereumUSDPrice","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2085,"value":"avgBankPriceInUsd = calculateBankDelta(\n stabilisationCase,\n floatMarketPrice,\n floatTargetPrice,\n startingBasketFactor,\n step\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2117,"value":"avgBankPriceInEth = avgBankPriceInUsd / bankMarketPrice","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2083,"value":"basketDeltaInEth = basketDeltaInUsd / ethereumUSDPrice","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2081,"value":"basketDeltaInUsd = avgEthPriceInUsd * neededFloatDelta","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2087,"value":"bankDeltaInUsd = avgBankPriceInUsd * neededFloatDelta","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2089,"value":"bankDeltaInBank = bankDeltaInUsd / bankUSDPrice","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2091,"value":"auctionCutoffPrice = avgEthPriceInUsd + avgBankPriceInUsd","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2064,"value":"bufferedMarketPrice = expansion\n ? floatMarketPrice * (1 + buffer)\n : floatMarketPrice * (1 - buffer)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1443,"value":"function calculateEthDelta(\n stabilisationCase,\n floatMarketPrice,\n floatTargetPrice,\n basketFactor,\n s\n) {\n const lastIndex = auctionLength - 1;\n if (stabilisationCase === STABILISATION_CASE.UP) {\n return floatTargetPrice;\n }\n\n if (stabilisationCase === STABILISATION_CASE.RESTOCK) {\n const deltaEth = Math.abs(bufferedMarketPrice - floatTargetPrice);\n const stepAdjustedEthComponent = deltaEth * (s / lastIndex);\n return bufferedMarketPrice - stepAdjustedEthComponent;\n }\n const deltaEth = Math.abs(bufferedMarketPrice - floatTargetPrice);\n const stepAdjustedEthComponent = deltaEth * (s / lastIndex);\n\n if (stabilisationCase === STABILISATION_CASE.CONFIDENCE) {\n return bufferedMarketPrice + stepAdjustedEthComponent;\n }\n if (stabilisationCase === STABILISATION_CASE.DOWN) {\n return basketFactor * (bufferedMarketPrice + stepAdjustedEthComponent);\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1560,"value":"function calculateBankDelta(\n stabilisationCase,\n floatMarketPrice,\n floatTargetPrice,\n basketFactor,\n s\n) {\n const lastIndex = auctionLength - 1;\n if (stabilisationCase === STABILISATION_CASE.RESTOCK) {\n return 0;\n }\n if (stabilisationCase === STABILISATION_CASE.CONFIDENCE) {\n return 0;\n }\n\n if (stabilisationCase === STABILISATION_CASE.UP) {\n return (bufferedMarketPrice - floatTargetPrice) * (1 - s / lastIndex);\n }\n\n const deltaEth = floatTargetPrice - bufferedMarketPrice;\n if (stabilisationCase === STABILISATION_CASE.DOWN) {\n const basketFactorAdjustedBankComponent =\n ((deltaEth * s) / lastIndex) * (1 - basketFactor);\n return (\n bufferedMarketPrice * (1 - basketFactor) +\n basketFactorAdjustedBankComponent\n );\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":118,"value":"finalBasketFactor = (valueInBasket + basketDeltaInUsd) /\n ((floatSupply + neededFloatDelta) * floatTargetPrice)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":601,"value":"STABILISATION_CASE = ({\n UP: \"up\",\n RESTOCK: \"restock\",\n CONFIDENCE: \"confidence\",\n DOWN: \"down\",\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":216,"value":"md`### Appendix: Parameters`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"viewof auctionPeriod = Input(24 * SECONDS_IN_AN_HOUR)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1451,"value":"viewof auctionLength = Input(150)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1779,"value":"viewof buffer = Input(0.1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":207,"value":"viewof twapWindow = Input(24 * SECONDS_IN_AN_HOUR)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":210,"value":"viewof twapGranularity = Input(12)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":396,"value":"viewof bankSupply = Input(168e3)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":408,"value":"viewof bankMarketPrice = Input(bankUSDPrice)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":460,"value":"viewof bankLiquidityQuotient = Input(0.4)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":476,"value":"viewof floatLiquidityQuotient = Input(0.8)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":261,"value":"viewof floatSupply = Input(1e6)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":270,"value":"viewof floatTargetPrice = Input(FLOAT_INITIAL_PRICE)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":274,"value":"viewof floatMarketPrice = Input(FLOAT_INITIAL_PRICE + 0.2)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":278,"value":"viewof auctionEfficiency = Input(0.5)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":290,"value":"viewof valueInBasket = Input(floatTargetPrice * floatSupply)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1696,"value":"md`### Appendix: Graph Data`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1413,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1711,"value":"data = Array.from({ length: 150 }, (_, i) => ({\n step: i,\n eth: calculateEthDelta(\n stabilisationCase,\n floatMarketPrice,\n floatTargetPrice,\n startingBasketFactor,\n i\n ),\n bank: calculateBankDelta(\n stabilisationCase,\n floatMarketPrice,\n floatTargetPrice,\n startingBasketFactor,\n i\n )\n}))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1720,"value":"series = d3.stack().keys(groups)(data)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1703,"value":"groups = [\"eth\", \"bank\"]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1699,"value":"color = d3\n .scaleOrdinal()\n .domain(groups)\n .range(d3.schemeCategory10)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1684,"value":"margin = ({\n top: 20,\n right: 20,\n bottom: 30,\n left: 40\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1686,"value":"height = width * 0.5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":416,"value":"md`### Appendix: Live Data`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":422,"value":"coingeckoPrice = (await fetch(`https://api.coingecko.com/api/v3/simple/price?ids=ethereum,float-protocol&vs_currencies=usd`)).json()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":421,"value":"ethereumUSDPrice = DEBUG ? 2130.5 : coingeckoPrice.ethereum.usd","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":432,"value":"bankUSDPrice = DEBUG ? 490.02 : coingeckoPrice[\"float-protocol\"].usd","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":411,"value":"md`### Appendix: Import`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":73,"value":"import {Input, Range, bind} from \"@observablehq/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":294,"value":"import {Tangle} from \"@mbostock/tangle\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":385,"value":"import { Pair } from \"@floatcoder/constant-product-pool\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1286,"value":"dot = require(\"@observablehq/graphviz@0.2\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1693,"value":"import { swatches } from \"@d3/color-legend\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1424,"value":"d3 = require(\"d3@6\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":1303,"value":"ethers = require(\"https://cdn.ethers.io/lib/ethers-5.0.umd.min.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W35","stdlib":"1","titling":"auto"}} 2f:"$2e:body"