31:T6bf,md` The long-term movements of the FLOAT target price are influenced by how the market sentiment changes over time. This is gauged by both observing the assets in the Basket and the market price of FLOAT. The Protocol also passes the regular short term price control into the hands of the market, where market participants will eventually be able to conduct Dutch Auctions on-demand, when they deem necessary. For example, an arbitrage opportunity arises due to a large enough delta between the FLOAT market price and Target Price. These processes align FLOAT as a crypto-native unit account that gradually trends with market sentiment rather than a USD peg. ## Auctions Initially, the time period of the auctions will be circadian, occurring every 24 hours and 150 Blocks in length. This enables human beings to participate easily but also will result in major market price volatility of FLOAT between auctions. We plan to double the frequency of the auctions held by the Protocol every two weeks as FLOAT is more widely used and more bots are built to participate in the auctions. We refer to this as the *tuning period*, where the auction frequency transitions from every 24 hours, to 12 hours, to 6 hours, to 3 hours, to 1.5 hours, to occur every 150 Blocks, the length of a standard auction. At the end of the *tuning period*, the Protocol will no longer hold auctions regularly. Participants will have the option to hold an auction on demand when they deem necessary, for example, there is an arbitrage opportunity due to a difference in the FLOAT market price and target price. Participants who start an on-demand auction will be required to pay the cost of updating the Oracles required for the auction to proceed. `32:T8f0,md` ## Purchasing Power Protection The other key part of FLOAT is protecting your purchasing power by a willingness to shift the target price according to the market rather than the decision of a central entity. The target price of FLOAT is only shifted if the Basket of the Protocol and the market are in alignment, i.e. in the cases where the market price is greater than the target price and the Basket Factor is greater than 1 or, the market price is less than the target price and the Basket Factor is less than 1. In all other cases, the target price does not change. If the market and the Basket are in alignment, we first look at the fractional difference between the FLOAT market (TWAP) price, ${tex`\bar{m}_u^{FLOAT}`} and the previous target price, ${tex`m_t`}. This difference is then normalised by factor, ${tex`D_{max}`} to account for a 400% market price increase in an expansion or a 80% market price decrease in a given contraction. This range is chosen to include *black swan events* which may occur between auctions. ${tex.block`{\delta} = \frac{\bar{m}_u^{FLOAT} - m_t}{m_t}`} In an expansion, ${tex.block`\hat{\delta} = \frac{\delta}{D_{max}}`} In a contraction, ${tex.block`\hat{\delta} = \left| \frac{1}{D_{max}} \left( \frac{\delta}{1 + \delta} \right) \right|`} within the limits ${tex.block` 0 \leq \hat{\delta}\leq 1`} To minimise both volatility and overreaction to market movements any change to the target price will be averaged out for a given number of Blocks. This adjustment period ${tex`T`} is given by, ${tex.block` T = T_{max} - \hat{\delta}^{r_f} \left ( T_{max} - T_{min} \right )`} within the limits ${tex.block` T_{min} \leq T \leq T_{max}`} where ${tex`T_{max}`} and ${tex`T_{min}`} are the maximum and minimum adjustment periods respectively and ${tex`r_{f}`} is the rate factor. The fractional change in target price is given by ${tex.block`\frac{m_t' - m_t}{m_t} = \frac{b-1}{f_A T}`} where ${tex`b`} is the Basket Factor, ${tex`f_A`} is the auction frequency (units: per Block) and ${tex`m_t'`} is the new target price. The auction frequency will change over time as these auctions will be able to be called on demand. In this case ${tex`f_A`} will be given by the reciprocal of the number of Block since the last auction. `33:T81c,adjustmentPeriod = { // Calculate the Percentage difference between the market and target price console.log(floatMarketPrice, floatTargetPrice); const marketPercentDiff = (floatMarketPrice - floatTargetPrice) / floatTargetPrice; console.log("marketPercentDiff: ", marketPercentDiff); // In a contraction if (floatMarketPrice < floatTargetPrice) { const contractionScaled = 1 / (1 + marketPercentDiff) - 1; console.log("contractionScaled: ", contractionScaled); const marketNormDiff = contractionScaled / MAX_PRICE_DELTA; console.log("marketNormDelta", marketNormDiff); // let adjustmentPeriod = // MAXIMUM_ADJUSTMENT_PERIOD - // marketNormDiff ** INITIAL_RATE_FACTOR * // (MAXIMUM_ADJUSTMENT_PERIOD - MINIMUM_ADJUSTMENT_PERIOD); let adjustmentPeriod = calculateAdjustmentPeriod( marketNormDiff, MAXIMUM_ADJUSTMENT_PERIOD, MINIMUM_ADJUSTMENT_PERIOD, INITIAL_RATE_FACTOR ); console.log("adjustmentPeriod, precap:", adjustmentPeriod); // maximum and min limits for adjustment period if (adjustmentPeriod > MAXIMUM_ADJUSTMENT_PERIOD) { adjustmentPeriod = MAXIMUM_ADJUSTMENT_PERIOD; } if (adjustmentPeriod < MINIMUM_ADJUSTMENT_PERIOD) { adjustmentPeriod = MINIMUM_ADJUSTMENT_PERIOD; } console.log("Capped adjustmnetPeriod", adjustmentPeriod); return adjustmentPeriod; } // In an expansion if (floatMarketPrice >= floatTargetPrice) { const marketNormDiff = marketPercentDiff / MAX_PRICE_DELTA; console.log("marketNormDiff", marketNormDiff); let adjustmentPeriod = calculateAdjustmentPeriod( marketNormDiff, MAXIMUM_ADJUSTMENT_PERIOD, MINIMUM_ADJUSTMENT_PERIOD, INITIAL_RATE_FACTOR ); // Max and min limits for adjustment period if (adjustmentPeriod > MAXIMUM_ADJUSTMENT_PERIOD) { adjustmentPeriod = MAXIMUM_ADJUSTMENT_PERIOD; } if (adjustmentPeriod < MINIMUM_ADJUSTMENT_PERIOD) { adjustmentPeriod = MINIMUM_ADJUSTMENT_PERIOD; } return adjustmentPeriod; } }34:Ta44,{ // defining width and height const w = 500; const h = 400; const svg = DOM.svg(w, h); // Margin object with four properties const margin = { top: 20, right: 20, bottom: 50, left: 60 }; //create innerWidth and innerHeight for our margin const innerW = w - margin.right - margin.left; const innerH = h - margin.top - margin.bottom; // append a g element to our svg and give it a new origin inside svg const g = d3 .select(svg) .append('g') .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); // create group elements for our axes const xAxisG = g.append('g').attr('transform', "translate(0," + innerH + ")"); const yAxisG = g.append('g'); //create functions that x data and y data const xValue = d => d.marketDiff; const yValue = d => d.targetChange; //define couple of linear scales const xScale = d3.scaleLinear(); const yScale = d3.scaleLinear(); const xAxis = d3 .axisBottom() .scale(xScale) .ticks(w / 50, "%"); const yAxis = d3 .axisLeft() .scale(yScale) .ticks(h / 40, ".2%"); // Axis Labels const xLabel = xAxisG.append('text'); const yLabel = yAxisG.append('text'); // create color function that is just an ordinal scale const color = d3.scaleOrdinal(d3.schemeSet1); //Let's give these scales a domain (actual values) and a range (plotted values) xScale .domain(d3.extent(data, xValue)) //d3.extent captures the min. & max from a set of values .range([0, innerW]); // map the sepalLength values in dataset to full width of svg yScale.domain(d3.extent(data, yValue)).range([innerH, 0]); // map the petalLength values in dataset to full height of svg // Create the line const line = d3 .line() .defined(d => !isNaN(d.targetChange)) .x(d => xScale(d.marketDiff)) .y(d => yScale(d.targetChange)); // Draw the line. g.append('path') .datum(data) .attr('d', line) .attr("fill", "none") .attr("stroke", "steelblue") .attr("stroke-width", 1.5) .attr("stroke-linejoin", "round") .attr("stroke-linecap", "round") .attr("d", line); // Axis Label Attributes xLabel .attr('x', innerW / 2) .attr('y', 30) .attr('font-size', 12) .attr('fill', 'steelblue') .text('Market Price Difference to Target Price (%)'); yLabel .attr('x', -(margin.top + (innerH - margin.top - margin.bottom) / 4)) .attr('y', -50) .attr('font-size', 12) .attr('fill', 'steelblue') .text('Target Price Change (%)') .attr('transform', 'rotate(-90)').attr; xAxisG.call(xAxis); yAxisG.call(yAxis); return svg; }35:T6a0,md`By tuning the parameters above (${tex`T_{min}`}, ${tex`T_{max}`}) we can see how the Target Price would behave given different ETH prices over extended periods of time using a toy model in the figures below, assuming auctions occur once every 24 hours. We simulate the ETH price using geometric Brownian motion with a drift, ${tex`\mu = -0.5\%`} and volatility, ${tex`\sigma = 5\%`}. This allows us to obtain random walk data while also obtaining *long tails* synonymous with the cryptocurrency bear market, due to the proportional volatility and the log-normal distribution of the geometric Brownian motion process. As shown in the figure above, the changes in the target price can depend heavily on the difference between the market price and Target Price. To cover as many different scenarios as efficiently as possible, FLOAT market price data is also generated via geometric Brownian motion, with ${tex`\mu = 0`} and ${tex`\sigma = 10\%`}. Geometric Brownian motion is a continuous-time stochastic process ${tex`S_t`}, which relies on the Wiener process ${tex`W_t`} to generate 1D-Brownian motion and is given by the equation ${tex.block` dS_t = \mu S_t dt + \sigma S_t dW_t`} By setting ${tex`\mu = 0`} we remove the assumption of a long-term trend behaviour of the market price of FLOAT while allowing the changes in price to be dominated by the volatility generated by the second term, ${tex`\sigma dW_t`} in the stochastic differential equation. This enables the generation of data expected of a token subject to market forces and speculation but with the aim of being stable. As the data is randomly generated, each time this page is refreshed a new outcome will be generated. `36:T841,{ // Pull data in const eth_change = ethRandom; const target_change = randomSim; // Margin object with four properties const margin = { top: 20, right: 20, bottom: 50, left: 50 }; // Mapping const x = d3 .scaleLinear() .domain(d3.extent(eth_change, d => d.index)) .range([margin.left, width - margin.right]); const y = d3 .scaleLinear() .domain(d3.extent(eth_change, d => d.granularChange)) .range([height - margin.bottom, margin.top]); // Lines const change_line = d3 .line() .x(d => x(d.index)) .y(d => y(d.granularChange)); // Axes const xAxis = g => g.attr("transform", `translate(0,${height - margin.bottom})`).call( d3 .axisBottom(x) .ticks(width / 80) .tickSizeOuter(0) ); const yAxis = g => g .attr("transform", `translate(${margin.left}, 0)`) .call(d3.axisLeft(y).ticks(height / 40, ".0%")) .call(g => g.select(".domain").remove()); const data_points = t * eth_change.length; return html``; }37:T839,{ // Pull data in const eth_change = ethRandom; const target_change = randomSim; // Margin object with four properties const margin = { top: 20, right: 20, bottom: 50, left: 50 }; // Mapping const x = d3 .scaleLinear() .domain(d3.extent(eth_change, d => d.index)) .range([margin.left, width - margin.right]); const y = d3 .scaleLinear() .domain(d3.extent(eth_change, d => d.percentage)) .range([height - margin.bottom, margin.top]); // Lines const change_line = d3 .line() .x(d => x(d.index)) .y(d => y(d.percentage)); // Axes const xAxis = g => g.attr("transform", `translate(0,${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, ".0%")) .call(g => g.select(".domain").remove()); const data_points = t * eth_change.length; return html``; }38:T67d,function updateTarget( previousTarget, marketPrice, basketFactor, maxAdjP = maxAdjustmentPeriod, minAdjP = minAdjustmentPeriod, rateF = rateFactor ) { let isExpansion = true; // check if we are in a contraction if (marketPrice < previousTarget) { isExpansion = false; } else { isExpansion = true; } // We only change the target price if the market and basket are in alignment if ( (marketPrice > previousTarget && basketFactor > 1) || (marketPrice < previousTarget && basketFactor < 1) ) { const delta = (marketPrice - previousTarget) / previousTarget; const normDelta = normaliseMarketDiff(delta, MAX_PRICE_DELTA, isExpansion); const adjustmentPeriod = calculateAdjustmentPeriod( normDelta, maxAdjP, minAdjP, rateF ); const targetChange = calulateTargetPriceChange( basketFactor, adjustmentPeriod, BLOCKS_HR, INITIAL_AUCTION_TIME_PERIOD ); const newTarget = previousTarget + previousTarget * targetChange; return newTarget; } else { return previousTarget; } // const delta = (marketPrice - previousTarget) / previousTarget; // const normDelta = normaliseMarketDiff(delta, MAX_PRICE_DELTA, isExpansion); // const adjustmentPeriod = calculateAdjustmentPeriod( // normDelta, // maxAdjP, // minAdjP, // rateF // ); // const targetChange = calulateTargetPriceChange( // basketFactor, // adjustmentPeriod, // BLOCKS_HR, // INITIAL_AUCTION_TIME_PERIOD // ); // const newTarget = previousTarget + previousTarget * targetChange; // return newTarget; }39:T56d,function geometricBrownian(initialPrice, mu = 0, sigma = 0.1, T = 365, dt = 1) { // Geometric Brownian Motion Equation: // dS_t = mu*S_t * dt + sigma * S_t * dWt // Analytical Solution to equation: // S_t = S_0 * exp((mu - sigma^2 / 2) * t + sigma * W_t) // mu equals the percentage drift - constant // sigma is the volatility (the percentage volatility) - constant // T = the time period, default 365 days // dt = granularity of stochastic process, default 1 day. // The number of steps const numberSteps = T / dt; // Initiate Array to hold prices let S = Array(numberSteps).fill(0); // Put the initial price into the first element of the array S[0] = initialPrice; for (let i = 1; i < numberSteps; i++) { let drift = dt * mu; let dW = gaussian() * Math.sqrt(dt); // Wiener Process let shock = sigma * dW; let dS = drift * S[i - 1] + shock * S[i - 1]; //Add updated price to price array S[i] = S[i - 1] + dS; } // Place data into an array of objects for plotting let data = []; for (let i = 0; i < S.length; i++) { // Calculate percentage change in every dt step let granularChange = 0; if (i > 0) { granularChange = S[i] / S[i - 1] - 1; } data.push({ index: i, price: S[i], percentage: S[i] / initialPrice, granularChange: granularChange }); } return data; }3a:Ta5b,function simulate(ethData, marketData) { // We want a Ethereum Price data // we want random/correlated Float market price data, // We want to calculate the basket factor // We want to then calculate the target price // Remember to push everything into an object at the end, time might be via UTC so it plots nicely hehehe // Maybe create basket factor helper function so it initialises to value of 1 in the first iterations regardless of what someone chooses for the ETH and Float target/market price. const numberSteps = ethData.length; const initialTargetPrice = 1.618; // Price of float at minting ceremony const initialEthPrice = ethData[0].price; const floatCirculation = 1e6; let targetPrice = [initialTargetPrice]; // empty basket factor array let basketFactor = [1]; // Value of basket factor at minting ceremony let dataFrame = []; // store everything in at the end for plotting // Careful with duplicate entry in the beginning // calculate basket factors and target prices for (let i = 1; i < numberSteps; i++) { // Calculate the basket Factor using previous target price const targetPriceGivenBasketFactor = calculateBasketFactor( ethData[i].price, targetPrice[i - 1], (initialTargetPrice * floatCirculation) / initialEthPrice, floatCirculation ); //basketFactor.push(targetPriceGivenBasketFactor); if (targetPriceGivenBasketFactor > 1) { basketFactor.push( targetPriceGivenBasketFactor - (targetPriceGivenBasketFactor - 1) * returnTo100Factor ); } else { basketFactor.push( targetPriceGivenBasketFactor + (1 - targetPriceGivenBasketFactor) * returnTo100Factor ); } // Calculate new Target price let newTargetPrice = updateTarget( targetPrice[i - 1], marketData[i].price, basketFactor[i] ); // Add new target price to target price array targetPrice.push(newTargetPrice); } // Add all data to the data frame: // May have idexing issues, as target price will be a bit longer than the other arrays for (let i = 0; i < ethData.length; i++) { // Calculate percentage change in every dt step let granularChange = 0; if (i > 0) { granularChange = targetPrice[i] / targetPrice[i - 1] - 1; } dataFrame.push({ index: i, marketPrice: marketData[i].price, basketFactor: basketFactor[i], ethPrice: ethData[i].price, timestamp: ethData[i].timestamp, price: targetPrice[i], percentage: targetPrice[i] / targetPrice[0], granularChange: granularChange }); } return dataFrame; }3b:T858,function pseudoTargetUpdate( marketPrice, priorTargetPrice, basketFactor, currentBlock, priorAuctionBlock ) { // What we want to get out let targetChange; let newTargetPrice; // Can be changed by governance const maxPriceDelta = 4; // Dmax const maxAdjustmentPeriod = 1e6; // T_max (BLOCKS) const minAdjustmentPeriod = 2e5; // T_min (BLOCKS) const rateFactor = 1; // r_f // Obtain f_A const auctionTimePeriod = currentBlock - priorAuctionBlock; const auctionFrequency = 1 / auctionTimePeriod; //Obtain scaled delta between market and target price const delta = (marketPrice - priorTargetPrice) / priorTargetPrice; // Normalise delta based on Dmax let normDelta; if (marketPrice >= priorTargetPrice) { normDelta = delta / maxPriceDelta; } else { normDelta = (1 / (1 + delta) - 1) / maxPriceDelta; //normDelta = (-1 / maxPriceDelta) * (delta / (1 + delta)); //normDelta = Math.abs((1 / maxPriceDelta) * (delta / (1 + delta))); } // Place max and min limits if (normDelta > 1) { normDelta = 1; } if (normDelta < 0) { normDelta = 0; } // calculate T, 'the adjustment period' let adjustmentPeriod = maxAdjustmentPeriod - normDelta ** rateFactor * (maxAdjustmentPeriod - minAdjustmentPeriod); // Max min limits for adjustment period if (adjustmentPeriod > maxAdjustmentPeriod) { adjustmentPeriod = maxAdjustmentPeriod; } if (adjustmentPeriod < minAdjustmentPeriod) { adjustmentPeriod = minAdjustmentPeriod; } adjustmentPeriod = Math.trunc(adjustmentPeriod); // Bung all of the above to get the target price change targetChange = (auctionTimePeriod * (basketFactor - 1)) / adjustmentPeriod; newTargetPrice = priorTargetPrice + priorTargetPrice * targetChange; return { scaledDelta: delta, normDelta: normDelta, adjustmentPeriod: adjustmentPeriod, basketFactorDiff: Math.abs(basketFactor - 1), targetPercentageChange: targetChange, targetChangeEth: (newTargetPrice - priorTargetPrice) / 2130.5, targetChangeUSD: newTargetPrice - priorTargetPrice, newTargetPrice: newTargetPrice }; }3c:[] 2f:{"title":"Target Prices / Float Protocol ","cells":[{"id":0,"value":"md`\n

Target Prices / Float Protocol

Float Protocol › Target Prices

\n\n# Target Prices\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1477,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":710,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":284,"value":"md`## Single Target Price Update\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1200,"value":"md`\nIn a single instance, if we take the FLOAT Target Price, ${tex`m_t`} as $1.618 USD and choose a market price, ${tex`\\bar{m}_u^{FLOAT}`} and a given Basket Factor, ${tex`b`} we can calculate the percentage change in the target price and the adjustment period, ${tex`T`}. Below, ${tex`r_f = 1`}, ${tex`T_{max}`} is set to 1 million Blocks and ${tex`T_{min}`} to 2 hundred thousand Blocks with ${tex`D_{max}`} set to 4 (400%).\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":336,"value":"floatTargetPrice = 1.618","pinned":false,"hidden":false,"mode":"ojs"},{"id":291,"value":"html`${bind(\n Range([0.01, 10], {\n step: 0.001,\n width: \"50%\",\n label: html`Float Market Price (USD) ${tex`\\bar{m}_\\star^{FLOAT}`}`\n }),\n viewof floatMarketPrice\n)} The current FLOAT TWAP price.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"html`${bind(\n Range([0.00, 2], {\n step: 0.00000001,\n width: \"50%\",\n label: html`Float Protocol Basket Factor ${tex`b`}`\n }),\n viewof singleBasketFactor\n)} `","pinned":false,"hidden":false,"mode":"ojs"},{"id":267,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":33,"value":"targetPercentageDelta = {\n let targetChange = 0;\n if (checkAlignment(floatMarketPrice, floatTargetPrice, singleBasketFactor)) {\n targetChange =\n calulateTargetPriceChange(\n singleBasketFactor,\n adjustmentPeriod,\n BLOCKS_HR,\n INITIAL_AUCTION_TIME_PERIOD\n ) * 100; // multiplied by 100 to get percentage }\n\n return targetChange;\n }\n\n return targetChange;\n}\n\n// targetPercentageDelta = ((singleBasketFactor - 1) / adjustmentPeriod) *\n// BLOCKS_HR *\n// INITIAL_AUCTION_FREQUENCY *\n// 100 // multiplied by 100 to put in terms of percentage","pinned":false,"hidden":false,"mode":"ojs"},{"id":1493,"value":"newFloatTargetPrice = floatTargetPrice +\n (floatTargetPrice * targetPercentageDelta) / 100","pinned":false,"hidden":false,"mode":"ojs"},{"id":1207,"value":"md`\nThe Target Price does not change if the Basket Factor is equal to one, as shown by the equations outlined above. Furthermore, if the market price of FLOAT and the Basket Factor are not in alignment with each other, the target price change is dominated by the Basket Factor component. The Protocol will have the ability to tune parameters throughout its lifetime to find the appropriate target price change gradients given the market conditions and the assets in the basket. Some of the key parameters available to tune are the minimum and maximum adjustment period (${tex`T_{max}`}, ${tex`T_{min}`}). As expected, these parameter changes will be voted on by governance.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":381,"value":"html`${bind(\n Range([2e5, 1e6], {\n step: 1e3,\n width: \"50%\",\n label: html`Minimum Adjustment Period (Blocks) ${tex``}`\n }),\n viewof minAdjustmentPeriod\n)} ${tex`T_{min}`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":391,"value":"html`${bind(\n Range([1e6, 2e7], {\n step: 1000,\n width: \"50%\",\n label: html`Maximum Adjustment Period (Blocks) ${tex``}`\n }),\n viewof maxAdjustmentPeriod\n)} ${tex`T_{max}`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":621,"value":"html`${bind(\n Range([0.25, 2], {\n step: 0.25,\n width: \"50%\",\n label: html`Float Protocol Basket Factor `\n }),\n viewof basketFactor\n)} ${tex`b`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":449,"value":"viewof caseChoice = Radio([\"Expansion\", \"Contraction\"], {\n label: \"Case:\",\n value: 'Expansion'\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":669,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":790,"value":"md`## Toy Model\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1379,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":1936,"value":"md`Below we include an \"auction effectiveness\" parameter. The auction effectiveness parameter controls how effective each auction is on average in returning the Basket Factor of the protocol back to 100% after each stabilisation event. This is a core strength of the Protocol where the Basket Factor is not solely influenced by the price of ETH but also how the Protocol rebalances the basket using Dutch auctions.\n\nThe monetary policy, i.e. the parameters used to control how the target price is changed, will be fine-tuned by governance as more data on the auction performance is obtained over time from the real market.\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1769,"value":"html`${bind(\n Range([0.5, 1], {\n step: 0.01,\n width: \"50%\",\n label: html`Auction Effectiveness `\n }),\n viewof returnTo100Factor\n)} ${tex`E`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1895,"value":"viewof generateMarket = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":1908,"value":"viewof generateEthRandom = html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":1028,"value":"html`${bind(\n Scrubber(d3.ticks(0, 1, 1000), {\n autoplay: true,\n loop: false,\n initial: 0,\n format: x => `Year = ${x.toFixed(3)}`\n }),\n viewof t\n)}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1297,"value":"md`### Random Ethereum Price Data`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1026,"value":"$36","pinned":false,"hidden":false,"mode":"ojs"},{"id":1116,"value":"$37","pinned":false,"hidden":false,"mode":"ojs"},{"id":2017,"value":"md`Next, we will simulate things in much more depth.\n\nNext`","pinned":false,"hidden":false,"mode":"ojs"},{"id":2,"value":"md`\n---\n\n## Appendix\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1155,"value":"md`### Data`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1337,"value":"md`#### Target price change vs market price delta`","pinned":false,"hidden":false,"mode":"ojs"},{"id":628,"value":"data = {\n if (caseChoice === \"Expansion\") {\n return expansionData;\n } else {\n return contractionData;\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":75,"value":"// For Expansion data calculation\nexpansionData = {\n let x = 0; // index counter\n let stepSize = 0.05; // Granularity between market prices\n let marketDiff = 0 - stepSize;\n let steps = 5 / stepSize,\n test = [];\n for (let x = 0; x < steps; ++x) {\n marketDiff = marketDiff + stepSize;\n let marketNorm = normaliseMarketDiff(marketDiff, MAX_PRICE_DELTA, true);\n\n let adjP = calculateAdjustmentPeriod(\n marketNorm,\n maxAdjustmentPeriod,\n minAdjustmentPeriod,\n rateFactor\n );\n // Change target price only in alignment\n let targetChange = 0;\n if (basketFactor > 1) {\n targetChange = calulateTargetPriceChange(\n basketFactor,\n adjP,\n BLOCKS_HR,\n INITIAL_AUCTION_TIME_PERIOD\n );\n }\n test.push({\n index: x,\n marketDiff: marketDiff,\n adjustmentPeriod: adjP,\n targetChange: targetChange\n });\n }\n return test;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1630,"value":"contractionData = {\n //const rateFactor = 1;\n let x = 0; // index counter\n let stepSize = 0.01; // Granularity between market prices\n let marketDiff = 0 + stepSize;\n let steps = -(-1) / stepSize,\n test = [];\n for (let x = 0; x < steps; ++x) {\n marketDiff = marketDiff - stepSize;\n let market_norm_diff = normaliseMarketDiff(\n marketDiff,\n MAX_PRICE_DELTA,\n false\n );\n\n let adjP = calculateAdjustmentPeriod(\n market_norm_diff,\n maxAdjustmentPeriod,\n minAdjustmentPeriod,\n rateFactor\n );\n\n // Change target price only in alignment\n let targetChange = 0;\n if (basketFactor < 1) {\n targetChange = calulateTargetPriceChange(\n basketFactor,\n adjP,\n BLOCKS_HR,\n INITIAL_AUCTION_TIME_PERIOD\n );\n }\n\n test.push({\n index: x,\n marketDiff: marketDiff,\n adjustmentPeriod: adjP,\n targetChange: targetChange\n });\n }\n return test;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1341,"value":"md`#### Randomly generated ETH and market data`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1077,"value":"ethRandom = {\n generateEthRandom;\n // viewof t.value = 0;\n // viewof t.dispatchEvent(new CustomEvent(\"input\"));\n let ethRandom = geometricBrownian(2000, -0.005, 0.05);\n\n return ethRandom;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1100,"value":"market = {\n generateMarket;\n // viewof t.value = 0;\n // viewof t.dispatchEvent(new CustomEvent(\"input\"));\n // Generate random market Price data\n let market = geometricBrownian(1.618, 0, 0.1);\n return market;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1915,"value":"randomSim = simulate(ethRandom, market)","pinned":false,"hidden":false,"mode":"ojs"},{"id":2012,"value":"minChange = randomSim.reduce(\n (acc, a) => (a.granularChange < acc ? a.granularChange : acc),\n 0\n) * 100","pinned":false,"hidden":false,"mode":"ojs"},{"id":1999,"value":"maxChange = randomSim.reduce(\n (acc, a) => (a.granularChange > acc ? a.granularChange : acc),\n 0\n) * 100","pinned":false,"hidden":false,"mode":"ojs"},{"id":1343,"value":"md`#### Real ETH data`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1187,"value":"coingeckoData = (await fetch(\n `https://api.coingecko.com/api/v3/coins/ethereum/market_chart/range?vs_currency=usd&from=${(\n from.getTime() / 1e3\n ).toFixed()}&to=${(to.getTime() / 1e3).toFixed()}`\n)).json()","pinned":false,"hidden":false,"mode":"ojs"},{"id":1189,"value":"ethReal = {\n const startingPrice = coingeckoData[\"prices\"][0][1];\n return coingeckoData.prices\n .map(([timestamp, price], index) => ({\n price: price,\n percentage: price / startingPrice,\n granularChange:\n price /\n ((index && coingeckoData[\"prices\"][index - 1][1] - 1) || price) -\n 1,\n timestamp: new Date(timestamp)\n }))\n .sort((a, b) => a.timestamp - b.timestamp);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"md`### Constants`","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"BLOCK_TIME = 13.7","pinned":false,"hidden":false,"mode":"ojs"},{"id":21,"value":"BLOCKS_HR = (60 * 60) / BLOCK_TIME","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"FLOAT_INITIAL_PRICE = 1.618","pinned":false,"hidden":false,"mode":"ojs"},{"id":288,"value":"INITIAL_MARKET_PRICE = 1.7","pinned":false,"hidden":false,"mode":"ojs"},{"id":309,"value":"INITIAL_BASKET_FACTOR = 2","pinned":false,"hidden":false,"mode":"ojs"},{"id":348,"value":"INITIAL_RATE_FACTOR = 1","pinned":false,"hidden":false,"mode":"ojs"},{"id":17,"value":"INITIAL_AUCTION_TIME_PERIOD = 24 // In Hours","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"MINIMUM_ADJUSTMENT_PERIOD = 2e5","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"MAXIMUM_ADJUSTMENT_PERIOD = 1e6","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"MAX_PRICE_DELTA = 4","pinned":false,"hidden":false,"mode":"ojs"},{"id":234,"value":"MIN_PRICE_DELTA = -0.8","pinned":false,"hidden":false,"mode":"ojs"},{"id":1758,"value":"RETURN_TO_100_FACTOR = 0.9","pinned":false,"hidden":false,"mode":"ojs"},{"id":50,"value":"md`\n### Parameters\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":292,"value":"viewof floatMarketPrice = Input(INITIAL_MARKET_PRICE)","pinned":false,"hidden":false,"mode":"ojs"},{"id":370,"value":"viewof singleBasketFactor = Input(INITIAL_BASKET_FACTOR)","pinned":false,"hidden":false,"mode":"ojs"},{"id":383,"value":"viewof minAdjustmentPeriod = Input(MINIMUM_ADJUSTMENT_PERIOD)","pinned":false,"hidden":false,"mode":"ojs"},{"id":386,"value":"viewof maxAdjustmentPeriod = Input(MAXIMUM_ADJUSTMENT_PERIOD)","pinned":false,"hidden":false,"mode":"ojs"},{"id":307,"value":"viewof basketFactor = Input(INITIAL_BASKET_FACTOR)","pinned":false,"hidden":false,"mode":"ojs"},{"id":60,"value":"viewof rateFactor = Input(INITIAL_RATE_FACTOR)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1765,"value":"viewof returnTo100Factor = Input(RETURN_TO_100_FACTOR)","pinned":false,"hidden":false,"mode":"ojs"},{"id":451,"value":"isExpansionForTargetPrice = {\n if (caseChoice === 'Expansion') {\n let isExpansionForTargetPrice = true;\n return isExpansionForTargetPrice;\n }\n if (caseChoice === 'Contraction') {\n let isExpansionForTargetPrice = false;\n return isExpansionForTargetPrice;\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1029,"value":"viewof t = Input(0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1180,"value":"default_period = {\n const now = new Date();\n var yearAgo = new Date();\n yearAgo.setFullYear(now.getFullYear() - 1);\n return {\n from: yearAgo,\n to: now\n };\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1182,"value":"viewof from = Input(default_period.from)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1184,"value":"viewof to = Input(default_period.to)","pinned":false,"hidden":false,"mode":"ojs"},{"id":412,"value":"md`\n### Functions\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1977,"value":"function checkAlignment(marketPrice, previousTarget, basketFactor) {\n let alignment = false;\n\n if (\n (marketPrice > previousTarget && basketFactor > 1) ||\n (marketPrice < previousTarget && basketFactor < 1)\n ) {\n alignment = true;\n } else alignment = false;\n\n return alignment;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":575,"value":"function normaliseMarketDiff(\n market_diff,\n max_price_delta = MAX_PRICE_DELTA,\n isExpansion\n) {\n let market_norm_diff;\n\n if (isExpansion === true) {\n market_norm_diff = market_diff / max_price_delta;\n } else {\n // These two equations below are equivalent\n market_norm_diff = (1 / (1 + market_diff) - 1) / max_price_delta;\n // market_norm_diff = Math.abs((1 / max_price_delta) * (market_diff / (1 + market_diff));\n }\n\n // Place max and min limits\n if (market_norm_diff > 1) {\n market_norm_diff = 1;\n }\n if (market_norm_diff < 0) {\n market_norm_diff = 0;\n }\n\n return market_norm_diff;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":414,"value":"function calculateAdjustmentPeriod(\n market_norm_diff,\n max_adjustment_time = MAXIMUM_ADJUSTMENT_PERIOD,\n min_adjustment_time = MINIMUM_ADJUSTMENT_PERIOD,\n rate_factor = INITIAL_RATE_FACTOR\n) {\n let adjustment_period =\n max_adjustment_time -\n market_norm_diff ** rate_factor *\n (max_adjustment_time - min_adjustment_time);\n\n // Max min limits for adjustment period\n if (adjustment_period > max_adjustment_time) {\n adjustment_period = max_adjustment_time;\n }\n if (adjustment_period < min_adjustment_time) {\n adjustment_period = min_adjustment_time;\n }\n\n return adjustment_period;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":551,"value":"function calulateTargetPriceChange(\n basket_factor,\n adjustment_period,\n blocks_hr = BLOCKS_HR,\n auction_time_period = INITIAL_AUCTION_TIME_PERIOD\n) {\n let target_change =\n ((basket_factor - 1) / adjustment_period) * blocks_hr * auction_time_period;\n\n return target_change;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":868,"value":"// Calculate basketFactor function\nfunction calculateBasketFactor(\n ethPrice = 2000,\n floatTargetPrice = 1.618,\n ethInBasket = (1.618 * 1e6) / 2000,\n floatInCirculation = 1e6\n) {\n const basketFactor =\n (ethPrice * ethInBasket) / (floatTargetPrice * floatInCirculation);\n return basketFactor;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":805,"value":"$38","pinned":false,"hidden":false,"mode":"ojs"},{"id":923,"value":"// Standard Normal variate using Box-Muller transform.\nfunction gaussian() {\n var u = 0, // mean\n v = 0; // varaince\n while (u === 0) u = Math.random(); //Converting [0,1) to (0,1)\n while (v === 0) v = Math.random();\n return Math.sqrt(-2.0 * Math.log(u)) * Math.cos(2.0 * Math.PI * v);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":920,"value":"function wienerProcess(initialValue = 0, numberSteps = 365) {\n //Initiate an array full\n let w = Array(numberSteps).fill(0);\n\n // Weiner process\n for (let i = 0; i < numberSteps; i++) {\n // Sample from the normal distribution\n let sample = gaussian();\n // Weiner Equation\n if (i < 1) {\n w[i] = initialValue;\n } else {\n w[i] = w[i - 1] + sample / Math.sqrt(numberSteps);\n }\n // Put in a Stop from going below zero\n if (w[i] < 0) {\n w[i] = w[i] + 2 * Math.abs(sample / Math.sqrt(numberSteps));\n }\n }\n\n return w;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1068,"value":"$39","pinned":false,"hidden":false,"mode":"ojs"},{"id":1249,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs"},{"id":1512,"value":"md`#### pseudo code for the whole target price update`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1514,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs"},{"id":1573,"value":"md`Test cases: Compare with Single target price update section (hence 24 * BLOCKS_HR)\nN.B. reduced decimal places for basket factor due to reduced decimal imput on viewof in Single TargetPrice Update section`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1528,"value":"pseudoTargetUpdate(2, 1.618, 1.13207664, 24 * BLOCKS_HR, 0)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1532,"value":"pseudoTargetUpdate(5.2, 1.618, 0.91872682, 24 * BLOCKS_HR, 0)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1534,"value":"pseudoTargetUpdate(0.5, 1.618, 1, 24 * BLOCKS_HR, 0)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1539,"value":"pseudoTargetUpdate(0.8, 1.618, 1.7476272, 24 * BLOCKS_HR, 0)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1696,"value":"pseudoTargetUpdate(0.1, 1.618, 0.67904821, 24 * BLOCKS_HR, 0)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1562,"value":"md`Test cases 1\n**Always check parameters being used in pseudoTargetUpdate function**\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1543,"value":"pseudoTargetUpdate(2.0, 1.618, 1.1320766378244747, 300, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1560,"value":"pseudoTargetUpdate(5.2, 1.618, 0.9187268232385661, 300, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1558,"value":"pseudoTargetUpdate(0.5, 1.6180, 1, 300, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1615,"value":"pseudoTargetUpdate(0.8, 1.618, 1.7476272, 300, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1547,"value":"pseudoTargetUpdate(0.1, 1.618, 0.6790482076637825, 300, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1731,"value":"pseudoTargetUpdate(0.1, 1, 0.5, 300, 100)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1169,"value":"md`### Formatting`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1176,"value":"margin = ({top: 20, right: 30, bottom: 30, left: 40})","pinned":true,"hidden":false,"mode":"ojs"},{"id":1177,"value":"height = 400","pinned":true,"hidden":false,"mode":"ojs"},{"id":1171,"value":"formatDate = d3.utcFormat(\"%b %-d, '%y\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":1172,"value":"formatPrice = d3.format(\"$.2f\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":108,"value":"md`\n### Imports\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":110,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":295,"value":"import { Input, Range, bind, Radio } from \"@observablehq/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":1032,"value":"import { Scrubber } from \"@mbostock/scrubber\"","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W3c","stdlib":"1","titling":"auto"}