Implement zargham math review and vesting period floor price
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dapplion
parent
28215fef56
commit
9bc519be2d
79
src/App.tsx
79
src/App.tsx
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@ -20,10 +20,16 @@ import { getLast, getAvg, pause } from "./utils";
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import {
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getInitialParams,
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getPriceR,
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getMinPrice,
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getS,
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vest_tokens,
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getMinR,
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getSlippage,
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getTxDistribution,
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getDeltaR_priceGrowth,
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rv_U
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rv_U,
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getMedian,
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getSum
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} from "./math";
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import { throttle } from "lodash";
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// General styles
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@ -199,7 +205,7 @@ export default function App() {
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const {
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k, // Invariant power kappa (.)
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R0, // Initial reserve (DAI)
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// S0, // initial supply of tokens (token)
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S0, // initial supply of tokens (token)
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V0 // invariant coef
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} = getInitialParams({
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d0,
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@ -210,6 +216,7 @@ export default function App() {
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const [priceTimeseries, setPriceTimeseries] = useState([0]);
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const [withdrawFeeTimeseries, setWithdrawFeeTimeseries] = useState([0]);
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const [floorpriceTimeseries, setFloorpriceTimeseries] = useState([0]);
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const [totalReserve, setTotalReserve] = useState(R0);
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const [withdrawCount, setWithdrawCount] = useState(0);
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const [avgSlippage, setAvgSlippage] = useState(0);
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@ -248,48 +255,97 @@ export default function App() {
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async function simulateRandomDelta() {
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const R_t: number[] = [R0];
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const S_t: number[] = [S0];
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const p_t: number[] = [getPriceR({ R: R0, V0, k })];
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const wFee_t: number[] = [0];
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const slippage_t: number[] = [];
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const avgTxSize_t: number[] = [];
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// hatchers tokens = S0[section added by Z]
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const H_t: number[] = [S0]; // total hatcher tokens not vested
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const floorprice_t: number[] = []; // initially the price is the floor as all tokens are hatcher tokens
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// Random walk
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const numSteps = 52;
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const u_min = 0.97;
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const u_max = 1.04;
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const tx_spread = 10;
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// vesting(should this be exposed in the app ?)
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const cliff = 8; // weeks before vesting starts ~2 months
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const halflife = 52; // 26 weeks, half life is ~6 months
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// percentage of the hatch tokens which vest per week(since that is our timescale in the sim)
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// numSteps = 52 take 8ms to run
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setSimulationRunning(true);
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for (let t = 0; t < numSteps; t++) {
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const txsWeek = Math.ceil(t < 5 ? rv_U(0, 5) : rv_U(5, 2 * t));
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const priceGrowth = rv_U(0.99, 1.03);
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const txsWeek = rv_U(5, 2 * t + 5);
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const R = getLast(R_t);
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const deltaR = getDeltaR_priceGrowth({ R, k, priceGrowth });
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const S = getLast(S_t);
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const H = getLast(H_t);
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// enforce the effects of the unvested tokens not being burnable
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let u_lower;
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if (H === S) {
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u_lower = 1;
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} else {
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const R_ratio = getMinR({ S, H, V0, k }) / R;
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u_lower = Math.max(1 - R_ratio, u_min);
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}
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const priceGrowth = rv_U(u_lower, u_max);
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const deltaR = getDeltaR_priceGrowth({ R, k, priceGrowth });
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const R_next = R + deltaR;
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const txs = getTxDistribution({ sum: deltaR, num: txsWeek });
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const txs = getTxDistribution({
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sum: deltaR,
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num: txsWeek,
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spread: tx_spread
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});
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// Compute slippage
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const slippage = getAvg(
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txs.map(txR => getSlippage({ R, deltaR: txR, V0, k }))
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const slippage_txs = txs.map(txR =>
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getSlippage({ R, deltaR: txR, V0, k })
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);
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const slippage = getMedian(slippage_txs);
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const txsWithdraw = txs.filter(tx => tx < 0);
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const wFees = -wFee * txsWithdraw.reduce((t, c) => t + c, 0);
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const _avgTxSize =
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txs.reduce((t, c) => t + Math.abs(c), 0) / txs.length;
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const wFees = -wFee * getSum(txsWithdraw);
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// txsWithdraw.reduce((t, c) => t + c, 0);
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// Vest
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const delta_H = vest_tokens({ week: t, H, halflife, cliff });
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const H_next = H - delta_H;
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// find floor price
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const S_next = getS({ R, V0, k });
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const floorprice_next = getMinPrice({
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S: S_next,
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H: S0 - H_next,
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V0,
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k
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});
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const _avgTxSize = getMedian(txsWithdraw);
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R_t.push(R_next);
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p_t.push(getPriceR({ R: R_next, V0, k }));
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slippage_t.push(slippage);
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avgTxSize_t.push(_avgTxSize);
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wFee_t.push(getLast(wFee_t) + wFees);
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H_t.push(H_next);
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floorprice_t.push(floorprice_next);
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setWithdrawCount(c => c + txsWithdraw.length);
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// Stop the simulation if it's no longer active
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if (!simulationActive || !canContinueSimulation) break;
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}
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// floorprice_t is missing one data point
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floorprice_t[floorprice_t.length] = floorprice_t[floorprice_t.length - 1];
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setPriceTimeseries(p_t);
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setWithdrawFeeTimeseries(wFee_t);
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setFloorpriceTimeseries(floorprice_t);
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setAvgSlippage(getAvg(slippage_t));
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setAvgTxSize(getAvg(avgTxSize_t));
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setTotalReserve(getLast(R_t));
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@ -465,6 +521,7 @@ export default function App() {
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<PriceSimulationChart
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priceTimeseries={priceTimeseries}
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withdrawFeeTimeseries={withdrawFeeTimeseries}
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floorpriceTimeseries={floorpriceTimeseries}
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p0={p0}
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p1={p1}
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/>
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@ -17,6 +17,7 @@ import { linspace } from "./utils";
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const keyHorizontal = "x";
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const keyVerticalLeft = "Price (DAI/token)";
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const keyVerticalRight = "Total exit tributes (DAI)";
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const keyVerticalLeft2 = "Floor price (DAI/token)";
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const useStyles = makeStyles((theme: Theme) =>
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createStyles({
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@ -32,11 +33,13 @@ const useStyles = makeStyles((theme: Theme) =>
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function PriceSimulationChart({
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priceTimeseries,
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withdrawFeeTimeseries,
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floorpriceTimeseries,
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p0,
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p1
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}: {
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priceTimeseries: number[];
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withdrawFeeTimeseries: number[];
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floorpriceTimeseries: number[];
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p0: number;
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p1: number;
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}) {
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@ -51,6 +54,7 @@ function PriceSimulationChart({
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data.push({
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[keyHorizontal]: t,
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[keyVerticalLeft]: priceTimeseries[t] || 0,
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[keyVerticalLeft2]: floorpriceTimeseries[t] || 0,
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[keyVerticalRight]: withdrawFeeTimeseries[t] || 0
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});
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}
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@ -70,8 +74,8 @@ function PriceSimulationChart({
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const { textAnchor, viewBox, text } = props;
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return (
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<text
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x={viewBox.x + 10}
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y={viewBox.y - 10}
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x={viewBox.x + 8}
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y={viewBox.y + 17}
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fill={theme.palette.text.secondary}
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textAnchor={textAnchor}
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>
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@ -83,10 +87,12 @@ function PriceSimulationChart({
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function CustomTooltip({ active, payload, label }: any) {
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if (active) {
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const price = payload[0].value;
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const exit = payload[1].value;
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const floor = payload[1].value;
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const exit = payload[2].value;
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const weekNum = label;
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const toolTipData: string[][] = [
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["Price", price.toFixed(2), "DAI/tk"],
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["Floor", floor.toFixed(2), "DAI/tk"],
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["Exit t.", formatter(exit), "DAI"],
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["Week", weekNum, ""]
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];
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@ -148,12 +154,10 @@ function PriceSimulationChart({
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{/* Capital collected from withdraw fees - AXIS */}
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<YAxis
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yAxisId="right"
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// domain={[
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// Math.floor(Math.min(...withdrawFeeTimeseries)),
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// Math.ceil(Math.max(...withdrawFeeTimeseries))
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// ]}
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domain={[0, +(2 * withdrawFeeTimeseries.slice(-1)[0]).toPrecision(1)]}
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orientation="right"
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tick={{ fill: theme.palette.text.secondary }}
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tickFormatter={formatter}
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stroke={theme.palette.text.secondary}
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/>
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@ -166,7 +170,20 @@ function PriceSimulationChart({
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dataKey={keyVerticalLeft}
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stroke={theme.palette.primary.main}
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fill={theme.palette.primary.main}
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fillOpacity={0.3}
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strokeWidth={2}
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/>
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<Area
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isAnimationActive={false}
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yAxisId="left"
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type="monotone"
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dataKey={keyVerticalLeft2}
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stroke={"#adcd2e"}
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fill={"#adcd2e"}
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fillOpacity={0.05}
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strokeWidth={2}
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/>
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<ReferenceLine
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y={p0}
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yAxisId="left"
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@ -188,9 +205,10 @@ function PriceSimulationChart({
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yAxisId="right"
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type="monotone"
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dataKey={keyVerticalRight}
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stroke={theme.palette.secondary.dark}
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stroke={"#0085ff"}
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fill={theme.palette.secondary.dark}
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fillOpacity="0.8"
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fillOpacity={0.5}
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strokeWidth={2}
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/>
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{/* <ReferenceLine
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@ -186,6 +186,8 @@ function SupplyVsDemandChart({
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dataKey={keyVertical}
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stroke={theme.palette.primary.main}
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fill={theme.palette.primary.main}
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fillOpacity={0.3}
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strokeWidth={2}
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/>
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<ReferenceLine
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x={R0_round}
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95
src/math.ts
95
src/math.ts
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@ -23,6 +23,51 @@ export function getInitialParams({
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return { k, R0, S0, V0 };
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}
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function getR({ S, V0, k }: { S: number; V0: number; k: number }) {
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return S ** k / V0;
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}
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export function getS({ R, V0, k }: { R: number; V0: number; k: number }) {
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return (V0 * R) ** (1 / k);
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}
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// compute the reserve if all that supply is burned
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export function getMinR({
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S,
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H,
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V0,
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k
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}: {
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S: number;
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H: number;
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V0: number;
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k: number;
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}) {
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return getR({ S: S - H, V0, k });
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}
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// compute the price if all that supply is burned
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export function getMinPrice({
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S,
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H,
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V0,
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k
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}: {
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S: number;
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H: number;
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V0: number;
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k: number;
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}) {
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if (S === H) {
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const myR = getR({ S, V0, k });
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const myP = getPriceR({ R: myR, V0, k }); // numerical precision make complex numbers just suppress it
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return Math.abs(myP);
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} else {
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const minR = getMinR({ S, H, V0, k });
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return getPriceR({ R: minR, V0, k });
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}
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}
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/**
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* Computes the price at a specific reserve `R`
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*/
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@ -75,17 +120,47 @@ export function getDeltaR_priceGrowth({
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* Demo: https://codepen.io/anon/pen/mNqJjv?editors=0010#0
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* Very quick: < 10ms for 10000 txs
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*/
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export function getTxDistribution({ sum, num }: { sum: number; num: number }) {
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export function getTxDistribution({
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sum,
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num,
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spread
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}: {
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sum: number;
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num: number;
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spread: number;
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}) {
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const mean = sum / num;
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const off = mean * 4;
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const off = mean * spread;
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const x: number[] = [];
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for (let i = 0; i < num; i++) {
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x[i] = randn_bm(mean - off, mean + off);
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x.push(randn_bm(mean - off, mean + off));
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}
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return x;
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}
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// Minor utils
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export function vest_tokens({
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week,
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H, // unvested_hatch_tokens
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halflife,
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cliff
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}: {
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week: number;
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H: number;
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halflife: number;
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cliff: number;
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}) {
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// check cliff
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if (week < cliff) {
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return 0;
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} else {
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// rate of release given half - life
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const vest_fraction = 0.5 ** (1 / halflife);
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// number of tokens that vest in this week
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return H * (1 - vest_fraction);
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}
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}
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// Statistics utils
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/**
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* Random variable uniformly distributed
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@ -111,3 +186,15 @@ function randn_bm(min: number, max: number) {
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num += min; // offset to min
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return num;
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}
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// Array utils
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export function getMedian(arr: number[]) {
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const mid = Math.floor(arr.length / 2);
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const nums = [...arr].sort((a, b) => a - b);
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return arr.length % 2 !== 0 ? nums[mid] : (nums[mid - 1] + nums[mid]) / 2;
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}
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export function getSum(arr: number[]) {
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return arr.reduce((a, b) => a + b, 0);
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}
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