31:Tf8d,class PricingModel { constructor(S, K, r, b, sigma, T, dayCountingConvention) { this.S = Math.max(1e-4, Number(S)); if (this.S <= 0.0) throw RangeError("Spot price must be positive"); this.K = Math.max(1e-4, Number(K)); if (this.K <= 0.0) throw RangeError("Strike price must be positive"); this.r = Number(r); this.b = Number(b); this.sigma = Math.max(1e-4, Number(sigma)); if (this.sigma <= 0.0) throw RangeError("Volatility must be positive"); T = Math.max(1e-4, Number(T)); if (this.T <= 0.0) throw RangeError("Strike price must be positive"); dayCountingConvention = Number(dayCountingConvention); if (ALLOWED_DAY_COUNTING_CONVENTION.indexOf(dayCountingConvention) === -1) throw RangeError("Invalid day counting convention"); this.T = T / dayCountingConvention; } Price() { throw TypeError("This method must be overridden"); } __FiniteDifferenceFirstDerivative(paramDelegate) { const dp = 1e-4; paramDelegate(this, dp); const [callPriceUp, putPriceUp] = this.Price(); paramDelegate(this, -2.0 * dp); const [callPriceDown, putPriceDown] = this.Price(); paramDelegate(this, dp); const callDerivative = (callPriceUp - callPriceDown) / (2.0 * dp); const putDerivative = (putPriceUp - putPriceDown) / (2.0 * dp); return [callDerivative, putDerivative]; } __FiniteDifferenceSecondDerivative(paramDelegate) { const dp = 1e-4; paramDelegate(this, dp); const [callPriceUp, putPriceUp] = this.Price(); paramDelegate(this, -2.0 * dp); const [callPriceDown, putPriceDown] = this.Price(); paramDelegate(this, dp); const [callPrice, putPrice] = this.Price(); const callDerivative = (callPriceUp - 2.0 * callPrice + callPriceDown) / (dp * dp); const putDerivative = (putPriceUp - 2.0 * putPrice + putPriceDown) / (dp * dp); return [callDerivative, putDerivative]; } __FiniteDifferenceSecondPartialDerivative(paramDelegate1, paramDelegate2) { const dp = 1e-4; const dq = 1e-4; paramDelegate1(this, dp); paramDelegate1(this, dq); const [callPriceUpUp, putPriceUpUp] = this.Price(); paramDelegate2(this, -2.0 * dq); const [callPriceUpDown, putPriceUpDown] = this.Price(); paramDelegate1(this, -2.0 * dp); const [callPriceDownDown, putPriceDownDown] = this.Price(); paramDelegate2(this, +2.0 * dq); const [callPriceDownUp, putPriceDownUp] = this.Price(); paramDelegate1(this, +dp); paramDelegate2(this, -dq); const callDerivative = (callPriceUpUp - callPriceUpDown - callPriceDownUp + callPriceDownDown) / (4.0 * dp * dq); const putDerivative = (putPriceUpUp - putPriceUpDown - putPriceDownUp + putPriceDownDown) / (4.0 * dp * dq); return [callDerivative, putDerivative]; } Delta() { return this.__FiniteDifferenceFirstDerivative(function(that, dp) { that.S += dp; }); } Gamma() { return this.__FiniteDifferenceSecondDerivative(function(that, dp) { that.S += dp; }); } Vega() { return this.__FiniteDifferenceFirstDerivative(function(that, dp) { that.sigma += dp; }); } Rho() { const rho = this._Rho(); const rhoB = this.CarryRho(); return [rho[0] + rhoB[0], rho[1] + rhoB[1]]; } _Rho() { return this.__FiniteDifferenceFirstDerivative(function(that, dp) { that.r += dp; }); } CarryRho() { return this.__FiniteDifferenceFirstDerivative(function(that, dp) { that.b += dp; }); } Theta() { return this.__FiniteDifferenceFirstDerivative(function(that, dp) { that.T -= dp; }); } Charm() { return this.__FiniteDifferenceSecondPartialDerivative( function(that, dp) { that.T -= dp; }, function(that, dp) { that.S += dp; } ); } Theta2() { return this.__FiniteDifferenceSecondDerivative(function(that, dp) { that.T -= dp; }); } }32:T993,class BlackScholes extends PricingModel { constructor(S, K, r, b, sigma, T, dayCountingConvention) { super(S, K, r, b, sigma, T, dayCountingConvention); } Price() { var [d1, d2] = this.GetD(); var Nd1 = std_cdf(d1), Nd2 = std_cdf(d2); const discountFactor = Math.exp(-this.r * this.T); const growthFactor = Math.exp(this.b * this.T); const callPrice = discountFactor * (this.S * growthFactor * Nd1 - this.K * Nd2); const forwardPrice = discountFactor * (this.S * growthFactor - this.K); const putPrice = callPrice - forwardPrice; // call-put parity return [callPrice, putPrice]; } Delta() { var [d1, _] = this.GetD(); var Nd1 = std_cdf(d1); const growthFactorTimesDiscountFactor = Math.exp( (this.b - this.r) * this.T ); const callDelta = growthFactorTimesDiscountFactor * Nd1; const putDelta = growthFactorTimesDiscountFactor * (Nd1 - 1.0); return [callDelta, putDelta]; } Gamma() { var [d1, _] = this.GetD(); const Pd1 = std_pdf(d1); const oneOverS = 1.0 / this.S; const oneOverSigmaSqrtT = 1.0 / (this.sigma * Math.sqrt(this.T)); const growthFactorTimesDiscountFactor = Math.exp( (this.b - this.r) * this.T ); const gamma = oneOverS * Pd1 * oneOverSigmaSqrtT * growthFactorTimesDiscountFactor; return [gamma, gamma]; } Vega() { var [d1, _] = this.GetD(); const Pd1 = std_pdf(d1); const growthFactorTimesDiscountFactor = Math.exp( (this.b - this.r) * this.T ); const vega = this.S * Math.sqrt(this.T) * growthFactorTimesDiscountFactor * Pd1; return [vega, vega]; } _Rho() { const price = this.Price(); return [-this.T * price[0], -this.T * price[1]]; } CarryRho() { var [d1, _] = this.GetD(); var Nd1 = std_cdf(d1); const growthFactorTimesDiscountFactor = Math.exp( (this.b - this.r) * this.T ); const callCarryRho = this.S * this.T * Nd1 * growthFactorTimesDiscountFactor; const putCarryRho = -this.S * this.T * (1.0 - Nd1) * growthFactorTimesDiscountFactor; return [callCarryRho, putCarryRho]; } GetD() { const logMoneyness = Math.log(this.S / this.K); const sigmaSqrtT = this.sigma * Math.sqrt(this.T); const tmp = (logMoneyness + this.b * this.T) / sigmaSqrtT; const d1 = tmp + .5 * sigmaSqrtT; const d2 = tmp - .5 * sigmaSqrtT; return [d1, d2]; } }33:[] 2f:{"title":"Options Strategy Evaluation","cells":[{"id":0,"value":"md`# Options Strategy Evaluation`","pinned":true,"hidden":false,"mode":"ojs"},{"id":39,"value":"viewof amountToHedge = number({placeholder: 2000000, title: \"Amount to hedge USD\", value: 2000000})","pinned":false,"hidden":false,"mode":"ojs"},{"id":105,"value":"viewof percentAllocation = slider({\n title: \"Percent of call premium to allocate to puts\",\n description: \"Current volatility measure (percentage) for the underlying asset\",\n min: 0,\n max: 100,\n value: 5,\n step: 1\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":50,"value":"viewof Spot = slider({\n title: \"Current Spot Price\",\n description: \"Current spot price of asset\",\n min: 1,\n max: 1000,\n value: 111\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":45,"value":"viewof Volatility = slider({\n title: \"Current Volatility:\",\n description: \"Current volatility measure (percentage) for the underlying asset\",\n min: 50,\n max: 400,\n value: 220,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":115,"value":"viewof sellDelta = slider({\n title: \"Call Delta to sell\",\n description: \"\",\n min: 1,\n max: 100,\n value: 35\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":125,"value":"viewof buyDelta = slider({\n title: \"Put Delta to buy\",\n description: \"\",\n min: 1,\n max: 100,\n value: 3\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":100,"value":"viewof futureVolatility = slider({\n title: \"Future Volatility:\",\n description: \"Future volatility measure (percentage) for the underlying asset\",\n min: 50,\n max: 400,\n value: 200,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":93,"value":"viewof futureSpot = slider({\n title: \"Future Spot Price\",\n description: \"Future spot price of asset\",\n min: 1,\n max: 1000,\n value: 111\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":215,"value":"viewof daysIntoFuture = slider({\n title: \"How many days elapsed since putting on positions\",\n description: \"\",\n min: 0,\n max: 365,\n value: 14,\n step: 1\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":349,"value":"md`# Expected payoff for above strategies based on future conditions`","pinned":false,"hidden":false,"mode":"ojs"},{"id":327,"value":"table = { \n const tbl = d3.select(html`

`);\n \n //headers\n tbl.append('thead').append('tr')\n .selectAll('th')\n .data(byPuts[0])\n .enter()\n .append('th')\n .text(d => d);\n \n //rows\n tbl.append('tbody');\n tbl.selectAll('tbody tr')\n .data(byPuts.slice(1))\n .enter()\n .append('tr')\n //cells\n .selectAll('td')\n .data(function(d) { return d; })\n .enter()\n .append('td')\n .text(d => d)\n .attr('class', function(d,i) {\n if (i===0) {\n return '';\n } else {\n return 'blog-table-nbr';\n }\n })\n .style('background-color', function(d) { \n var val = parseFloat(d);\n if (!isNaN(val)) { \n return color(val);\n }\n });\n \n return tbl.node();\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":371,"value":"md`## Call premium to be received across different strikes and expirations`","pinned":false,"hidden":false,"mode":"ojs"},{"id":356,"value":"callDataTable = {\n \n const div = d3.select(html`

d);\n \n const rows = table.selectAll(\".row\")\n .data(chainByOnlyCall)\n .enter().append(\"tr\")\n .attr(\"class\", \"row\")\n \n const cells = rows.selectAll(\".cell\")\n .data(d => Object.values(d))\n .enter().append(\"td\")\n .attr(\"class\", \"cell\")\n .text(d => d);\n \n return div.node()\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":386,"value":"md`## Put premium to be paid across different strikes and expirations`","pinned":false,"hidden":false,"mode":"ojs"},{"id":384,"value":"putDataTable = {\n \n const div = d3.select(html`

d);\n \n const rows = table.selectAll(\".row\")\n .data(chainByOnlyPut)\n .enter().append(\"tr\")\n .attr(\"class\", \"row\")\n \n const cells = rows.selectAll(\".cell\")\n .data(d => Object.values(d))\n .enter().append(\"td\")\n .attr(\"class\", \"cell\")\n .text(d => d);\n \n return div.node()\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":210,"value":"futureNetValue = futureCallValue.map((call,i) => {\n const netCallValue = callPremiumReceived[i] - call\n return netFuturePutValue.map(put => netCallValue + put)\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":140,"value":"callPremiumReceived = chainByCallDelta.map(opt => Math.floor(callsSold * opt.callPrice))","pinned":true,"hidden":false,"mode":"ojs"},{"id":242,"value":"netFuturePutValue = futurePutValue.map((value, i) => value - putPremiumSpent)","pinned":true,"hidden":false,"mode":"ojs"},{"id":312,"value":"puts = ['PUTS', ..._.uniq(futureNetValueIndexed.flat().map(x => x.y))]","pinned":true,"hidden":false,"mode":"ojs"},{"id":322,"value":"byPuts = {\n const flattened = futureNetValueIndexed.flat()\n const grouping = []\n flattened.forEach((pair,i) => {\n const idx = puts.findIndex(x => x == pair.y)\n if (!grouping[idx]) {\n grouping[idx] = [pair.y]\n }\n grouping[idx].push(pair.value.toLocaleString(undefined, { style: 'currency', currency: 'USD'}))\n })\n grouping[0] = calls\n return grouping\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":301,"value":"calls = ['CALLS', ..._.uniq(futureNetValueIndexed.flat().map(x => x.x))]","pinned":true,"hidden":false,"mode":"ojs"},{"id":252,"value":"futureNetValueIndexed = futureNetValue.map((callSeries, callIdx) => {\n return callSeries.map((value, putIdx) => {\n const call = chainByCallDelta[callIdx]\n const put = chainByPutDelta[putIdx]\n return {\n x: `${call.strike}-STRIKE-${call.expiration}DTE-CALL`,\n y: `${put.strike}-STRIKE-${put.expiration}DTE-PUT`,\n value: `${value}`\n }\n })\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":311,"value":"putRows = futureNetValue.map((callSeries, callIdx) => {\n return callSeries.map((value, putIdx) => {\n const call = chainByCallDelta[callIdx]\n const put = chainByPutDelta[putIdx]\n return {\n x: `${call.strike}-STRIKE-${call.expiration}DTE-CALL`,\n y: `${put.strike}-STRIKE-${put.expiration}DTE-PUT`,\n value: `${value}`\n }\n })\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":160,"value":"netCallPremiumReceived = {\n return callPremiumReceived.map((call, i) => {\n const put = putPremiumSpent\n return call - put\n })\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":179,"value":"callsSold = {\n const allocation = amountToHedge * (100-percentAllocation)/100\n const ethAmount = Math.floor(allocation/Spot)\n return ethAmount\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":157,"value":"putPremiumSpent = {\n const allocation = amountToHedge * percentAllocation/100\n const amount = Math.floor(allocation)\n return amount\n //return chainByPutDelta.map(opt => Math.floor(ethAmount * opt.put))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":184,"value":"putsBought = {\n const allocation = amountToHedge * percentAllocation/100\n const premium = Math.floor(allocation)\n return chainByPutDelta.map(opt => Math.floor(premium / opt.put))\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":117,"value":"chainByCallDelta = {\n return chains.map(e => {\n const optionToSell = e.find(x => x.callDelta <= sellDelta/100)\n return optionToSell\n }).filter(x => x != undefined)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":359,"value":"chainByOnlyCall = chainByCallDelta.map((c, i) => {\n const { callPrice, callDelta, strike, expiration } = c\n const premiumAmt = callsSold * callPrice\n const premium = Math.round(premiumAmt).toLocaleString()\n const futureAmt = futureCallValue[i]\n const futureValue = futureAmt.toLocaleString()\n const net = Math.round(premiumAmt - futureAmt).toLocaleString()\n return {\n callPrice,\n callDelta,\n strike,\n expiration,\n premium,\n futureValue,\n net\n }\n \n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":127,"value":"chainByPutDelta = {\n return chains.map(e => {\n const optionToBuy = e.find(x => x.putDelta <= -buyDelta/100)\n return optionToBuy\n })\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":380,"value":"chainByOnlyPut = chainByPutDelta.map((c, i) => {\n const { put, putDelta, strike, expiration } = c\n const amountBought = putsBought[i]\n const premiumAmt = amountBought * put\n const premium = Math.round(premiumAmt).toLocaleString()\n const futureAmt = futurePutValue[i]\n const futureValue = futureAmt.toLocaleString()\n const net = Math.round(futureAmt - premiumAmt).toLocaleString()\n return {\n putPrice: put,\n putDelta,\n strike,\n expiration,\n premium,\n futureValue,\n net\n }\n \n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":171,"value":"callDeltaIndex = {\n return chains.map((e,i) => {\n const optionToSell = e.findIndex(x => x.callDelta <= sellDelta/100)\n return [i, optionToSell]\n }).filter(x => x[1] != -1)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":168,"value":"putDeltaIndex = {\n return chains.map((e,i) => {\n const optionToBuy = e.findIndex(x => x.putDelta <= -buyDelta/100)\n return [i, optionToBuy]\n })\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":68,"value":"chains = {\n return EXPIRATIONS.map(e => {\n return strikes.map(s => {\n const time = e/365\n const volatility = Volatility / 100\n const callArgs = [Spot, s, time, volatility, RFR, 'call']\n const putArgs = [Spot, s, time, volatility, RFR, 'put']\n const callPrice = blackScholes.blackScholes(...callArgs)\n const callDelta = greeks.getDelta(...callArgs)\n const put = blackScholes.blackScholes(...putArgs)\n const putDelta = greeks.getDelta(...putArgs)\n return { callPrice, callDelta, put, putDelta, strike: s, expiration: e }\n })\n })\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":203,"value":"futureCallValue = futureChainCalls.map(({call}) => Math.floor(callsSold * call))","pinned":true,"hidden":false,"mode":"ojs"},{"id":206,"value":"futurePutValue = futureChainPuts.map(({ put }, i) => Math.floor(putsBought[i] * put))","pinned":true,"hidden":false,"mode":"ojs"},{"id":189,"value":"futureChainCalls = callDeltaIndex.map(([e,o]) => futureChains[e][o])","pinned":true,"hidden":false,"mode":"ojs"},{"id":201,"value":"futureChainPuts = putDeltaIndex.map(([e,o]) => futureChains[e][o])","pinned":true,"hidden":false,"mode":"ojs"},{"id":98,"value":"futureChains = {\n return EXPIRATIONS.map(e => {\n return strikes.map(s => {\n const timeRemaining = e - daysIntoFuture\n const time = timeRemaining <= 0 ? 0 : e/365\n const volatility = futureVolatility / 100\n const callArgs = [futureSpot, s, time, volatility, RFR, 'call']\n const putArgs = [futureSpot, s, time, volatility, RFR, 'put']\n const call = blackScholes.blackScholes(...callArgs)\n const put = blackScholes.blackScholes(...putArgs)\n return { call, put, strike: s, expiration: e }\n })\n })\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":58,"value":"strikes = {\n const strike = []\n for(let i=5;i<900;i+=5) {\n strike.push(i)\n }\n return strike\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":72,"value":"dcc = 365","pinned":true,"hidden":false,"mode":"ojs"},{"id":66,"value":"RFR = 0.01","pinned":true,"hidden":false,"mode":"ojs"},{"id":54,"value":"EXPIRATIONS = [15, 30, 45, 60, 90, 180, 275, 365]","pinned":false,"hidden":false,"mode":"ojs"},{"id":10,"value":"ALLOWED_DAY_COUNTING_CONVENTION = [365, 252]","pinned":false,"hidden":false,"mode":"ojs"},{"id":108,"value":"greeks = require('https://bundle.run/greeks@1.0.0')","pinned":true,"hidden":false,"mode":"ojs"},{"id":79,"value":"blackScholes = require('https://bundle.run/black-scholes@1.1.0')","pinned":false,"hidden":false,"mode":"ojs"},{"id":8,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":18,"value":"oneOverSqrt2PI = 1.0 / Math.sqrt(2.0 * Math.PI)","pinned":false,"hidden":false,"mode":"ojs"},{"id":22,"value":"function erf(x) {\n // save the sign of x\n const sign = x >= 0 ? 1 : -1;\n x = Math.abs(x);\n\n const a1 = 0.254829592;\n const a2 = -0.284496736;\n const a3 = 1.421413741;\n const a4 = -1.453152027;\n const a5 = 1.061405429;\n const p = 0.3275911;\n\n // Abramovitz-Stegun formula 7.1.26\n const t = 1.0 / (1.0 + p * x);\n const y =\n 1.0 - ((((a5 * t + a4) * t + a3) * t + a2) * t + a1) * t * Math.exp(-x * x);\n return sign * y;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"function cdf(x, mean, variance) {\n return 0.5 * (1 + erf((x - mean) / Math.sqrt(2 * variance)));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":16,"value":"function pdf(x, mean, variance) {\n const z = (x - mean) / variance;\n return Math.exp(-.5 * z * z) * oneOverSqrt2PI;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"function std_cdf(x) {\n return cdf(x, 0.0, 1.0);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"function std_pdf(x) {\n return pdf(x, 0.0, 1.0);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":263,"value":"treemap = data => d3.treemap()\n .round(true)\n .tile(d3.treemapSliceDice)\n .size([\n width - margin.left - margin.right, \n height - margin.top - margin.bottom\n ])\n (d3.hierarchy(\n {\n values: d3.nest()\n .key(d => d.x)\n .key(d => d.y)\n .entries(data)\n },\n d => d.values\n ).sum(d => d.value))\n .each(d => {\n d.x0 += margin.left;\n d.x1 += margin.left;\n d.y0 += margin.top;\n d.y1 += margin.top;\n })","pinned":true,"hidden":false,"mode":"ojs"},{"id":256,"value":"margin = ({top: 30, right: -1, bottom: -1, left: 1})","pinned":true,"hidden":false,"mode":"ojs"},{"id":261,"value":"format = d => d.toLocaleString()","pinned":true,"hidden":false,"mode":"ojs"},{"id":265,"value":"height = 954","pinned":true,"hidden":false,"mode":"ojs"},{"id":331,"value":"color = d3.scaleLinear().domain(d3.extent(futureNetValue.flat())).range(['#d3e4ff','#2275f9'])","pinned":true,"hidden":false,"mode":"ojs"},{"id":267,"value":"width = height","pinned":true,"hidden":false,"mode":"ojs"},{"id":4,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":6,"value":"import { text, slider, radio, number } from '@jashkenas/inputs'","pinned":true,"hidden":false,"mode":"ojs"},{"id":288,"value":"import { tile } from '@d3/treemap'","pinned":true,"hidden":false,"mode":"ojs"},{"id":304,"value":"_ = require(\"lodash\");","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}