31:Tacf,OptionChartBuilder = (chartID, calls, strikes, puts) => { let options = [...calls, ...puts]; let put_zip = d3.zip(strikes, puts); let call_zip = d3.zip(strikes, calls); const svg = d3 .create("svg") .attr("width", width) .attr("viewBox", [0, 0, width, height]) .attr("fill", "none") .attr("stroke-linejoin", "round") .attr("stroke-linecap", "round") .attr("id", chartID) .attr("class", "SVG"); let xScale = x.copy(); // x = d3 // .scalePoint() // .range([margin.left, width - margin.right]); let y = d3 .scaleLinear() .domain(d3.extent(options)) .nice() .range([height - margin.bottom, margin.top]); let line = d3 .line() .x((d, i) => x(d[0])) .y((d, i) => y(d[1])); let xAxis = (g) => g .attr("transform", `translate(0,${height - margin.bottom})`) .call(d3.axisBottom(x).tickFormat(d3.format("3,.4")).tickSizeOuter(0)) .call((g) => g .selectAll("text") .clone() .attr( "transform", `rotate(90) translate(10,${-width / strikes.length / 3})` ) .attr("dominant-baseline", "middle") .attr("text-anchor", "center") ); let yAxis = (g) => g .attr("transform", `translate(${margin.left},0)`) .call(d3.axisLeft(y).ticks(5)) .call((g) => g.select(".domain").remove()) .call((g) => g .select(".tick:last-of-type text") .clone() .attr("x", 3) .attr("text-anchor", "start") .attr("font-weight", "bold") .text((d) => " ") ); let call_dots = svg .selectAll(".call_option") .data(call_zip) .enter() .append("circle") .attr("class", "call_option") .attr("cx", (d, i) => x(d[0])) .attr("cy", (d, i) => y(d[1])) .attr("fill", "steelblue") .attr("r", 3); let put_dots = svg .selectAll(".put_option") .data(put_zip) .enter() .append("circle") .attr("class", "put_option") .attr("cx", (d, i) => x(d[0])) .attr("cy", (d, i) => y(d[1])) .attr("fill", "gold") .attr("r", 3); let call_line = svg .append("g") .attr("class", "call_line") .append("path") .attr("stroke", "gold") .attr("d", line(call_zip)); let put_line = svg .append("g") .attr("class", "put_line") .append("path") .style("stroke", "steelblue") .attr("d", line(put_zip)); svg.append("g").call(xAxis); svg.append("g").call(yAxis); svg .append("path") .datum([""]) .attr("fill", "none") .attr("stroke", "steelblue") .attr("stroke-width", 1.5) .attr("stroke-linejoin", "round") .attr("stroke-linecap", "round") .attr("d", line); return svg.node(); }32:T936,OptionsBreakdown = { const kMin = parseFloat(MinStrike); const kMax = parseFloat(MaxStrike); const nStrikes = parseInt(NumOfStrikes); const dK = (kMax - kMin) / (nStrikes - 1); var strikes = []; var callPrice = [], putPrice = []; var callDelta = [], putDelta = []; var callGamma = [], putGamma = []; var callVega = [], putVega = []; var callRho = [], putRho = []; var callCarryRho = [], putCarryRho = []; var callTheta = [], putTheta = []; var callCharm = [], putCharm = []; var callTheta2 = [], putTheta2 = []; var tmpC = 0.0, tmpP = 0.0; for (let i = 0; i < nStrikes; ++i) { strikes.push(kMin + i * dK); model.K = strikes[strikes.length - 1]; [tmpC, tmpP] = model.Price(); callPrice.push(tmpC), putPrice.push(tmpP); [tmpC, tmpP] = model.Delta(); callDelta.push(tmpC), putDelta.push(tmpP); [tmpC, tmpP] = model.Gamma(); callGamma.push(tmpC), putGamma.push(tmpP); [tmpC, tmpP] = model.Vega(); callVega.push(tmpC), putVega.push(tmpP); [tmpC, tmpP] = model.Rho(); callRho.push(tmpC), putRho.push(tmpP); [tmpC, tmpP] = model.CarryRho(); callCarryRho.push(tmpC), putCarryRho.push(tmpP); [tmpC, tmpP] = model.Theta(); callTheta.push(tmpC), putTheta.push(tmpP); [tmpC, tmpP] = model.Charm(); callCharm.push(tmpC), putCharm.push(tmpP); [tmpC, tmpP] = model.Theta2(); callTheta2.push(tmpC), putTheta2.push(tmpP); } // Plot(strikes, callPrice, putPrice, "Price", "price-chart"); // Plot(strikes, callDelta, putDelta, "Delta", "delta-chart"); // Plot(strikes, callGamma, putGamma, "Gamma", "gamma-chart"); // Plot(strikes, callVega, putVega, "Vega", "vega-chart"); // Plot(strikes, callRho, putRho, "Rho", "rho-chart"); // Plot(strikes, callCarryRho, putCarryRho, "Carry Rho", "carry-rho-chart"); // Plot(strikes, callTheta, putTheta, "Theta", "theta-chart"); // Plot(strikes, callCharm, putCharm, "Charm", "charm-chart"); // Plot(strikes, callTheta2, putTheta2, "Theta2", "theta2-chart"); return { strikes, callPrice, putPrice, callDelta, putDelta, callGamma, putGamma, callVega, putVega, callRho, putRho, callCarryRho, putCarryRho, callTheta, putTheta, callCharm, putCharm, callTheta2, putTheta2 }; }33:Tf38,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"); if (![252, 365].includes(dayCountingConvention)) 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; }); } }34:Ta17,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]; } }35:[] 2f:{"title":"Option Price Breakdown","cells":[{"id":0,"value":"md`# Option Price Breakdown`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1777,"value":"Charts = html`\n

\n${ChartConfig.map((x) => {\n let formula = x[1].map(\n (eq) =>\n html`

${eq.node}

`\n );\n\n let svg = OptionChartBuilder(\n x[1].chartID,\n OptionsBreakdown[\"call\" + x[0]],\n OptionsBreakdown.strikes,\n OptionsBreakdown[\"put\" + x[0]]\n );\n\n d3.select(svg).append(\"g\").attr(\"class\", \"tooltip-group\");\n\n return html`${`

${x[0]}

`}${formula}${svg}

`;\n})}

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1776,"value":"width = 300","pinned":false,"hidden":false,"mode":"ojs"},{"id":1775,"value":"height = 200","pinned":false,"hidden":false,"mode":"ojs"},{"id":1771,"value":"pad = 25","pinned":false,"hidden":false,"mode":"ojs"},{"id":1369,"value":"line = d3\n .line()\n .x((d, i) => x(d[0]))\n .y((d, i) => y(d[1]))","pinned":false,"hidden":false,"mode":"ojs"},{"id":1371,"value":"y = d3\n .scaleLinear()\n .domain(d3.extent(OptionsBreakdown.callPrice))\n .nice()\n .range([height - margin.bottom, margin.top])","pinned":false,"hidden":false,"mode":"ojs"},{"id":1373,"value":"x = d3\n .scaleLinear()\n .domain(d3.extent(OptionsBreakdown.strikes))\n .range([margin.left, width - margin.right])","pinned":false,"hidden":false,"mode":"ojs"},{"id":456,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":1326,"value":"md`## DATA`","pinned":false,"hidden":false,"mode":"ojs"},{"id":200,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":1321,"value":"md`### Configs`","pinned":false,"hidden":false,"mode":"ojs"},{"id":464,"value":"margin = ({ top: pad, right: pad, bottom: pad, left: pad })","pinned":false,"hidden":false,"mode":"ojs"},{"id":962,"value":"OptionFormulas = [\n { name: \"Call_Price_Formula\", node: Call_Price_Formula },\n { name: \"Put_Price_Formula\", node: Put_Price_Formula },\n { name: \"Call_Delta_Formula\", node: Call_Delta_Formula },\n { name: \"Put_Delta_Formula\", node: Put_Delta_Formula },\n { name: \"Gamma_Formula\", node: Gamma_Formula },\n { name: \"Vega_Formula\", node: Vega_Formula },\n { name: \"Rho_Formula\", node: Rho_Formula },\n { name: \"Rho_Partial_Formula\", node: Rho_Partial_Formula },\n { name: \"CarryRho_Formula\", node: CarryRho_Formula },\n { name: \"CarryRho_Partial_Formula\", node: CarryRho_Partial_Formula },\n { name: \"Theta_Formula\", node: Theta_Formula },\n { name: \"Charm_Formula\", node: Charm_Formula },\n { name: \"Theta2_Formula\", node: Theta2_Formula }\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":1029,"value":"ChartConfig = d3.groups(\n [\n ...OptionFormulas.map(({ name: x, node }) => {\n let name = x\n .replace('Call_', '')\n .replace('Put_', '')\n .replace('_Formula', '')\n .replace('_Partial', '');\n let chartID = `${name}_Chart`;\n return { name, chartID, formula: x, node };\n })\n ],\n d => d.name\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":784,"value":"ConfigInfo = [\n{id:\"Price_Chart\",},\n{id:\"Delta_Chart\",},\n{id:\"Gamma_Chart\",},\n{id:\"Vega_Chart\",},\n{id:\"Rho_Chart\",},\n{id:\"CarryRho_Chart\",},\n{id:\"Theta_Chart\",},\n{id:\"Charm_Chart\",},\n{id:\"Theta2_Chart \",}\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":198,"value":"md`## Setup`","pinned":false,"hidden":false,"mode":"ojs"},{"id":320,"value":"maxPrice = 200","pinned":false,"hidden":false,"mode":"ojs"},{"id":339,"value":"viewof MaxStrike = slider({title: \"MAX STRIKE\",description: \"\",min:Spot ,max:maxPrice ,value:Spot+10,step:1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":270,"value":"viewof MinStrike = slider({title: \"Min\", description: \"\", min:1, max: Spot, value:Spot-10, step:1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":272,"value":"viewof NumOfStrikes = slider({\n title: \"Number of Strikes\",\n description:\n \"the number of possibilities are same on both higher and lower side of spot.\",\n min: 5,\n max: 50,\n value: 21,\n step: 1\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":279,"value":"viewof Spot = slider({\n title: \"SPOT\",\n description: \"this is the current price of the underlying\",\n min: 0.01,\n max: maxPrice,\n value: 102\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1652,"value":"viewof RiskFreeRate = slider({\n title: \"Risk-Free Interest Rate (%):\",\n description: \"Discounting Rate / Borrowing rate\",\n min: -5,\n max: 5,\n value: -0.01,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":285,"value":"viewof CarryRate = slider({\n title: \"Carry Rate (%):\",\n description:\n \"Cost of carrying the option's underlying. If there's no borrow rate, use the same value as the risk-free interest rate\",\n min: -100,\n max: 100,\n value: -0.01,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":314,"value":"viewof Volatility = slider({\n title: \"Volatility:\",\n description: \"a measure of expectations based on past and future\",\n min: .01,\n max: Infinity,\n value: 30,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":316,"value":"sigma = 0.01 * Volatility","pinned":true,"hidden":false,"mode":"ojs"},{"id":318,"value":"viewof DaysToExpiry=slider({title: \"Days to Expiry\",description: \"\",min:1 ,max:maxPrice ,value:30,step:1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":330,"value":"viewof DayCountingConvention = radio({options:[\"CalendarDays\",\"BusinessDays\"],value:\"CalendarDays\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":419,"value":"md`\n----\n\n## Model`","pinned":false,"hidden":false,"mode":"ojs"},{"id":343,"value":"model = new BlackScholes(\n Spot,\n parseFloat(0),\n RiskFreeRate,\n CarryRate,\n sigma,\n DaysToExpiry,\n DayCountingConvention === \"CalendarDays\" ? 252 : 365\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":114,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":148,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":422,"value":"md`### Utility`","pinned":false,"hidden":false,"mode":"ojs"},{"id":103,"value":"oneOverSqrt2PI = 1.0 / Math.sqrt(2.0 * Math.PI)","pinned":false,"hidden":false,"mode":"ojs"},{"id":112,"value":"function std_cdf(x) {\n return cdf(x, 0.0, 1.0);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":110,"value":"function std_pdf(x) {\n return pdf(x, 0.0, 1.0);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":108,"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":106,"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":101,"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":866,"value":"Call_Price_Formula = tex`P_C = e^{-rT} \\left(S e^{bT} \\cdot N(d_1) - K \\cdot N(d_2)\\right)`","pinned":true,"hidden":false,"mode":"ojs"},{"id":870,"value":"Put_Price_Formula=tex`P_P = e^{-rT} \\left(K \\cdot N(-d_2) - S e^{bT} \\cdot N(-d_1)\\right)`","pinned":true,"hidden":false,"mode":"ojs"},{"id":882,"value":"Call_Delta_Formula=tex`\\Delta_C = e^{(b - r)T} \\cdot N(d_1)`","pinned":true,"hidden":false,"mode":"ojs"},{"id":894,"value":"Put_Delta_Formula=tex`\\Delta_P = e^{(b - r)T} \\cdot N(-d_1)`","pinned":true,"hidden":false,"mode":"ojs"},{"id":932,"value":"Gamma_Formula=tex`\\Gamma_C = \\Gamma_P = {e^{(b - r)T} \\over S\\sigma\\sqrt{T} } \\cdot P(d_1)`","pinned":true,"hidden":false,"mode":"ojs"},{"id":928,"value":"Vega_Formula=tex`V_C = V_P = e^{(b - r)T} S\\sqrt{T} \\cdot P(d_1)`","pinned":true,"hidden":false,"mode":"ojs"},{"id":918,"value":"Theta_Formula=tex`\\theta^C_{C, P} = {\\partial P_{C, P}\\over \\partial t}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":912,"value":"Theta2_Formula=tex`\\theta^2_{C, P} = {\\partial^2 P_{C, P}\\over \\partial t^2}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":905,"value":"Rho_Formula=tex`\\rho_{C, P} = {\\partial P_{C, P}\\over \\partial r} + {\\partial P_{C, P}\\over \\partial b}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":925,"value":"Rho_Partial_Formula=tex` {\\partial P_{C, P}\\over \\partial r} = -T \\cdot P_{C, P} `","pinned":true,"hidden":false,"mode":"ojs"},{"id":908,"value":"CarryRho_Formula = tex`\\rho^C_{C, P} = {\\partial P_{C, P}\\over \\partial b}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":922,"value":"CarryRho_Partial_Formula=tex`{\\partial P_{C, P}\\over \\partial b} = S\\cdot T \\cdot \\Delta_{C, P} `","pinned":true,"hidden":false,"mode":"ojs"},{"id":914,"value":"Charm_Formula=tex`c_{C, P} = {\\partial^2 P_{C, P}\\over \\partial t\\partial S}`","pinned":true,"hidden":false,"mode":"ojs"},{"id":265,"value":"md`## ANX`","pinned":false,"hidden":false,"mode":"ojs"},{"id":10,"value":"d3 = require(\"d3@6\", \"d3-array@2\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"import { text, slider, radio } from '@jashkenas/inputs'","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W35","stdlib":"1","titling":"auto"}