31:T88d,OutputTable=html`

	Call	Put
Price	${Price[0]}	${Price[1]}
Delta	${Delta[0]}	${Delta[1]}
Gamma	${Gamma[0]}	${Gamma[1]}
Vega	${Vega[0]}	${Vega[1]}
Rho	${Rho[0]}	${Rho[1]}
Carry Rho	${CarryRho[0]}	${CarryRho[1]}
Theta	${Theta[0]}	${Theta[2]}
Charm	${Charm[0]}	${Charm[1]}
Theta 2	${Theta2[0]}	${Theta2[1]}

`32: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; }); } }33: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]; } }34:[] 2f:{"title":"Option Price Calculator","cells":[{"id":52,"value":"md`# Option Price Calculator`","pinned":false,"hidden":false,"mode":"ojs"},{"id":44,"value":"viewof Spot = slider({\n title: \"SPOT\",\n description: \"\",\n min: 0.01,\n max: maxPrice,\n value: 55\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":43,"value":"viewof Strike = slider({\n title: \"STRIKE\",\n description: \"Select the Strike Price\",\n min: 0.01,\n max: maxPrice,\n value: 50\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":132,"value":"viewof Volatility = slider({\n title: \"Volatility:\",\n description: \"Volatility measure for the underlying asset\",\n min: .01,\n max: Infinity,\n value: 30,\n step: 0.01\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":79,"value":"viewof DaysToExpiry = slider({\n title: \"Days to Expiry\",\n description: \"Select time to expiration (unit:days)\",\n min: 1,\n max: 365 * 5,\n value: 365,\n step: 7\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":497,"value":"md`\n---\n## Option Valuation Breakdown`","pinned":false,"hidden":false,"mode":"ojs"},{"id":487,"value":"md`When Spot price is *$${Spot}* and volatility is at *${sigma}*\nThe option with the strike price of ${Strike} and ${DaysToExpiry} days to expiry has the following breakdown`","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":243,"value":"md`---\n## More Configs`","pinned":false,"hidden":false,"mode":"ojs"},{"id":67,"value":"maxPrice=500;","pinned":false,"hidden":false,"mode":"ojs"},{"id":103,"value":"S=parseFloat(Spot)","pinned":false,"hidden":false,"mode":"ojs"},{"id":106,"value":"K=parseFloat(Strike)","pinned":false,"hidden":false,"mode":"ojs"},{"id":39,"value":"viewof RiskFreeRate = slider({\n title: \"Risk-Free Interest Rate (%):\",\n description: \"Discounting Rate\",\n min: -100,\n max: 100,\n value: -0.01,\n step: 0.01,\n fixed: false\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":126,"value":"r= 0.01 * parseFloat(RiskFreeRate)","pinned":false,"hidden":false,"mode":"ojs"},{"id":38,"value":"viewof CarryRate=slider({title: \"Carry Rate (%):\",description: \"Cost of carrying the option's underlying. If there's no borrow rate, use the same value as the risk-free interest rate\",min:-100 ,max: 100,value:-0.01,step:0.01})","pinned":false,"hidden":false,"mode":"ojs"},{"id":124,"value":"b= 0.01 * parseFloat(CarryRate);","pinned":false,"hidden":false,"mode":"ojs"},{"id":141,"value":"sigma = 0.01 * parseFloat(Volatility)","pinned":false,"hidden":false,"mode":"ojs"},{"id":118,"value":"T = DaysToExpiry","pinned":false,"hidden":false,"mode":"ojs"},{"id":98,"value":"viewof DayCountingConvention = radio({\n options: [\"CalendarDays\", \"BusinessDays\"],\n value: \"CalendarDays\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":33,"value":"ALLOWED_DAY_COUNTING_CONVENTION = [365, 252]","pinned":false,"hidden":false,"mode":"ojs"},{"id":240,"value":"md`### Calculations`","pinned":false,"hidden":false,"mode":"ojs"},{"id":131,"value":"black_scholes_data = new BlackScholes(S, K, r, b, sigma, T, dcc)","pinned":false,"hidden":false,"mode":"ojs"},{"id":156,"value":"Price = black_scholes_data.Price()","pinned":false,"hidden":false,"mode":"ojs"},{"id":149,"value":"Delta = black_scholes_data.Delta()","pinned":false,"hidden":false,"mode":"ojs"},{"id":165,"value":"Gamma = black_scholes_data.Gamma()","pinned":false,"hidden":false,"mode":"ojs"},{"id":167,"value":"Vega = black_scholes_data.Vega()","pinned":false,"hidden":false,"mode":"ojs"},{"id":171,"value":"Rho = black_scholes_data.Rho()","pinned":false,"hidden":false,"mode":"ojs"},{"id":169,"value":"CarryRho = black_scholes_data.CarryRho()","pinned":false,"hidden":false,"mode":"ojs"},{"id":173,"value":"Theta = black_scholes_data.Theta()","pinned":false,"hidden":false,"mode":"ojs"},{"id":175,"value":"Charm = black_scholes_data.Charm()","pinned":false,"hidden":false,"mode":"ojs"},{"id":159,"value":"Theta2 = black_scholes_data.Theta2()","pinned":false,"hidden":false,"mode":"ojs"},{"id":112,"value":"dcc = DayCountingConvention === \"CalendarDays\" ? 252 : 365","pinned":false,"hidden":false,"mode":"ojs"},{"id":235,"value":"md`## MODEL`","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":34,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":237,"value":"md`### Utility`","pinned":false,"hidden":false,"mode":"ojs"},{"id":31,"value":"oneOverSqrt2PI = 1.0 / Math.sqrt(2.0 * Math.PI)","pinned":false,"hidden":false,"mode":"ojs"},{"id":30,"value":"function std_cdf(x) {\n return cdf(x, 0.0, 1.0);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":29,"value":"function std_pdf(x) {\n return pdf(x, 0.0, 1.0);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":28,"value":"function cdf(x, mean, variance) {\n return 0.5 * (1 + erf((x - mean) / Math.sqrt(2 * variance)));\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"function pdf(x, mean, variance) {\n const z = (x - mean) / variance;\n return Math.exp(-.5 * z * z) * oneOverSqrt2PI;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":26,"value":"function erf(x) {\n // save the sign of x\n const sign = x >= 0 ? 1 : -1;\n x = Math.abs(x);\n\n const a1 = 0.254829592;\n const a2 = -0.284496736;\n const a3 = 1.421413741;\n const a4 = -1.453152027;\n const a5 = 1.061405429;\n const p = 0.3275911;\n\n // Abramovitz-Stegun formula 7.1.26\n const t = 1.0 / (1.0 + p * x);\n const y =\n 1.0 - ((((a5 * t + a4) * t + a3) * t + a2) * t + a1) * t * Math.exp(-x * x);\n return sign * y;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"md`## ANX`","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"d3 = require('d3', 'd3-array')","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"import { text, slider, radio } from '@jashkenas/inputs'","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}