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2028 lines (1730 loc) · 75.4 KB
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Options Pricing Helper</title>
<style>
* {
box-sizing: border-box;
margin: 0;
padding: 0;
}
body {
font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, sans-serif;
background: #f8fafc;
color: #1e293b;
line-height: 1.5;
padding: 20px;
}
.container {
max-width: 900px;
margin: 0 auto;
}
header {
text-align: center;
margin-bottom: 24px;
}
.header-row {
display: flex;
justify-content: center;
align-items: center;
gap: 12px;
margin-bottom: 8px;
}
.mode-toggle {
display: flex;
justify-content: center;
margin-bottom: 20px;
}
.mode-toggle button {
padding: 10px 24px;
font-size: 0.95rem;
font-weight: 500;
border: 1px solid #e2e8f0;
background: #f8fafc;
color: #64748b;
cursor: pointer;
transition: all 0.2s;
}
.mode-toggle button:first-child {
border-radius: 8px 0 0 8px;
}
.mode-toggle button:last-child {
border-radius: 0 8px 8px 0;
border-left: none;
}
.mode-toggle button.active {
background: #2563eb;
border-color: #2563eb;
color: white;
}
.mode-toggle button:hover:not(.active) {
background: #e2e8f0;
}
body.dark .mode-toggle button {
border-color: #475569;
background: #334155;
color: #94a3b8;
}
body.dark .mode-toggle button.active {
background: #2563eb;
border-color: #2563eb;
color: white;
}
body.dark .mode-toggle button:hover:not(.active) {
background: #475569;
}
.normal-inputs {
display: none;
gap: 24px;
margin-bottom: 16px;
}
.normal-inputs.visible {
display: flex;
flex-wrap: wrap;
justify-content: center;
}
.input-group {
display: flex;
flex-direction: column;
align-items: center;
gap: 8px;
}
.input-group label {
font-weight: 600;
color: #475569;
font-size: 0.9rem;
}
body.dark .input-group label {
color: #94a3b8;
}
.input-row {
display: flex;
align-items: center;
gap: 12px;
}
.input-group input[type="range"] {
width: 150px;
cursor: pointer;
}
.input-group input[type="number"] {
width: 80px;
padding: 6px 10px;
border: 1px solid #e2e8f0;
border-radius: 6px;
font-size: 0.95rem;
font-family: 'SF Mono', Monaco, 'Consolas', monospace;
text-align: center;
}
.input-group input[type="number"]:focus {
outline: none;
border-color: #2563eb;
box-shadow: 0 0 0 3px rgba(37, 99, 235, 0.1);
}
body.dark .input-group input[type="number"] {
background: #334155;
border-color: #475569;
color: #e2e8f0;
}
body.dark .input-group input[type="number"]:focus {
border-color: #60a5fa;
box-shadow: 0 0 0 3px rgba(96, 165, 250, 0.1);
}
h1 {
font-size: 1.75rem;
font-weight: 600;
color: #0f172a;
margin: 0;
}
.header-btn {
background: #f1f5f9;
border: 1px solid #e2e8f0;
border-radius: 8px;
padding: 8px 16px;
cursor: pointer;
font-size: 0.9rem;
font-weight: 500;
color: #64748b;
transition: background 0.2s, color 0.2s;
}
.header-btn:hover {
background: #e2e8f0;
color: #475569;
}
.theme-toggle {
background: #f1f5f9;
border: 1px solid #e2e8f0;
border-radius: 8px;
padding: 8px;
cursor: pointer;
display: flex;
align-items: center;
justify-content: center;
color: #64748b;
transition: background 0.2s, color 0.2s;
}
.theme-toggle:hover {
background: #e2e8f0;
color: #475569;
}
.theme-toggle .moon-icon {
display: none;
}
body.dark .theme-toggle .sun-icon {
display: none;
}
body.dark .theme-toggle .moon-icon {
display: block;
}
.instructions {
color: #64748b;
font-size: 0.95rem;
}
.graph-container {
background: white;
border-radius: 12px;
box-shadow: 0 1px 3px rgba(0,0,0,0.1);
padding: 20px;
margin-bottom: 20px;
position: relative;
}
.graph-hint {
position: absolute;
top: 12px;
left: 50%;
transform: translateX(-50%);
font-size: 0.8rem;
color: #94a3b8;
pointer-events: none;
}
.graph-hint.hidden {
display: none;
}
#pdfCanvas {
display: block;
width: 100%;
cursor: default;
}
.results-container {
background: white;
border-radius: 12px;
box-shadow: 0 1px 3px rgba(0,0,0,0.1);
padding: 20px;
max-width: none;
width: calc(100vw - 40px);
margin-left: calc(-50vw + 50% + 20px);
overflow-x: auto;
}
.results-header {
font-size: 1.1rem;
font-weight: 600;
margin-bottom: 16px;
color: #0f172a;
}
.price-table {
width: 100%;
border-collapse: collapse;
}
.price-table th {
padding: 8px 4px;
background: #f1f5f9;
font-weight: 700;
font-size: 0.85rem;
color: #334155;
text-transform: uppercase;
letter-spacing: 0.05em;
text-align: center;
}
.price-table th.strike-header {
font-size: 1.1rem;
font-weight: 800;
color: #0f172a;
letter-spacing: 0.08em;
}
.price-table th:first-child {
border-radius: 6px 0 0 6px;
}
.price-table th:last-child {
border-radius: 0 6px 6px 0;
}
.price-table td {
padding: 8px 4px;
border-bottom: 1px solid #e2e8f0;
text-align: center;
vertical-align: middle;
}
.price-table tr:last-child td {
border-bottom: none;
}
.price-table .strike {
font-weight: 700;
color: #0f172a;
font-size: 1.4rem;
padding-left: 24px;
padding-right: 24px;
}
.price-table .price {
font-family: 'SF Mono', Monaco, 'Consolas', monospace;
color: #059669;
font-size: 0.9rem;
padding-left: 16px;
padding-right: 16px;
}
/* Trader controls */
.trader-cell {
white-space: nowrap;
}
.trader-cell.pad-left {
padding-left: 12px;
}
.trader-cell.pad-right {
padding-right: 12px;
}
.price-table tbody tr:nth-child(odd) {
background: rgba(0, 0, 0, 0.02);
}
body.dark .price-table tbody tr:nth-child(odd) {
background: rgba(255, 255, 255, 0.02);
}
.trader-input {
width: 50px;
padding: 6px 8px;
border: 1px solid #e2e8f0;
border-radius: 4px;
font-size: 0.85rem;
text-align: center;
font-family: 'SF Mono', Monaco, 'Consolas', monospace;
}
.trader-input.edge {
-moz-appearance: textfield;
}
.trader-input.edge::-webkit-outer-spin-button,
.trader-input.edge::-webkit-inner-spin-button {
-webkit-appearance: none;
margin: 0;
}
.trader-input:focus {
outline: none;
border-color: #2563eb;
}
.trader-btn {
padding: 4px 8px;
border: none;
border-radius: 4px;
font-size: 0.7rem;
font-weight: 600;
cursor: pointer;
text-transform: uppercase;
}
.trader-btn.bid {
background: #059669;
color: white;
}
.trader-btn.bid:hover {
background: #047857;
}
.trader-btn.offer {
background: #dc2626;
color: white;
}
.trader-btn.offer:hover {
background: #b91c1c;
}
.trader-btn.clear {
background: #64748b;
color: white;
font-size: 0.65rem;
padding: 4px 6px;
}
.trader-btn.clear:hover {
background: #475569;
}
/* Dark mode trader styles */
body.dark .trader-input {
background: #334155;
border-color: #475569;
color: #e2e8f0;
}
body.dark .trader-input:focus {
border-color: #60a5fa;
}
body.dark .trader-btn.clear {
background: #475569;
}
body.dark .trader-btn.clear:hover {
background: #64748b;
}
.trader-checkbox {
width: 16px;
height: 16px;
cursor: pointer;
accent-color: #2563eb;
}
.expected-value {
margin-top: 20px;
padding-top: 16px;
border-top: 2px solid #e2e8f0;
display: flex;
justify-content: space-between;
align-items: center;
}
.expected-value .label {
font-weight: 600;
color: #475569;
}
.expected-value .value {
font-size: 1.25rem;
font-weight: 600;
color: #2563eb;
font-family: 'SF Mono', Monaco, 'Consolas', monospace;
}
@media (max-width: 600px) {
body {
padding: 12px;
}
h1 {
font-size: 1.5rem;
}
.price-table th,
.price-table td {
padding: 8px;
font-size: 0.9rem;
}
}
body.dark {
background: #0f172a;
color: #e2e8f0;
}
body.dark h1 {
color: #f1f5f9;
}
body.dark .instructions {
color: #94a3b8;
}
body.dark .graph-container,
body.dark .results-container {
background: #1e293b;
box-shadow: 0 1px 3px rgba(0,0,0,0.3);
}
body.dark .results-header {
color: #f1f5f9;
}
body.dark .price-table th {
background: #334155;
color: #cbd5e1;
}
body.dark .price-table th.strike-header {
color: #f1f5f9;
}
body.dark .price-table td {
border-bottom-color: #334155;
}
body.dark .price-table .strike {
color: #f1f5f9;
}
body.dark .price-table .price {
color: #34d399;
}
body.dark .expected-value {
border-top-color: #334155;
}
body.dark .expected-value .label {
color: #94a3b8;
}
body.dark .expected-value .value {
color: #60a5fa;
}
body.dark .header-btn {
background: #334155;
border-color: #475569;
color: #94a3b8;
}
body.dark .header-btn:hover {
background: #475569;
color: #e2e8f0;
}
body.dark .theme-toggle {
background: #334155;
border-color: #475569;
color: #94a3b8;
}
body.dark .theme-toggle:hover {
background: #475569;
color: #e2e8f0;
}
</style>
</head>
<body>
<div class="container">
<header>
<div class="header-row">
<h1>Options Pricing Helper</h1>
<button class="header-btn" id="resetBtn">Reset</button>
<button class="theme-toggle" id="themeToggle" aria-label="Toggle dark mode">
<svg class="sun-icon" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<circle cx="12" cy="12" r="5"></circle>
<line x1="12" y1="1" x2="12" y2="3"></line>
<line x1="12" y1="21" x2="12" y2="23"></line>
<line x1="4.22" y1="4.22" x2="5.64" y2="5.64"></line>
<line x1="18.36" y1="18.36" x2="19.78" y2="19.78"></line>
<line x1="1" y1="12" x2="3" y2="12"></line>
<line x1="21" y1="12" x2="23" y2="12"></line>
<line x1="4.22" y1="19.78" x2="5.64" y2="18.36"></line>
<line x1="18.36" y1="5.64" x2="19.78" y2="4.22"></line>
</svg>
<svg class="moon-icon" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<path d="M21 12.79A9 9 0 1 1 11.21 3 7 7 0 0 0 21 12.79z"></path>
</svg>
</button>
</div>
<p class="instructions" id="instructions">
Drag sliders to shape your probability distribution.
</p>
</header>
<div class="mode-toggle">
<button id="customModeBtn" class="active">Custom Distribution</button>
<button id="normalModeBtn">Normal Distribution</button>
</div>
<div class="normal-inputs" id="normalInputs">
<div class="input-group">
<label>Mean (μ)</label>
<div class="input-row">
<input type="range" id="meanSlider" min="0" max="30" step="0.1" value="15">
<input type="number" id="meanInput" min="0" max="30" step="0.1" value="15">
</div>
</div>
<div class="input-group">
<label>Std Dev (σ)</label>
<div class="input-row">
<input type="range" id="stddevSlider" min="0.5" max="15" step="0.1" value="5">
<input type="number" id="stddevInput" min="0.5" max="15" step="0.1" value="5">
</div>
</div>
</div>
<div class="graph-container">
<canvas id="pdfCanvas" width="860" height="350"></canvas>
<div class="graph-hint" id="graphHint">Double-click to add or remove sliders</div>
</div>
<div class="results-container">
<div class="results-header">Scales Auto Trader</div>
<table class="price-table">
<thead>
<tr>
<th colspan="4">Over Bids</th>
<th></th>
<th rowspan="2">Over</th>
<th></th>
<th colspan="4">Over Offers</th>
<th rowspan="2" class="strike-header">Strike</th>
<th colspan="4">Under Bids</th>
<th></th>
<th rowspan="2">Under</th>
<th></th>
<th colspan="4">Under Offers</th>
</tr>
<tr>
<th></th>
<th></th>
<th>size</th>
<th>edge</th>
<th></th>
<th></th>
<th>edge</th>
<th>size</th>
<th></th>
<th></th>
<th></th>
<th></th>
<th>size</th>
<th>edge</th>
<th></th>
<th></th>
<th>edge</th>
<th>size</th>
<th></th>
<th></th>
</tr>
</thead>
<tbody id="priceTableBody">
</tbody>
</table>
<div class="expected-value">
<span class="label">Expected Settlement Value</span>
<span class="value" id="expectedValue">$15.00</span>
</div>
</div>
</div>
<script>
// ============================================================
// CONFIGURATION
// ============================================================
const DEFAULT_CONTROL_POINTS = [0, 10, 20, 30];
const STRIKES = [5, 10, 15, 20, 25];
// ============================================================
// NORMAL DISTRIBUTION FUNCTIONS
// ============================================================
// Standard normal PDF
function normalPDF(x) {
return Math.exp(-0.5 * x * x) / Math.sqrt(2 * Math.PI);
}
// Standard normal CDF (approximation)
function normalCDF(x) {
const a1 = 0.254829592;
const a2 = -0.284496736;
const a3 = 1.421413741;
const a4 = -1.453152027;
const a5 = 1.061405429;
const p = 0.3275911;
const sign = x < 0 ? -1 : 1;
x = Math.abs(x) / Math.sqrt(2);
const t = 1.0 / (1.0 + p * x);
const y = 1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * Math.exp(-x * x);
return 0.5 * (1.0 + sign * y);
}
// Price "Over K" option under normal distribution N(mu, sigma^2)
// E[max(0, C-K)] = sigma * phi(d) + (mu - K) * Phi(d)
// where d = (mu - K) / sigma
function priceOverNormal(K, mu, sigma) {
if (sigma < 0.01) {
// Degenerate case: all mass at mu
return Math.max(0, mu - K);
}
const d = (mu - K) / sigma;
return sigma * normalPDF(d) + (mu - K) * normalCDF(d);
}
// Price "Under K" option under normal distribution N(mu, sigma^2)
// E[max(0, K-C)] = sigma * phi(d) + (K - mu) * Phi(-d)
// where d = (mu - K) / sigma
function priceUnderNormal(K, mu, sigma) {
if (sigma < 0.01) {
// Degenerate case: all mass at mu
return Math.max(0, K - mu);
}
const d = (mu - K) / sigma;
return sigma * normalPDF(d) + (K - mu) * normalCDF(-d);
}
// Get PDF value at x for normal distribution
function getNormalPDFValue(x, mu, sigma) {
if (sigma < 0.01) return 0;
const z = (x - mu) / sigma;
return normalPDF(z) / sigma;
}
// ============================================================
// SPLINE ENGINE
// ============================================================
class SplineEngine {
constructor() {
this.segments = [];
}
// Compute natural cubic spline coefficients using tridiagonal solver
computeCoefficients(controlPoints, heights) {
const n = heights.length;
const x = controlPoints;
const y = heights;
// Step 1: Compute h[i] = x[i+1] - x[i]
const h = [];
for (let i = 0; i < n - 1; i++) {
h.push(x[i + 1] - x[i]);
}
// Step 2: Set up tridiagonal system for second derivatives
// Natural spline: M[0] = M[n-1] = 0
const alpha = [0];
for (let i = 1; i < n - 1; i++) {
alpha.push(
(3 / h[i]) * (y[i + 1] - y[i]) -
(3 / h[i - 1]) * (y[i] - y[i - 1])
);
}
// Tridiagonal solver
const l = [1];
const mu = [0];
const z = [0];
for (let i = 1; i < n - 1; i++) {
l.push(2 * (x[i + 1] - x[i - 1]) - h[i - 1] * mu[i - 1]);
mu.push(h[i] / l[i]);
z.push((alpha[i] - h[i - 1] * z[i - 1]) / l[i]);
}
l.push(1);
z.push(0);
// Back substitution for second derivatives (c values)
const c = new Array(n).fill(0);
for (let j = n - 2; j >= 0; j--) {
c[j] = z[j] - mu[j] * c[j + 1];
}
// Compute a, b, d coefficients for each segment
this.segments = [];
for (let i = 0; i < n - 1; i++) {
const a = y[i];
const b = (y[i + 1] - y[i]) / h[i] - h[i] * (c[i + 1] + 2 * c[i]) / 3;
const d = (c[i + 1] - c[i]) / (3 * h[i]);
this.segments.push({
a: a,
b: b,
c: c[i],
d: d,
x0: x[i],
x1: x[i + 1]
});
}
return this.segments;
}
// Evaluate spline at point x
evaluate(x) {
// Find segment
let segIdx = 0;
for (let i = 0; i < this.segments.length; i++) {
if (x >= this.segments[i].x0 && x <= this.segments[i].x1) {
segIdx = i;
break;
}
if (x > this.segments[i].x1) {
segIdx = i;
}
}
const seg = this.segments[segIdx];
const u = x - seg.x0;
return seg.a + seg.b * u + seg.c * u * u + seg.d * u * u * u;
}
// Find roots of cubic segment (where it crosses zero)
findRoots(segIdx) {
const seg = this.segments[segIdx];
const { a, b, c, d, x0, x1 } = seg;
const roots = [];
if (Math.abs(d) < 1e-12) {
// Quadratic or lower
if (Math.abs(c) < 1e-12) {
// Linear
if (Math.abs(b) > 1e-12) {
const r = -a / b;
if (r > 0 && r < x1 - x0) roots.push(r + x0);
}
} else {
// Quadratic: c*u^2 + b*u + a = 0
const disc = b * b - 4 * c * a;
if (disc >= 0) {
const sqrtDisc = Math.sqrt(disc);
const r1 = (-b + sqrtDisc) / (2 * c);
const r2 = (-b - sqrtDisc) / (2 * c);
if (r1 > 0 && r1 < x1 - x0) roots.push(r1 + x0);
if (r2 > 0 && r2 < x1 - x0 && Math.abs(r2 - r1) > 1e-12) roots.push(r2 + x0);
}
}
} else {
// Cubic: use Cardano's formula
// Normalize: u^3 + pu^2 + qu + r = 0 where coeffs are d, c, b, a
// Convert to depressed cubic t^3 + pt + q = 0
const A = c / d;
const B = b / d;
const C = a / d;
const p = B - A * A / 3;
const q = 2 * A * A * A / 27 - A * B / 3 + C;
const disc = q * q / 4 + p * p * p / 27;
if (disc > 1e-12) {
// One real root
const sqrtDisc = Math.sqrt(disc);
const u1 = Math.cbrt(-q / 2 + sqrtDisc);
const u2 = Math.cbrt(-q / 2 - sqrtDisc);
const t = u1 + u2;
const r = t - A / 3;
if (r > 0 && r < x1 - x0) roots.push(r + x0);
} else if (disc < -1e-12) {
// Three real roots (casus irreducibilis)
const m = 2 * Math.sqrt(-p / 3);
const theta = Math.acos(3 * q / (p * m)) / 3;
for (let k = 0; k < 3; k++) {
const t = m * Math.cos(theta - 2 * Math.PI * k / 3);
const r = t - A / 3;
if (r > 1e-10 && r < x1 - x0 - 1e-10) roots.push(r + x0);
}
} else {
// Repeated roots
const t1 = 3 * q / p;
const t2 = -t1 / 2;
const r1 = t1 - A / 3;
const r2 = t2 - A / 3;
if (r1 > 0 && r1 < x1 - x0) roots.push(r1 + x0);
if (Math.abs(r2 - r1) > 1e-12 && r2 > 0 && r2 < x1 - x0) roots.push(r2 + x0);
}
}
return roots.sort((a, b) => a - b);
}
}
// ============================================================
// PDF MANAGER
// ============================================================
class PDFManager {
constructor(splineEngine) {
this.spline = splineEngine;
this.controlPoints = DEFAULT_CONTROL_POINTS;
this.clampedRegions = [];
this.normalizationConstant = 1;
this._wasClamped = false;
}
buildPDF(controlPoints, heights) {
// Store control points for integration
this.controlPoints = controlPoints;
const segmentCount = controlPoints.length - 1;
// Build spline
this.spline.computeCoefficients(controlPoints, heights);
// Find clamped regions (where spline goes negative)
this.clampedRegions = [];
this._wasClamped = false;
for (let i = 0; i < segmentCount; i++) {
const seg = this.spline.segments[i];
const roots = this.spline.findRoots(i);
// Check if segment goes negative anywhere
const testPoints = [seg.x0, (seg.x0 + seg.x1) / 2, seg.x1];
roots.forEach(r => testPoints.push(r - 0.01, r + 0.01));
for (const x of testPoints) {
if (x >= seg.x0 && x <= seg.x1) {
const val = this.spline.evaluate(x);
if (val < -1e-10) {
this._wasClamped = true;
break;
}
}
}
}
// Compute normalization constant (integral of clamped spline)
this.normalizationConstant = this.integrateRaw(0, 30);
if (this.normalizationConstant < 1e-10) {
this.normalizationConstant = 1; // Avoid division by zero
}
return this;
}
wasClamped() {
return this._wasClamped;
}
// Integrate raw (clamped) spline from a to b
integrateRaw(a, b) {
let total = 0;
const segmentCount = this.controlPoints.length - 1;
for (let i = 0; i < segmentCount; i++) {
const seg = this.spline.segments[i];
// Determine overlap with [a, b]
const left = Math.max(a, seg.x0);
const right = Math.min(b, seg.x1);
if (left >= right) continue;
// Get roots within this segment for clamping
const roots = this.spline.findRoots(i);
const breakpoints = [left, ...roots.filter(r => r > left && r < right), right];
for (let j = 0; j < breakpoints.length - 1; j++) {
const subLeft = breakpoints[j];
const subRight = breakpoints[j + 1];
const midVal = this.spline.evaluate((subLeft + subRight) / 2);
if (midVal > 0) {
// Integrate this positive region
total += this.integrateSegment(seg, subLeft, subRight);
}
// Skip negative regions (clamped to zero)
}
}
return total;
}
// Integrate x * raw (clamped) spline from a to b
integrateXRaw(a, b) {
let total = 0;
const segmentCount = this.controlPoints.length - 1;
for (let i = 0; i < segmentCount; i++) {
const seg = this.spline.segments[i];
const left = Math.max(a, seg.x0);
const right = Math.min(b, seg.x1);
if (left >= right) continue;
const roots = this.spline.findRoots(i);
const breakpoints = [left, ...roots.filter(r => r > left && r < right), right];
for (let j = 0; j < breakpoints.length - 1; j++) {
const subLeft = breakpoints[j];
const subRight = breakpoints[j + 1];
const midVal = this.spline.evaluate((subLeft + subRight) / 2);
if (midVal > 0) {
total += this.integrateXSegment(seg, subLeft, subRight);
}
}
}
return total;
}
// Integral of S(x) = a + b*u + c*u^2 + d*u^3 from x=left to x=right