Implied Volatility Calculation

Calculate Implied Volatility

Calculation Results

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Implied Volatility (IV) is the market's forecast of a likely movement in an asset's price. It is derived by using an options pricing model (like Black-Scholes) and solving for volatility given the market price of the option. This calculator uses a numerical method (like the Newton-Raphson method) to find the IV that makes the Black-Scholes theoretical price match the observed market option price.

Key Assumptions: Black-Scholes model, constant risk-free rate and dividend yield, no transaction costs, options are European style.

What is Implied Volatility?

Implied Volatility (IV) is a crucial concept in options trading, representing the market's expectation of future price fluctuations of an underlying asset. Unlike historical volatility, which measures past price movements, implied volatility is forward-looking. It is embedded within the current market price of an option. In essence, it's the volatility derived from the option's price itself, rather than from statistical analysis of historical price data. High implied volatility suggests traders expect significant price swings, while low IV indicates expectations of stability.

Who should use it? Implied volatility is essential for options traders, portfolio managers, risk managers, and financial analysts. Traders use it to assess whether an option is relatively "expensive" or "cheap" and to gauge market sentiment. Portfolio managers may use IV to hedge their positions or to understand potential downside risks. Financial analysts use it in risk modeling and derivative valuation.

Common misconceptions One common misconception is that implied volatility predicts the direction of the asset's price movement; it only predicts the magnitude of movement. Another is confusing implied volatility with historical volatility; IV is forward-looking and market-driven, while historical volatility is backward-looking and statistically calculated. Some also mistakenly believe a high IV always means an option is overpriced; it simply means the market expects larger moves, which can be justified if those moves materialize. Understanding implied volatility is key to grasping options pricing dynamics.

Implied Volatility Calculation: Formula and Mathematical Explanation

Calculating implied volatility isn't as straightforward as plugging numbers into a single formula. Instead, it involves an iterative process using an options pricing model, most commonly the Black-Scholes-Merton (BSM) model. The core idea is to work backward: you know the market price of the option, and you want to find the volatility that, when input into the BSM model, yields that specific market price.

The Black-Scholes formulas for call (C) and put (P) options are:

C = S₀ * N(d₁) - K * e^(-rT) * N(d₂)

P = K * e^(-rT) * N(-d₂) - S₀ * N(-d₁)

Where:

• S₀: Current price of the underlying asset
• K: Strike price of the option
• r: Risk-free annual interest rate
• T: Time to expiration in years
• σ (Sigma): Volatility of the underlying asset's return (This is what we're solving for!)
• N(x): Cumulative standard normal distribution function
• e: The base of the natural logarithm (approx. 2.71828)
• d₁ = [ln(S₀/K) + (r + σ²/2)T] / (σ√T)
• d₂ = d₁ - σ√T

Since there is no algebraic solution for σ (volatility) in these equations, we use numerical methods. The most common is the Newton-Raphson method. This involves:

1. Making an initial guess for volatility (σ₀).
2. Calculating the theoretical option price using the BSM model with σ₀.
3. Comparing this theoretical price to the actual market option price.
4. Calculating the difference (error) and the derivative of the BSM price with respect to volatility (Vega).
5. Adjusting the volatility guess using the formula: σ_next = σ_current - (BSM_Price(σ_current) - Market_Price) / Vega(σ_current)
6. Repeating steps 2-5 until the calculated price is sufficiently close to the market price, or a maximum number of iterations is reached.

The resulting σ is the implied volatility.

Variable Explanations Table

Variable	Meaning	Unit	Typical Range
Option Price (C or P)	Market price of the option contract	Currency Unit (e.g., USD)	> 0
S₀	Current price of the underlying asset	Currency Unit	> 0
K	Strike price of the option	Currency Unit	> 0
T	Time to expiration	Years	(0, 1] (Typically less than 1 year)
r	Risk-free interest rate	Decimal (e.g., 0.05 for 5%)	0.01 to 0.10 (Varies with market conditions)
q (Dividend Yield)	Continuous dividend yield of the underlying asset	Decimal (e.g., 0.01 for 1%)	0 to 0.05 (Varies significantly)
σ (Implied Volatility)	Expected future volatility of the underlying asset's returns	Decimal (e.g., 0.20 for 20%)	0.05 to 1.00+ (Highly variable)

Practical Examples (Real-World Use Cases)

Implied volatility calculations are fundamental to options trading. Here are two examples:

Example 1: Calculating IV for a Call Option

An investor is looking at Apple (AAPL) call options. The current market price for an AAPL call option with a strike price of $180 expiring in 3 months is $5.50. The current AAPL stock price is $175. The risk-free rate is 4.5% (0.045), and AAPL has an expected dividend yield of 0.5% (0.005) over the next three months.

Inputs:

• Option Price: $5.50
• Strike Price (K): $180
• Underlying Price (S₀): $175
• Time to Expiration (T): 0.25 years (3 months)
• Risk-Free Rate (r): 4.5% (0.045)
• Dividend Yield (q): 0.5% (0.005)

Using the implied volatility calculator, after inputting these values and running the iterative process, we might find the implied volatility to be approximately 28%.

Interpretation: The market is pricing this option with an expectation that AAPL's price could move significantly enough to make this $180 strike call profitable within the next three months. A trader might compare this 28% IV to historical volatility or IV of other options to decide if it represents good value.

Example 2: Calculating IV for a Put Option (High Uncertainty Event)

Consider a biotechnology company's stock, which is trading at $50. A major FDA drug approval decision is expected in 45 days. A put option with a strike price of $45 expiring in 60 days is trading for $3.00. The risk-free rate is 4.0% (0.040), and there are no expected dividends.

Inputs:

• Option Price: $3.00
• Strike Price (K): $45
• Underlying Price (S₀): $50
• Time to Expiration (T): 60/365 ≈ 0.164 years
• Risk-Free Rate (r): 4.0% (0.040)
• Dividend Yield (q): 0% (0.000)

Inputting these values into the calculator reveals a high implied volatility of, say, 75%.

Interpretation: The market is pricing in a substantial risk that the drug approval might fail, causing the stock price to drop sharply. The high implied volatility reflects the significant uncertainty and potential for large price swings around the upcoming event. Traders often see IV spikes before such events.

How to Use This Implied Volatility Calculator

Our Implied Volatility Calculator simplifies the process of determining the market's volatility expectations for an underlying asset. Follow these steps to get started:

1. Gather Necessary Data: You'll need the current market price of the specific option contract (call or put), its strike price, the current price of the underlying asset (stock, ETF, index), the time remaining until the option expires (in years), the prevailing risk-free interest rate, and optionally, the underlying asset's dividend yield.
2. Input Option Details: Enter the option's market price, the strike price, and the underlying asset's price into the respective fields. Ensure you use consistent currency units.
3. Input Time & Rates: Accurately input the time to expiration in years (e.g., 3 months is 0.25 years, 6 months is 0.5 years). Enter the risk-free interest rate and dividend yield as percentages (e.g., 5% should be entered as 5.0).
4. Calculate: Click the "Calculate" button. The calculator will use a numerical method to solve for the implied volatility based on the Black-Scholes model.
5. Review Results: The primary result displayed is the calculated Implied Volatility (IV), expressed as a percentage. You'll also see the inputs you used and the theoretical option price generated by the Black-Scholes model using the calculated IV.
6. Interpret the IV: A higher IV suggests greater expected price movement (up or down) and typically leads to higher option premiums. A lower IV suggests less expected movement, often resulting in lower premiums. Compare the IV to historical volatility or the IV of related options to assess if the option is relatively cheap or expensive.
7. Copy or Reset: Use the "Copy Results" button to easily share or record the findings. Click "Reset" to clear the fields and start a new calculation.

Decision-making guidance: Implied volatility is a critical component of an option's price. Traders use it to:

• Gauge Market Sentiment: Spikes in IV often precede major news events or periods of uncertainty.
• Assess Option Value: High IV relative to historical volatility might suggest an option is overpriced, while low IV might indicate an opportunity if you expect volatility to increase.
• Stratify Risk: Understanding IV helps in setting realistic profit targets and stop-loss levels.

Key Factors That Affect Implied Volatility Results

Implied volatility isn't static; it's influenced by a dynamic interplay of market forces and option characteristics. Understanding these factors is crucial for interpreting IV accurately.

• Supply and Demand for Options: Like any market price, the option's price is determined by buyers and sellers. If more traders want to buy options (speculating on price moves) than sell them, demand increases, pushing option prices up and thus increasing implied volatility. This is particularly evident before earnings announcements or major economic events.
• Time to Expiration (Theta): Options with longer times to expiration generally have higher implied volatilities, all else being equal. This is partly because there's more time for significant price movements to occur. As expiration approaches, time value decays (Theta), and IV tends to decrease unless specific event risk remains.
• Implied vs. Historical Volatility: IV reflects future expectations, while historical volatility (HV) measures past price activity. When IV is significantly higher than HV, it suggests the market anticipates greater future movement than what has occurred recently. Conversely, IV lower than HV might indicate market complacency or a belief that recent volatility was an anomaly.
• Interest Rates (Cost of Carry): Higher interest rates increase the cost of carrying a position, particularly affecting the pricing of futures and options. For call options, higher rates slightly increase the theoretical price (and thus can indirectly affect IV if other inputs are held constant), while for put options, they decrease the theoretical price.
• Dividends: Expected dividends reduce the price of the underlying stock on the ex-dividend date. This directly impacts option pricing models. For call options, expected dividends decrease the theoretical price (potentially lowering IV), while for put options, they increase the theoretical price (potentially raising IV) because the holder of the put benefits from a lower underlying price post-dividend.
• Market Sentiment and Uncertainty: Broader market conditions significantly influence IV. During periods of economic uncertainty, geopolitical tension, or sector-specific news, overall market volatility expectations rise, leading to higher IV across many assets. Conversely, stable markets tend to exhibit lower IV.
• Moneyness (Option Strike vs. Underlying Price): Out-of-the-money (OTM) options, especially those with longer expirations, often carry higher implied volatilities than at-the-money (ATM) or in-the-money (ITM) options. This is known as the "volatility skew" or "smile," reflecting the market's higher demand for OTM options as insurance against extreme price moves.

Frequently Asked Questions (FAQ)

What's the difference between implied volatility and historical volatility?

Implied volatility (IV) is forward-looking, derived from an option's market price and representing the market's expectation of future volatility. Historical volatility (HV) is backward-looking, calculated from the actual past price movements of the underlying asset.

Can implied volatility predict the direction of the underlying asset's price?

No, implied volatility only measures the expected magnitude of price movement, not the direction. High IV means large moves are expected, but the asset could move up or down.

Does a higher implied volatility always mean an option is overpriced?

Not necessarily. A higher IV indicates the market expects larger price swings, which might be justified by upcoming events (like earnings or news). An option might be "expensive" relative to historical volatility, but its IV could be appropriate given future expectations.

What does it mean if implied volatility is higher for puts than for calls?

This often occurs in equity markets and suggests a greater market demand for downside protection (puts), indicating increased fear or hedging activity among traders.

How long does it take for the calculator to compute implied volatility?

Our calculator uses an efficient numerical method, typically completing the calculation in milliseconds after you click "Calculate."

Can I use this calculator for options with less than a year to expiration?

Yes, absolutely. Simply ensure you input the time to expiration accurately in years (e.g., 3 months = 0.25 years).

What is the 'Risk-Free Rate' in the context of implied volatility?

The risk-free rate represents the theoretical return of an investment with zero risk, typically approximated by government debt yields (like U.S. Treasury bills) with a maturity matching the option's expiration. It accounts for the time value of money.

Why is dividend yield an input for implied volatility?

Dividends affect the expected future price of the underlying asset. Incorporating the dividend yield into the pricing model provides a more accurate calculation of the option's theoretical value, which is necessary for deriving a precise implied volatility.

Option Price Sensitivity to Volatility

Option price changes based on varying implied volatility, holding other factors constant.

Key Inputs and Calculated Black-Scholes Price

Input Parameter	Value
Option Price (Market)	--
Strike Price (K)	--
Underlying Price (S₀)	--
Time to Expiration (T)	-- years
Risk-Free Rate (r)	-- %
Dividend Yield (q)	-- %
Calculated Black-Scholes Price	--

Related Tools and Internal Resources

• Implied Volatility Calculator

  Our primary tool for estimating future volatility expectations based on option prices.

• Black-Scholes Model Explained

  Deep dive into the mathematics behind options pricing, including the Greeks.

• Popular Options Trading Strategies

  Learn about strategies like straddles, strangles, and spreads, often employed based on volatility expectations.

• Historical Volatility Calculator

  Analyze past price movements to understand an asset's historical trading range.

• Navigating Earnings Season with Options

  Understand how earnings reports impact option prices and implied volatility.

• Understanding the Option Greeks

  Learn about Delta, Gamma, Theta, Vega, and Rho, and how they relate to risk and pricing.

var chartInstance = null; function nCr(n, r) { if (r n) return 0; if (r === 0 || r === n) return 1; if (r > n / 2) r = n - r; var res = 1; for (var i = 1; i <= r; i++) { res = res * (n - i + 1) / i; } return res; } function gaussianProbability(x) { return 0.5 * (1 + erf(x / Math.sqrt(2))); } function erf(x) { // Abramowitz and Stegun approximation var a1 = 0.254829592; var a2 = -0.284496736; var a3 = 1.421413741; var a4 = -1.453152027; var a5 = 1.061405429; var p = 0.3275911; var sign = 1; if (x < 0) { sign = -1; x = -x; } var t = 1.0 / (1.0 + p * x); var y = 1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * Math.exp(-x * x); return sign * y; } function blackScholes(S, K, T, r, sigma, q, type) { var d1 = (Math.log(S / K) + (r - q + 0.5 * sigma * sigma) * T) / (sigma * Math.sqrt(T)); var d2 = d1 - sigma * Math.sqrt(T); if (type === 'call') { return S * Math.exp(-q * T) * gaussianProbability(d1) - K * Math.exp(-r * T) * gaussianProbability(d2); } else if (type === 'put') { return K * Math.exp(-r * T) * gaussianProbability(-d2) - S * Math.exp(-q * T) * gaussianProbability(-d1); } return NaN; } function blackScholesVega(S, K, T, r, sigma, q) { var d1 = (Math.log(S / K) + (r - q + 0.5 * sigma * sigma) * T) / (sigma * Math.sqrt(T)); return S * Math.exp(-q * T) * gaussianProbability(d1) * Math.sqrt(T); } function impliedVolatility(marketPrice, S, K, T, r, q, type, maxIterations = 100, tolerance = 1e-6) { var sigma = 0.5; // Initial guess for volatility var price = blackScholes(S, K, T, r, sigma, q, type); var vega = blackScholesVega(S, K, T, r, sigma, q); for (var i = 0; i < maxIterations; i++) { price = blackScholes(S, K, T, r, sigma, q, type); var diff = price - marketPrice; if (Math.abs(diff) < tolerance) { return sigma * 100; // Return as percentage } vega = blackScholesVega(S, K, T, r, sigma, q); if (vega === 0) { // Avoid division by zero // Try adjusting sigma slightly or return current best guess sigma += 0.01; continue; } sigma = sigma - diff / vega; // Ensure sigma stays within reasonable bounds if (sigma 2.0) { // Typical vol range up to 200% // Adjust guess or signal failure // For simplicity, we might return the last valid sigma or a default max error value return -1; // Indicate an issue or inability to converge } } // If loop finishes without convergence return sigma * 100; // Return the best estimate found } function calculateImpliedVolatility() { var optionPrice = parseFloat(document.getElementById("optionPrice").value); var strikePrice = parseFloat(document.getElementById("strikePrice").value); var underlyingPrice = parseFloat(document.getElementById("underlyingPrice").value); var timeToExpiration = parseFloat(document.getElementById("timeToExpiration").value); var riskFreeRate = parseFloat(document.getElementById("riskFreeRate").value) / 100.0; // Convert % to decimal var dividendYield = parseFloat(document.getElementById("dividendYield").value) / 100.0; // Convert % to decimal var errors = false; var errorMessages = document.querySelectorAll('.error-message'); errorMessages.forEach(function(el) { el.classList.remove('visible'); }); if (isNaN(optionPrice) || optionPrice <= 0) { document.getElementById("optionPriceError").innerText = "Please enter a valid positive option price."; document.getElementById("optionPriceError").classList.add('visible'); errors = true; } if (isNaN(strikePrice) || strikePrice <= 0) { document.getElementById("strikePriceError").innerText = "Please enter a valid positive strike price."; document.getElementById("strikePriceError").classList.add('visible'); errors = true; } if (isNaN(underlyingPrice) || underlyingPrice <= 0) { document.getElementById("underlyingPriceError").innerText = "Please enter a valid positive underlying asset price."; document.getElementById("underlyingPriceError").classList.add('visible'); errors = true; } if (isNaN(timeToExpiration) || timeToExpiration 10) { // Max 10 years, adjust as needed document.getElementById("timeToExpirationError").innerText = "Please enter time to expiration between 0 and 10 years."; document.getElementById("timeToExpirationError").classList.add('visible'); errors = true; } if (isNaN(riskFreeRate) || riskFreeRate < 0) { document.getElementById("riskFreeRateError").innerText = "Please enter a valid non-negative risk-free rate."; document.getElementById("riskFreeRateError").classList.add('visible'); errors = true; } if (isNaN(dividendYield) || dividendYield K, put if S < K, user needs to adjust logic if needed) // A more robust calculator might ask the user for option type. var optionType = 'call'; // Default assumption if (underlyingPrice < strikePrice) { optionType = 'put'; } else if (underlyingPrice === strikePrice) { // Ambiguous, let's default to call for calculation purposes or prompt user optionType = 'call'; // Could also be put depending on context } // NOTE: A real-world scenario would likely need explicit user input for option type. // For this calculator, we'll try to infer, but it's a simplification. var calculatedBSPrice = blackScholes(underlyingPrice, strikePrice, timeToExpiration, riskFreeRate, 0.5, dividendYield, optionType); // Use a guess for BS price for comparison var iv = impliedVolatility(optionPrice, underlyingPrice, strikePrice, timeToExpiration, riskFreeRate, dividendYield, optionType); var resultText = "--"; if (iv !== -1 && !isNaN(iv)) { resultText = iv.toFixed(2) + "%"; } else { resultText = "N/A (Convergence Error)"; } document.getElementById("primaryResult").innerText = resultText; document.getElementById("inputOptionPrice").querySelector('span').innerText = optionPrice.toFixed(2); document.getElementById("inputStrikePrice").querySelector('span').innerText = strikePrice.toFixed(2); document.getElementById("inputUnderlyingPrice").querySelector('span').innerText = underlyingPrice.toFixed(2); document.getElementById("inputTimeToExpiration").querySelector('span').innerText = timeToExpiration.toFixed(2) + " years"; document.getElementById("inputRiskFreeRate").querySelector('span').innerText = (riskFreeRate * 100).toFixed(2) + "%"; document.getElementById("inputDividendYield").querySelector('span').innerText = (dividendYield * 100).toFixed(2) + "%"; var bsPriceDisplay = calculatedBSPrice !== null && !isNaN(calculatedBSPrice) ? calculatedBSPrice.toFixed(2) : "--"; document.getElementById("blackScholesPrice").querySelector('span').innerText = bsPriceDisplay; updateTableValues(optionPrice, strikePrice, underlyingPrice, timeToExpiration, riskFreeRate * 100, dividendYield * 100, bsPriceDisplay); // Update chart updateChart(optionPrice, strikePrice, underlyingPrice, timeToExpiration, riskFreeRate, dividendYield, optionType); } function updateTableValues(optionPrice, strikePrice, underlyingPrice, timeToExpiration, riskFreeRate, dividendYield, bsPrice) { document.getElementById("tableOptionPrice").innerText = typeof optionPrice === 'number' ? optionPrice.toFixed(2) : optionPrice; document.getElementById("tableStrikePrice").innerText = typeof strikePrice === 'number' ? strikePrice.toFixed(2) : strikePrice; document.getElementById("tableUnderlyingPrice").innerText = typeof underlyingPrice === 'number' ? underlyingPrice.toFixed(2) : underlyingPrice; document.getElementById("tableTimeToExpiration").innerText = typeof timeToExpiration === 'number' ? timeToExpiration.toFixed(2) + " years" : timeToExpiration; document.getElementById("tableRiskFreeRate").innerText = typeof riskFreeRate === 'number' ? riskFreeRate.toFixed(2) + " %" : riskFreeRate; document.getElementById("tableDividendYield").innerText = typeof dividendYield === 'number' ? dividendYield.toFixed(2) + " %" : dividendYield; document.getElementById("tableBlackScholesPrice").innerText = bsPrice; } function copyResults() { var primaryResult = document.getElementById("primaryResult").innerText; var inputs = document.querySelectorAll('.intermediate-results span'); var formulaExplanation = document.querySelector('.formula-explanation').innerText; var keyAssumptions = document.querySelector('.key-assumption').innerText; var resultsText = "Implied Volatility Calculation Results:\n\n"; resultsText += "Primary Result (Implied Volatility): " + primaryResult + "\n\n"; resultsText += "Inputs Used:\n"; inputs.forEach(function(span) { var label = span.closest('div').querySelector('span').previousElementSibling.innerText; resultsText += "- " + label + ": " + span.innerText + "\n"; }); resultsText += "\n"; resultsText += "Formula: " + formulaExplanation + "\n\n"; resultsText += "Key Assumptions: " + keyAssumptions + "\n"; navigator.clipboard.writeText(resultsText).then(function() { alert("Results copied to clipboard!"); }).catch(function(err) { console.error('Failed to copy results: ', err); alert("Failed to copy results. Please copy manually."); }); } function resetCalculator() { document.getElementById("optionPrice").value = "5.50"; document.getElementById("strikePrice").value = "180"; document.getElementById("underlyingPrice").value = "175"; document.getElementById("timeToExpiration").value = "0.25"; document.getElementById("riskFreeRate").value = "4.5"; document.getElementById("dividendYield").value = "0.5"; // Clear error messages var errorMessages = document.querySelectorAll('.error-message'); errorMessages.forEach(function(el) { el.classList.remove('visible'); }); calculateImpliedVolatility(); // Recalculate with defaults } function toggleFaq(element) { var answer = element.nextElementSibling; if (answer.style.display === "block") { answer.style.display = "none"; element.querySelector('.faq-item .question::before').innerText = '+'; } else { answer.style.display = "block"; element.querySelector('.faq-item .question::before').innerText = '-'; } } function updateChart(marketPrice, strikePrice, underlyingPrice, timeToExpiration, riskFreeRate, dividendYield, optionType) { var canvas = document.getElementById('volatilityChart'); var ctx = canvas.getContext('2d'); // Clear previous chart instance if it exists if (chartInstance) { chartInstance.destroy(); } var volatilities = [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]; // Percentages var prices = []; var actualOptionPrice = parseFloat(document.getElementById("optionPrice").value); // Get the current input price if (isNaN(actualOptionPrice) || actualOptionPrice <= 0) { // Don't draw chart if essential input is missing/invalid return; } volatilities.forEach(function(volPercent) { var sigma = volPercent / 100.0; var calculatedPrice = blackScholes(underlyingPrice, strikePrice, timeToExpiration, riskFreeRate, sigma, dividendYield, optionType); if (calculatedPrice !== null && !isNaN(calculatedPrice)) { prices.push(calculatedPrice); } else { prices.push(null); // Placeholder for invalid calculations } }); // Filter out null values for plotting var validPrices = []; var validVols = []; for (var i = 0; i < prices.length; i++) { if (prices[i] !== null) { validPrices.push(prices[i]); validVols.push(volatilities[i]); } } if (validVols.length === 0) return; // No data to plot // Add a vertical line for the current market price var marketPricePoint = [actualOptionPrice]; // Single point for reference var marketVolPoint = []; // Find where the market price falls on the curve (approximate) for (var i = 0; i < validPrices.length - 1; i++) { if ((validPrices[i] <= actualOptionPrice && actualOptionPrice <= validPrices[i+1]) || (validPrices[i+1] <= actualOptionPrice && actualOptionPrice <= validPrices[i])) { // Interpolate volatility for the market price var volInterpolated = validVols[i] + (actualOptionPrice - validPrices[i]) * (validVols[i+1] - validVols[i]) / (validPrices[i+1] - validPrices[i]); marketVolPoint.push(volInterpolated); break; } } // If market price is outside the calculated range, place point at boundaries if (marketVolPoint.length === 0) { if (actualOptionPrice validPrices[validPrices.length - 1]) marketVolPoint.push(validVols[validVols.length - 1]); } // Create the chart chartInstance = new Chart(ctx, { type: 'line', data: { labels: validVols.map(function(v) { return v + '%'; }), // X-axis labels: Volatility % datasets: [{ label: 'Theoretical Option Price', data: validPrices, borderColor: 'rgb(0, 74, 153)', // Primary color backgroundColor: 'rgba(0, 74, 153, 0.1)', fill: true, tension: 0.1 }] }, options: { responsive: true, maintainAspectRatio: false, scales: { x: { title: { display: true, text: 'Implied Volatility (%)' } }, y: { title: { display: true, text: 'Option Price' }, beginAtZero: true } }, plugins: { tooltip: { callbacks: { label: function(context) { var label = context.dataset.label || ''; if (label) { label += ': '; } if (context.parsed.y !== null) { label += context.parsed.y.toFixed(2); } return label; } } } } } }); } // Initial chart setup and calculator run on load document.addEventListener('DOMContentLoaded', function() { // Set default values and trigger calculation resetCalculator(); // Initial chart render with defaults var canvas = document.getElementById('volatilityChart'); var ctx = canvas.getContext('2d'); ctx.clearRect(0, 0, canvas.width, canvas.height); // Clear canvas initially // Trigger initial chart update after potential default calculations var defaultOptionPrice = parseFloat(document.getElementById("optionPrice").value); var defaultStrikePrice = parseFloat(document.getElementById("strikePrice").value); var defaultUnderlyingPrice = parseFloat(document.getElementById("underlyingPrice").value); var defaultTimeToExpiration = parseFloat(document.getElementById("timeToExpiration").value); var defaultRiskFreeRate = parseFloat(document.getElementById("riskFreeRate").value) / 100.0; var defaultDividendYield = parseFloat(document.getElementById("dividendYield").value) / 100.0; var defaultOptionType = 'call'; // Placeholder for default if (defaultUnderlyingPrice < defaultStrikePrice) defaultOptionType = 'put'; updateChart(defaultOptionPrice, defaultStrikePrice, defaultUnderlyingPrice, defaultTimeToExpiration, defaultRiskFreeRate, defaultDividendYield, defaultOptionType); }); // Helper function for FAQ toggling function toggleFaq(element) { var answer = element.nextElementSibling; if (answer.style.display === "block") { answer.style.display = "none"; } else { answer.style.display = "block"; } }