Calculate Options Price

Black-Scholes Options Price Calculator

// Cumulative Standard Normal Distribution Function (CNDF) function CND(x) { var a1 = 0.31938153; var a2 = -0.356563782; var a3 = 1.781477937; var a4 = -1.821255978; var a5 = 1.330274429; var L = Math.abs(x); var K = 1.0 / (1.0 + 0.2316419 * L); var w = 1.0 – (((((a5 * K + a4) * K + a3) * K + a2) * K + a1) * K) * Math.exp(-L * L / 2.0) / Math.sqrt(2 * Math.PI); if (x < 0) { w = 1.0 – w; } return w; } function calculateOptionPrice() { var stockPrice = parseFloat(document.getElementById("stockPrice").value); var strikePrice = parseFloat(document.getElementById("strikePrice").value); var timeToExpiration = parseFloat(document.getElementById("timeToExpiration").value); var riskFreeRate = parseFloat(document.getElementById("riskFreeRate").value) / 100; // Convert percentage to decimal var volatility = parseFloat(document.getElementById("volatility").value) / 100; // Convert percentage to decimal var optionType = document.querySelector('input[name="optionType"]:checked').value; var resultDiv = document.getElementById("result"); // Input validation if (isNaN(stockPrice) || isNaN(strikePrice) || isNaN(timeToExpiration) || isNaN(riskFreeRate) || isNaN(volatility) || stockPrice <= 0 || strikePrice <= 0 || timeToExpiration <= 0 || volatility <= 0) { resultDiv.innerHTML = "Please enter valid positive numbers for all fields."; return; } var d1, d2; var optionPrice; // Calculate d1 and d2 d1 = (Math.log(stockPrice / strikePrice) + (riskFreeRate + Math.pow(volatility, 2) / 2) * timeToExpiration) / (volatility * Math.sqrt(timeToExpiration)); d2 = d1 – volatility * Math.sqrt(timeToExpiration); if (optionType === "call") { // Call option price optionPrice = (stockPrice * CND(d1)) – (strikePrice * Math.exp(-riskFreeRate * timeToExpiration) * CND(d2)); resultDiv.innerHTML = "Estimated Call Option Price: $" + optionPrice.toFixed(2) + ""; } else { // Put option price optionPrice = (strikePrice * Math.exp(-riskFreeRate * timeToExpiration) * CND(-d2)) – (stockPrice * CND(-d1)); resultDiv.innerHTML = "Estimated Put Option Price: $" + optionPrice.toFixed(2) + ""; } }

Understanding Options Pricing with the Black-Scholes Model

Options are financial derivatives that give the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price (the strike price) on or before a certain date (the expiration date). Understanding how options are priced is crucial for traders and investors.

The Black-Scholes Model

The Black-Scholes model, developed by Fischer Black, Myron Scholes, and Robert Merton, is one of the most widely used models for pricing European-style options. It provides a theoretical estimate of the price of an option by taking into account several key variables. While it has limitations (e.g., assuming constant volatility and no dividends), it remains a fundamental tool in financial markets.

Key Inputs for Options Pricing:

• Current Stock Price (Spot Price): This is the current market price of the underlying asset (e.g., a stock). A higher stock price generally increases the value of a call option and decreases the value of a put option.
• Option Strike Price: This is the predetermined price at which the option holder can buy (for a call) or sell (for a put) the underlying asset. For call options, a lower strike price means a higher option value; for put options, a higher strike price means a higher option value.
• Time to Expiration (Years): This is the remaining time until the option contract expires, expressed in years. Generally, the longer the time to expiration, the more valuable an option is, as there's more time for the underlying asset's price to move favorably.
• Risk-Free Rate (Annual %): This represents the theoretical rate of return of an investment with zero risk, typically approximated by the yield on short-term government bonds. A higher risk-free rate generally increases call option prices and decreases put option prices.
• Volatility (Annual %): This measures the expected fluctuation of the underlying asset's price over a given period. Higher volatility means a greater chance of significant price movements, which increases the value of both call and put options.
• Option Type (Call/Put):
  • Call Option: Gives the holder the right to buy the underlying asset. Investors buy calls when they expect the price to rise.
  • Put Option: Gives the holder the right to sell the underlying asset. Investors buy puts when they expect the price to fall.

How the Calculator Works:

Our calculator uses the Black-Scholes formula to estimate the theoretical price of a European-style call or put option. By inputting the current stock price, strike price, time to expiration, risk-free rate, and volatility, it computes the fair value of the option based on these parameters.

Example Calculation:

Let's consider an example:

• Current Stock Price: $100
• Option Strike Price: $100
• Time to Expiration: 0.5 years (6 months)
• Risk-Free Rate: 2% (0.02)
• Volatility: 20% (0.20)
• Option Type: Call

Using these inputs in the Black-Scholes model, the calculator would determine the theoretical price for this call option. For these specific values, the estimated call option price would be approximately $6.88.

If we change the option type to a Put with the same parameters, the estimated put option price would be approximately $4.99.

While the Black-Scholes model is a powerful tool, remember that actual market prices can deviate due to factors not captured by the model, such as dividends, American-style exercise features, and market sentiment.