Options contracts are powerful financial instruments that give the holder 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.
This calculator uses a simplified version of the Black-Scholes model, a widely recognized mathematical model for pricing European-style options. The Black-Scholes model considers several key factors to estimate the theoretical value of an option contract.
Key Factors in Options Pricing:
Underlying Asset Price: The current market price of the asset (e.g., stock, index, commodity) on which the option is based. Higher underlying prices generally increase call option values and decrease put option values.
Strike Price: The predetermined price at which the underlying asset can be bought (for a call option) or sold (for a put option). The relationship between the underlying price and the strike price determines if an option is in-the-money, at-the-money, or out-of-the-money.
Time to Expiration: The remaining time until the option contract expires. Options are wasting assets; as time passes, their value erodes (time decay). Longer times to expiration generally increase both call and put option values, as there's more time for the underlying asset's price to move favorably.
Annual Volatility: A measure of how much the underlying asset's price is expected to fluctuate over a given period. Higher volatility generally increases both call and put option values because there's a greater chance of significant price movements that could make the option profitable.
Annual Risk-Free Rate: The theoretical rate of return of an investment with zero risk, typically represented by the yield on government bonds. This rate affects the present value of the strike price and the cost of carrying the underlying asset.
By inputting these variables, the calculator will provide an estimated theoretical price for both a European Call Option and a European Put Option based on the Black-Scholes framework.
function calculateOptionPrice() {
// Helper function for cumulative standard normal distribution (N(x))
function N(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_val = 1.0 / (1.0 + 0.2316419 * L);
var W = 1.0 – 1.0 / Math.sqrt(2 * Math.PI) * Math.exp(-L * L / 2) * (a1 * K_val + a2 * Math.pow(K_val, 2) + a3 * Math.pow(K_val, 3) + a4 * Math.pow(K_val, 4) + a5 * Math.pow(K_val, 5));
if (x < 0) {
W = 1.0 – W;
}
return W;
}
var S = parseFloat(document.getElementById('underlyingPrice').value);
var K = parseFloat(document.getElementById('strikePrice').value);
var T = parseFloat(document.getElementById('timeToExpiration').value);
var sigma = parseFloat(document.getElementById('annualVolatility').value) / 100; // Convert percentage to decimal
var r = parseFloat(document.getElementById('riskFreeRate').value) / 100; // Convert percentage to decimal
var resultDiv = document.getElementById('result');
resultDiv.innerHTML = ''; // Clear previous results
// Input validation
if (isNaN(S) || isNaN(K) || isNaN(T) || isNaN(sigma) || isNaN(r)) {
resultDiv.innerHTML = 'Please enter valid numbers for all fields.';
return;
}
if (S <= 0 || K <= 0 || T <= 0 || sigma <= 0) {
resultDiv.innerHTML = 'Underlying Asset Price, Strike Price, Time to Expiration, and Annual Volatility must be positive.';
return;
}
if (r < 0) {
resultDiv.innerHTML = 'Annual Risk-Free Rate cannot be negative.';
return;
}
// Black-Scholes calculation
var d1 = (Math.log(S / K) + (r + Math.pow(sigma, 2) / 2) * T) / (sigma * Math.sqrt(T));
var d2 = d1 – sigma * Math.sqrt(T);
// Call Option Price
var callPrice = S * N(d1) – K * Math.exp(-r * T) * N(d2);
// Put Option Price
var putPrice = K * Math.exp(-r * T) * N(-d2) – S * N(-d1);
resultDiv.innerHTML =
'