Calculate stock option values using Black-Scholes model with current price, strike price, volatility, time to expiration, and risk-free rate.
The Black-Scholes model prices an option from five inputs: the current stock price, the strike price, time to expiration, volatility, and the risk-free rate. This tool takes those five numbers and returns the theoretical fair value of the call and the put. The surprise is how much of an option's value is time value: an at-the-money option with zero intrinsic value is still worth real money because it captures the upside of any future move while risking only the premium. The result is a model price under the formula's assumptions, not a market quote.
A concrete input and expected output from the current implementation.
Input
Stock price 100; strike 100; volatility 20% per year; time to expiration 1 year; risk-free rate 3%
Expected output
Call value: about $9.41. Put value: about $6.46.
The stock equals the strike, so the option has no intrinsic value; the whole $9.41 is time value. For these inputs d1 = 0.25 and d2 = 0.05, so the call is S*N(d1) - K*e^(-rT)*N(d2), which comes to 59.87 - 50.46 = 9.41. The put follows from put-call parity, P = C - S + K*e^(-rT), giving about $6.46.
The tool applies the Black-Scholes formula to the five inputs. It computes d1 = [ln(S/K) + (r + sigma^2/2)T] / (sigma*sqrt(T)) and d2 = d1 - sigma*sqrt(T), then prices the call as S*N(d1) - K*e^(-rT)*N(d2), where N is the standard normal cumulative distribution function. The put value comes from put-call parity. Time must be in years, with volatility and the risk-free rate in annual terms.
Each input pushes the value in a predictable direction: a higher stock price raises the call and lowers the put, and a higher strike does the opposite. Higher volatility, longer time to expiration, and a higher risk-free rate all increase a call's value. Volatility is the only input you cannot observe directly, so it is typically estimated from historical price data or read from the market's implied volatility.
Because you do not have to exercise it today. It is a one-year right to buy at $100, and with 20% annual volatility the stock has a real chance of ending well above $100, with the option capturing all of that upside and risking only the premium. The $9.41 is the discounted, probability-weighted value of those future payoffs, not a payoff available today.
As a ballpark, yes: enter the grant strike, the company's latest 409A or share price, the remaining term, and an assumed volatility. The model prices a plain European option, so the result is an order-of-magnitude check. Employee options also have vesting, forfeiture on departure, early-exercise, and tax features the model ignores, which usually lower their true value, so do not treat the number as an accounting valuation.
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