How to calculate an option price
A Black-Scholes Calculator can be used to figure the price (fair market value) of a put or call option contract based on the Black-Scholes pricing model. It also calculates and plots the Greeks: Delta, Gamma, Theta, Vega, Rho.
Enter your own values through the website in the link below and press the calculate button to see the results.
There are both American and European options with the key difference between the two being when the options can be exercised. A European option may be exercised only at the expiration date of the option, at that pre-defined set point in time. An American option can be exercised at any time before the expiration date. This can slightly effect pricing however it is rare for any option to be worth exercising before the expiration date.
The Black-Scholes Option Pricing Formula
Option prices can be compared by calculating the Black-Scholes formula. It’s the formula used to calculate theoretical values of an option contract based on the metrics of stock prices, interest rates, time to expiration, and volatility. The Black-Scholes formula allows option traders and option writers to determine the optimum option pricing.
The Black Scholes Calculator uses these formulas for price calculations:
C = SP e-dt N(d1) – ST e-rt N(d2)
P = ST e-rt N(-d2) – SP e-dt N(-d1)
d1 = ( ln(SP/ST) + (r – d + (σ2/2)) t ) / σ √t
d2 = ( ln(SP/ST) + (r – d – (σ2/2)) t ) / σ √t = d1 – σ √t
C is the value of the call option,
P is the value of the put option,
N (.) is the cumulative standard normal distribution function,
SP is the current stock price (spot price),
ST is the strike price (exercise price),
e is the exponential constant (2.7182818),
ln is the natural logarithm,
r is the current risk-free interest rate (as a decimal),
t is the time to expiration in years,
σ is the annualized volatility of the stock (as a decimal),
d is the dividend yield (as a decimal).