This tool lets you value European put and call options using the Black-Scholes model. Change any of the sliders to see their effect on the call and put prices.
Talking through the example in the tool, let's imagine we have a European call option with a strike price of , expiring in months, on an asset with a current price of . Assume the underlying asset has a dividend yield of and the risk-free rate is currently . Using the Black-Scholes model with an implied volatility of , the value of this call option is .
In the Black-Scholes model, the value of a European call option with strike \(K\), expiring in \(T\) years from today on a stock with a current price of \(S\) and dividend yield of \(q\) is given by $$C = e^{-rT}\left[F \Phi\left(d_+\right) - K \Phi\left(d_-\right)\right]$$ where \(r\) is the risk-free rate, \(\Phi\) is the cumulative normal distribution function and $$ d_\pm = {\ln\left({F \over K}\right) \pm {\sigma^2 \tau \over 2} \over \sqrt{\sigma^2 \tau}},\quad \hbox{and} \quad F = Se^{(r-q)\tau}. $$ The value of a European put option with strike \(K\), expiring in \(T\) years on the same stock is $$P = e^{-rT}\left[ K \Phi\left(-d_-\right) - F \Phi\left(-d_+\right)\right].$$