## SLCG Option Value Calculator (Black-Scholes)

 Underlying asset price: Strike price: Risk-free rate: Dividend yield: Implied volatility: Term (months):
European call price: European put price: (at-the-money) (at-the-money)

### About the SLCG Option Value Calculator (Black-Scholes)

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 $$d_\pm = {\ln\left({F \over K}\right) \pm {\sigma^2 \tau \over 2} \over \sqrt{\sigma^2 \tau}},\quad \hbox{and} \quad F = e^{(r-q)\tau}.$$ The value of a European put option with strike $$K$$, expiring in $$T$$ years on the same stock is $$P = e^{-rT}\left[ K \Phi\left(-d_-\right) - F \Phi\left(-d_+\right)\right].$$