Black-Scholes-Merton Model

As a test for playing around with MDX, here is an interactive plot of the Black-Scholes-Merton model built with react and plotly

Black-Scholes-Merton Model

The price of a European call option is given by:

$C(S, t) = S \cdot N(d_1) - K e^{-r(T-t)} \cdot N(d_2)$

where: $d_1 = \frac{\ln\left(\frac{S}{K}\right) + \left(r + \frac{\sigma^2}{2}\right)(T-t)}{\sigma \sqrt{T-t}}$ $d_2 = d_1 - \sigma \sqrt{T-t}$

Parameters

• $S$: Current price of the underlying asset
• $K$: Strike price
• $T$: Time to maturity (years)
• $t$: Current time (years)
• $r$: Risk-free interest rate (annualized)
• $\sigma$: Volatility of the underlying asset (annualized)
• $N(\cdot)$: Cumulative distribution function of the standard normal distribution

Play around with it!