After deriving the Black-Scholes equation for a call option from the requirement to make a portfolio risk-free, the equation is solved using a number of variable substitutions, which transforms it into a diffusion equation. Using the latter’s Green’s function is then used to value European call options. The resemblance of the solution found in this chapter to that in Chapter 4 stimulates the discussion of martingale processes. In order to better understand the mechanics of using options for hedging, a MATLAB simulation for the temporal evolution of stocks, options and bank deposits is presented.