Consider a market made of a riskless asset priced \(A_{t}=A_{0}\) with zero interest rate, \(t \geqslant 0\), and a risky asset whose price modeled by a standard Brownian motion as \(S_{t}=B_{t}, t \geqslant 0\). Price the vanilla option with payoff \(C=\left(B_{T}ight)^{2}\), and recover the solution of the Black-Scholes PDE of Exercise 6.1.