This question is designed to make sure you know how to derive the Black-Scholes partial differential equation (pde). a) Write down the key assumptions of the Black-Scholes model. b) Why is Ito's lemma needed? c) Derive the Black-Scholes pde, d) What is the role of hedging? Why is this hedge portfolio also called a replicating portfolio? e) Why does the Black-Scholes pde not have a stochastic component