Consider a simple stock model, with one risky and one riskless asset and two times $T=0$ and $T=1.$ Consider an option that will allow you to buy unit of the risky asset at time $1$ for a strike price of $2$ dollars.

a$)$ Construct a replicating portfolio for the option, and use this to determine how much the option should cost.

b$)$ Construct a martingale measure, and use this to determine how much the option should cost.