The share price of DANF Digital is $$1000.$ Six months from now, it will be either $$150$ with probability of$\mathrm{.}70$ or $$90$ with probability $\mathrm{.}30.$ A call option exists on the stock that can be exercised only at the end of $6$ months at an exercise price of $$120.$

a$.$ If you wished to establish a perfectly hedged position, what would you do on the basis of the facts just presented?

b$.$ Under each of the two possibilities, what will be the value of your hedged position?

c$.$ What is the expected value of option price at the end of the period?