Stock ZYX has current price S₀ = $100. Use a 2-step binomial tree for the price of this stock, with up-factor u = 0.1 and down-factor d = −0.0909 per year in the next 2 years. The interest rate is zero.

(1) Use risk-neutral pricing to find the price of an European at-the-money call option with maturity T = 2 years based on the binomial tree.

(2) Assume that you sold this option. How would you hedge dynamically your position? Describe the strategy in detail, and show your stock and bond positions at each  node on the tree.

(3) A client calls you and wants to enter into an option which gives her the right (but not the obligation) to buy at time T = 1 for a strike price K = 5 the option described in point (1) above. As you see, this is an option on an option, and is also called a "compound option". What is the price of this compound option?