Problem 1: We consider a binomial model with the following parameters: T=2, r=0.1, u=0.2, d=0.2, p=1/2, S₀ =100.

(1) Compute the probability p^* corresponding to the risk-neutral probability measure.

(2) Compute the bond price at times 0, 1, 2.

(3) Draw the tree giving all the possible evolutions of the stock price.

(4) We consider a call option with maturity T = 2 and strike price K = 90. Compute

the payoff of this option, for each possible evolution of the stock price.

(5) We consider the replicating portfolio of the call option. Compute the number of bonds ₂ and the number of stocks ₂ held between time 1 and time 2, for each

possible value of the stock price at time 1.

(6) For the same replicating portfolio, compute the number of bonds ₁ and the number

of stocks ₁ held between time 0 and time 1.

(7) Compute the value V₀ of the same portfolio at time 0. Compute the value V₁ of the

portfolio at time 1, for each possible value of the stock price at time 1.

(8) We buy the call option described above at time 0. Which price should be pay?