Consider the three-step binomial model with the time 0 stock price S(0) = 60, the single step returns for the up/down jumps of the stock price u = 0.3 and d = 0.1, and with the single-step risk-free return r = 0.15. Consider a European put option with strike price K = 80 expiring after three time steps.

(a) Compute the price of this option at each time step and each node of the three step binomial tree. [8]

(b) Compute the replicating strategy for this option. [8]

(c) In the same market model, consider another option, D2. This option has a special condition: if, at any moment of time n = 0, 1, 2, 3, the price of the stock falls below the level 50, the option becomes void (hence its price becomes 0 at that time in that scenario and remains 0 until the end of that scenario). In those scenarios where the price of the option has never fallen below the level 50, its payoff at time 3 is equal to max (0, K S(3)) (the same formula as for the European put option with strike K as above).

Determine whether the option D2 has any no-arbitrage prices. If such no- arbitrage prices exist, then find them, as well as a replicating strategy forD2. If they do not, then show that the extended market (A, S, D2) contains arbitrage irrespective of the price of D2. [9]