In the coin toss economy, consider a call option with strike X = 0.2 and expiration in period 2, which is written on the number of heads. Formally, the payoff of this option is max(S −X, 0) where S is the total number of heads (0, 1 , or 2) and X = 0.2. Assume that the two securities traded in the economy are the Head and Tail assets.

(a) According to the LOOP, what is the price of this call option at date zero?

(b) Use backward induction to construct a dynamic trading strategy that replicates the payoff of the call option.

(c) Suppose that the coins being tossed are replaced, and that the new coins are not fair, so that the probability of heads is now 3/5. However, the prices and payoffs of the Head and Tail security are unchanged. Is the price of the call option affected?

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a According to the Law of One Price LOOP the price of the call option at date zero should be equal to the cost of replicating its payoff using the Head and Tail assets Let C0 be the price of the call ... View the full answer