This question is based on the following example:

Suppose the state of the economy in each quarter is either good (G) with probability q and bad (B) with probability 1-q. Consider a security that pays dt = $1 if the economy state in quarter t is G and dt = $0 if the economy state in quarter t is B.

Consider a security X with date-3 payoff defined as X = d + d2 +d3 Let Y be a call option on X with a strike price of K = 1 and maturity of T = 3. Recall that the payoff for this call option is Y = max(X K,0). (a) Describe Y as a map: Y:N + R. (b) Find the smallest o-algebra that makes Y a random variable. Consider a security X with date-3 payoff defined as X = d + d2 +d3 Let Y be a call option on X with a strike price of K = 1 and maturity of T = 3. Recall that the payoff for this call option is Y = max(X K,0). (a) Describe Y as a map: Y:N + R. (b) Find the smallest o-algebra that makes Y a random variable