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Question - Shares of XYZ are traded at $15. In six months, share price could either be $25 or $10 with probabilities of 0.5 and 0.5, respectively. The current 6-month risk-free rate is 5%. You want to use XYZ shares and the risk-free bond to replicate an exotic asset whose payoff in six months equals the square of XYZ's share price. That is, when XYZ price goes up to $25 this asset pays $25*$25=$625; and when the price goes down to $10, this asset pays $10*$10=$100. Using the above information to answer Questions-
1. What is the fair value of this exotic asset today?
2. Continue with the above, to form a replicating portfolio for this exotic asset, how many shares of XYZ do you need to hold?
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