7.13. A European “Tootsie Square” is a financial contract, which, at maturity, pays off the square of the price of the underlying stock on which it is written. For instance, if the price of the underlying stock is $3 at maturity, the Tootsie Square contract pays off $9. Consider a two period Tootsie Square written on ABC stock.

ABC stock is currently selling at $1 per share.

Each period the price either rises 10% or falls by 5% (i.e., after one period, the stock price of ABC can either rise to $1.10 or fall to $0.95). The probability of a rise is 0.5. The risk-free interest rate is 5% per period.

a. Determine the price at which you expect the Tootsie Square on ABC to trade.

b. Suppose that you wanted to form a portfolio to track the payoff on the Tootsie Square over the first period. How many shares of ABC stock should you hold in this portfolio?