Consider an economy with a risk-free bond and a stock (that does not pay dividends). The initial value of the bond is Bo = $1, the initial value of the stock is So = $10. The risk-free interest rate per annum with continuous compounding is r. Every year the value of the stock can either go up by 25% with probability 3/4 or go down by 15% with probability 1/4. The return of the stock over each 1 year period is independent of the return in previous years. For the rest of question, assume r = = In(1.05). Approximate your answers to the 4th decimal digit. c) Compute the price of a power option, i.e., an option with maturity 3 years that pays (S3)2. d) Find a self-financing replicating portfolio for the power option defined in (c) (meaning, write the replicating portfolio at each time t and each possible value of St until maturity). e) Assume that after 2 years the stock price is $10.625 and the observed market price for the power option defined in (c) (with maturity one year later) is $115. Find an arbitrage portfolio