5. A stock follows a binomial process for two periods. At time t=0 the price is $100, and at time t=1 the stock price is cither $120 or $90. If the time t=1 price is $120, the time t=2 price can be either $144 or $108. If the time t=1 price is $90, the time t=2 price is either $108 or $81. The riskless interest rate is 5% per period. A European put option has an exercise price of $100. a) Draw the binomial tree for this stock. Include the value at expiration in each of the final states of the European put option on the tree. b) Calculate the value of the put option at time t=1 if the stock price is $120. What is the hedge ratio for the put? c) Calculate the value of the put option at time t=1 if the stock price is $90. What is the hedge ratio for the put? d) Calculate the value of the put option at time t=0. What is the hedge ratio for the put at time t=0 ? e) In general, if the price of a stock declines, does the hedge ratio for a put option go up o down? Does the replicating portfolio for a put option buy shares or sell shares when the pric of the stock decreases? f) How might portfolio insurance (replication of a put option by trading stocks and bond have magnified the US stock market flash crash on May 6,2010