The current stock price of TTK is $30. You know that each half year the stock price will either increase by 100% or decrease by 50% with a half-and-half probability. The risk-free discount rate is 10% per annum. Assume that the stock pays no dividends.

a) What is the price of an 18-month Put option that allows you to exercise in 12 months or 18 months time from now with a strike price of $45 using a Binomial pricing model? Show your working.

b) Suppose Mr. T comes to you via a broker with an offer You will give me $4000 today. In return, 18 months from now I will guarantee to pay you whatever the square of the stock price of TTK is at the time. For example, if the stock price ends up at $80. I will pay you $80^2=$6400. Would you accept this offer? Why?

c) Suppose upon receiving the payment from Mr. T 18 months from now in the contract described in b), you will need to pay $400 to the broker. That is, if the TTKs stock price ends up at $80, you will receive $80*$80-400 = $6000; if the stock price ends up at $2, you will receive a net payoff of $2*$2-400 = -$-396. Assume that you are very risk averse, explain how this additional cost will affect your calculation of the lowest acceptable offer price for the offer described in b).

d) What do you think is the best estimate of the standard deviation of TTKs monthly stock return? Explain your answers.