Consider a put option on TTK Corp's common stock. The current TTK Corp stock price is $1,000 and it is expected to either increase by 25% or decrease by 20% each half year with equal probability. The option has a strike price of $1200, an expiration time 18-month from now and the underlying asset of each option is one unit of TTK Corp's common stock. In additional to the standard exercising right for the put buyer at maturity, this option has a special clause that gives the buyer an additional right to exercise the option 6-month from now. The risk-free interest rate is 1% per annum and the stock is not expected to pay any dividend over the next 3 years.

a) Use a three-period binomial model to calculate the current value of the put option. (12 marks)

b) Show how to calculate the value of this additional right to exercise the option in 6-month without computing the value of an otherwise-equal put option with no additional right. (3 marks)

c) What would be the price difference between the call and put options on TTK Corp stock with a strike price of $1200, 18-month maturity with no additional right? (2 marks)

d) How would the value of this additional right to exercise the put option in 6-month change if the risk-free interest rate increases? Answer this question analytically without doing any calculation. (3 marks)