A share in the firm Tamar is trading in the market at 2.90 today. In six months from now its price will either increase by 1.00 or decrease by 0.75. In the following six months, it will again either increase in value by 1.00 or decrease in value by 0.75. The six-month interest rate on a risk-free asset is 1% and it will remain at that value for the whole year. Tamar will not pay any dividends during this time. (a) Price a European put option on Tamars stock with one year to expiry and a strike price of 3.25. (9 marks) (b) Price a 1-year American put option on Tamars stock with one year to expiry and a strike price of 3.25. (6 marks) (c) Provide a theoretical explanation of the difference between your results for parts (a) and (b). Would you expect a European call option and an American call option on the same asset to be valued differently? Why/why not? (5 marks) (d) Explain how time to maturity and volatility of the underlying asset price affect the prices of put options. (5 marks) (Total 25 marks)