A student number is an eight digit number that an institution uses to identify each student

4. Your student number is made by 8 digits: 2122 ... dg. If a; = 0, redefine as ai = 10, for i = 1,...,8. You sell a European option: Call if a6 > 5 is even, Put otherwise. The option has maturity T = 3 years, strike 10a, and an underlying asset with current value 11a7. The risk-free yearly interest rate is 2%. The asset can go up or down each year by 5a5%. (a) Describe the detailed replicating strategy in the case that the stock goes up or down in the first year if a6 5, respectively, then it goes up or down in the second year if a7 5, respectively, then it goes up or down in the third year if ag 5, respectively. 16 marks (b) Find the value of a portfolio containing two Call options in short position, one Put option in long position and one stock (underlying asset) in long position. 5 marks 4. Your student number is made by 8 digits: 2122 ... dg. If a; = 0, redefine as ai = 10, for i = 1,...,8. You sell a European option: Call if a6 > 5 is even, Put otherwise. The option has maturity T = 3 years, strike 10a, and an underlying asset with current value 11a7. The risk-free yearly interest rate is 2%. The asset can go up or down each year by 5a5%. (a) Describe the detailed replicating strategy in the case that the stock goes up or down in the first year if a6 5, respectively, then it goes up or down in the second year if a7 5, respectively, then it goes up or down in the third year if ag 5, respectively. 16 marks (b) Find the value of a portfolio containing two Call options in short position, one Put option in long position and one stock (underlying asset) in long position. 5 marks