Question 2 (20 marks) a) Consider the prices of following American call options with different maturities and strike prices. Assume the current stock price is $30 and no dividends will be paid prior to the July expiration date. The risk-free interest rate is 5% and it is expected to remain constant over the next 2 years. It is currently 3-month away from the maturity date of January call options. Strike price January 20 10.25 25 4.90 35 0.26 April 10.50 5.90 0.77 July 10.77 7.85 1.28 i) Find three mispricings, explain what arbitrage restriction on call prices is being violated. For each of them, explain how you could take advantage of these mispricings and numerically illustrate how your designed strategy leads to an arbitrage profit(s). (10 marks) ii) What further information would you need to know if you would like to pin down the source of the mispricing? Explain why you do not need this information in identifying the arbitrage opportunities in i). (3 marks) b) Company ABC plans to issue a new class of shares, class X, which is different from its common stock. The class X shares can have a pre-set dividend schedule and the holders of the class X shares must be paid any promised but unpaid dividends before any common shareholders receive dividends. This class X shares come with a mandatory redemption at a predetermined time with a value equals to that of one unit of common share but up to a dollar value capped at some predetermined price (i.e. the value of one unit of the class X share is capped at this predetermined price after redemption). Suppose ABC's common stock is currently traded at $40 per share and has an annualized volatility of 0.20. The risk-free rate is 6% per annum. i) Suppose neither the common stock nor the Class X stock pays a dividend. The mandatory redemption is in three years time and the value is capped at $60 per share. Give you best estimate of the current per share price of this class X stock? (4 marks) ii) Suppose that company ABC's common stock pays no dividend but the Class X share will pay one dividend in 2 years time. If the firm wants to sell the Class X at par of $40 per 2 share, what does the dividend have to be? Explain your working. (3 marks) Question 2 (20 marks) a) Consider the prices of following American call options with different maturities and strike prices. Assume the current stock price is $30 and no dividends will be paid prior to the July expiration date. The risk-free interest rate is 5% and it is expected to remain constant over the next 2 years. It is currently 3-month away from the maturity date of January call options. Strike price January 20 10.25 25 4.90 35 0.26 April 10.50 5.90 0.77 July 10.77 7.85 1.28 i) Find three mispricings, explain what arbitrage restriction on call prices is being violated. For each of them, explain how you could take advantage of these mispricings and numerically illustrate how your designed strategy leads to an arbitrage profit(s). (10 marks) ii) What further information would you need to know if you would like to pin down the source of the mispricing? Explain why you do not need this information in identifying the arbitrage opportunities in i). (3 marks) b) Company ABC plans to issue a new class of shares, class X, which is different from its common stock. The class X shares can have a pre-set dividend schedule and the holders of the class X shares must be paid any promised but unpaid dividends before any common shareholders receive dividends. This class X shares come with a mandatory redemption at a predetermined time with a value equals to that of one unit of common share but up to a dollar value capped at some predetermined price (i.e. the value of one unit of the class X share is capped at this predetermined price after redemption). Suppose ABC's common stock is currently traded at $40 per share and has an annualized volatility of 0.20. The risk-free rate is 6% per annum. i) Suppose neither the common stock nor the Class X stock pays a dividend. The mandatory redemption is in three years time and the value is capped at $60 per share. Give you best estimate of the current per share price of this class X stock? (4 marks) ii) Suppose that company ABC's common stock pays no dividend but the Class X share will pay one dividend in 2 years time. If the firm wants to sell the Class X at par of $40 per 2 share, what does the dividend have to be? Explain your working
