Stock ABC is currently standing at 1,508. Consider the corresponding stock options that expire in 90 days. The current Treasury Bills have a risk-free annual rate 2 percent. On the market, the calls and puts listed for ABC have an exercise price of 1,550. (a) Assume there are no dividends paid for stock ABC.

(i) Explain the payoff diagrams for the put & call options for both European options and American options.

(ii) Explain the lowest and highest possible European put prices on Stock ABC.

(iii) Explain what the maximal possible loss are for European calls & puts. Assume that European calls and puts for ABC had the price of 59.54 and 92.91 respectively. Explain and compute the profits for both European calls and puts when Stock ABC stands at 1432 at expiry.

(iv) Explain whether an increase in volatility would have impacts on profits/payoffs diagrams of puts on stock ABC. If you are a hedger, why would you continue to buy such put options with increased uncertainty? Explain.

(b) (i) Assume that European calls and puts for ABC have the price of 59.54 and 92.91 respectively, and there are no dividends for stock ABC. Can you detect arbitrage opportunities for the options? Explain the equations you use and how you can construct a risk-free arbitrage portfolio to earn money.

(ii) How would your answers change if Stock ABC is a stock index and having 1.5% continuous-time dividend yield per year? Assume the same options prices as in (b)(i).

(c) Assume that European calls and puts for ABC have the prices of 74.40 and 108.78 respectively, and there are no dividends for stock ABC. For a speculator, what would be possible strategy or (strategies) if the speculator reckons there would be greater fluctuations for Stock ABC during the life of options? Explain the strategy/strategies. Also explain the outcome of the strategies if uncertainty about Stock ABC turns out be lower than expected.