(a) What is a lower bound for the price of a six-month call option on a non-dividend- paying stock when the stock price is $80, the strike price is $75, and the risk-free rate is 10% per annum simple?- (b) A stock trades at $50. An at the money call option trades at $4. The maturity of the option is two years. The present value of the strike price over the two years is $45. The stock pays a dividend of 3 dollars in one year and no other dividends prior to expiration. The present value of the dividend is $2. The price of the European call option is $5. The price of the European put is $1.0. Construct a strategy that guarantees riskless arbitrage profits. Provide full details of the strategy and identify the minimum and maximum possible profits. c) The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and in five months. The term structure is flat, with all risk-free interest rates being 10% per year continuously compounded. What is the price of a European put option that expires in six months and has a strike price of $30?- (d) Explain carefully the arbitrage opportunities in Problem c) if the European put price trades at $3