Carefully explain the arbitrage opportunities in the following market conditions: The price of a European put is $4.00; the price of a European call is $2.50; both options expire in six months, and have a strike price of $30; the underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. Risk-free interest rates for all maturities are 10%. (a) What is the price of the synthetic put? (b) What put would you buy?; (c) What put" would you sell? (d) What gains will you make? (e) When will you realize those gains? Note that [c+D* + Ke='T =p+ Sol; D* = Present value of dividends.] ; = None of the others (a) $4.1516; (b) The "real" or quoted; (c) The synthetic; (d) $0.1516; (e) In six months (a) $3.0082; (b) The synthetic; (c) The real or quoted; (d) $0.9918; (e) Today (a) $4.1516; (b) The real or quoted; (c) The synthetic; (d) $1.4918; (e) Today (a) $3.5082; (b) The synthetic; (c) The "real" or quoted put; (d) $1.4918; (e) In six months