(a) Derive the lower bound for a European put option written on a non-dividend paying stock. 

(b) The stock of MCGL trades for €86 per share and its price volatility is 35%. It is expected to pay a dividend of 2% in nine months. The risk-free rate is 5% per annum with continuous compounding. Using the Black-Scholes model of option pricing, compute the following:

(i) The current price of a 6-month European call option written on the stock of MCGL with a strike price of €90? 

(ii) The current price of a 6-month European put option written on the stock of MCGL with a strike price of €90? 

(iii) Write down the Put-Call parity condition for these options and verify that it holds. 

(iv) Explain (calculations are not necessary) what would happen to the prices of these options if the dividend was due in 3 months, holding all other factors constant. 

(c) Jim expects that the price of MCGL stock is going to experience a big jump over the next six months but is not sure in which direction the price will move. Use the options priced above to: 

(i) Design a trading strategy to allow Jim to back his expectation. 

(ii) What is the cashflow at initiation (t=0) to implement this strategy? 

(iii) For what range of prices will the strategy be in profit at maturity (t=T)?