(a) Consider a call option with a strike price of $50 and maturity of one year which is written on a stock that does not pay dividends. You expect that the stock will either increase to $70 or decrease to $35 over the next year. The current price of the underlying stock is $50, and the risk-free interest rate is 4% per annum. What is the price of this call option? (b) Suppose you are advising a client who wants to use index options to speculate on the performance of the UK stock market. Your client believes that the market is likely to be in the range 6225 to 6425 in three months' time. The prices for options of that maturity are given below. Describe a suitable strategy which you can recommend to your client. Estimate the cost of the position and its payoff. Strike 6225 6325 6425 Price of Calls 301 243 193 Price of Puts 123 164 213 (c) Foreseeing a major increase or decrease in the stock price, you set up a position in options where you buy a call at $8.75 and a put at $8.25, both with a strike price of $120. The stock is currently selling for $119 and both options have the same maturity. Calculate the cost of that position, break-even points in the upside and downside and draw the payoff diagram. What is the difference between the proposed strategy and the one implemented in part (b)? (d) You are given the following prices for three put options on a share, all with the same maturity. Strike Price 40 25 33 50 60 40 Show in detail that there exists an arbitrage opportunity associated with the butterfly strategy