You observe the market prices of European options written on a non-dividend paying stock expiring in...

 

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You observe the market prices of European options written on a non-dividend paying stock expiring in one month. Exercise Price X = $35 X = $45 C. Call Price C35 = $7.93 C45 = $2.71 Put Price P35 = $3.28 P45= $8.04 a. Suppose you write a call option with X = $35 and buy a call with X = $45. Graph the profit/loss of the individual call positions and the combined option portfolio as a function of the stock price at the expiry. Also indicate at what stock price you will just break even on the graph. (6 marks) b. Now suppose you further buy a put option with X = $35 and write a put option with X = $45 in addition to the call option positions in part a) i.e., now your portfolio consists of short call and long put with X = 35 and long call and short put at X = 45. Graph the payoff of the individual option positions and the combined option portfolio as a function of the stock price at the expiry. (3 marks) In light of your answer in part b) above, what should be the one-month risk-free rate to rule out any arbitrage. Hint: The arbitrage-free one-month risk-free rate should be the same: Rf = (risk-free cash flow in one month) / (initial cost of the risk-free investment) for any risk-free investment generating a constant cash flow in one month. (3 marks) You observe the market prices of European options written on a non-dividend paying stock expiring in one month. Exercise Price X = $35 X = $45 C. Call Price C35 = $7.93 C45 = $2.71 Put Price P35 = $3.28 P45= $8.04 a. Suppose you write a call option with X = $35 and buy a call with X = $45. Graph the profit/loss of the individual call positions and the combined option portfolio as a function of the stock price at the expiry. Also indicate at what stock price you will just break even on the graph. (6 marks) b. Now suppose you further buy a put option with X = $35 and write a put option with X = $45 in addition to the call option positions in part a) i.e., now your portfolio consists of short call and long put with X = 35 and long call and short put at X = 45. Graph the payoff of the individual option positions and the combined option portfolio as a function of the stock price at the expiry. (3 marks) In light of your answer in part b) above, what should be the one-month risk-free rate to rule out any arbitrage. Hint: The arbitrage-free one-month risk-free rate should be the same: Rf = (risk-free cash flow in one month) / (initial cost of the risk-free investment) for any risk-free investment generating a constant cash flow in one month. (3 marks)

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SOLUTION a ProfitLoss of Individual Call and Put Positions and Combined Option Portfolio Suppose we write a call option with X 35 and buy a call optio... View the full answer