Problem 5. You are given the following information regarding stock of the Amazing Gadget Corporation (AGC)....

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Problem 5. You are given the following information regarding stock of the Amazing Gadget Corporation (AGC). (1) The stock is currently selling for $50. (2) One year from now the stock will sell for either $40 or $55. (3) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 10%. The continuously compounded risk-free interest rate is 5%. Bob's brokerage account manager says that a one-year at-the-money European call written on stock AGC is currently selling for $1.90. Bob wonders whether this call is fairly priced. He uses the binomial option pricing model to determine if an arbitrage opportunity exists. (1) [5 points] Is there an arbitrage opportunity? (2) [5 points] What transactions should Bob enter into to exploit the arbitrage op- portunity (if one exists)? Problem 5. You are given the following information regarding stock of the Amazing Gadget Corporation (AGC). (1) The stock is currently selling for $50. (2) One year from now the stock will sell for either $40 or $55. (3) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 10%. The continuously compounded risk-free interest rate is 5%. Bob's brokerage account manager says that a one-year at-the-money European call written on stock AGC is currently selling for $1.90. Bob wonders whether this call is fairly priced. He uses the binomial option pricing model to determine if an arbitrage opportunity exists. (1) [5 points] Is there an arbitrage opportunity? (2) [5 points] What transactions should Bob enter into to exploit the arbitrage op- portunity (if one exists)?