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PROBLEM 5 (11 MARKS) A stock price is currently trading at $50. Assume that the stock follows a one-period binomial model with one period lasting for half a year. The stock will either increase in value by 20% or fall in value by 30% in the binomial tree. The annual effective risk-free interest rate is 2%. The stock pays no dividends. a. (5 MARKS) Find a fair (no-arbitrage) price of a European put option written on the stock with expiration in a half year and strike price of $55. P=$7.53 b. (6 MARKS) Assume that the actual price of the put from question a seen in the market has a price of $8.00. Also assume that there are no call options written on the stock available for trading. Does the market allow arbitrage opportunities? What will be an arbitrage strategy if your answer to the previous question is "Yes"? Short the put option and buy a synthetic put option comprised from a short position in .8 stock shares and $47.53 long position in T-bills