A stock is currently trading at $50. Paul Tripp, CFA wants to value one-year index option using the single-period binomial model. The stock will either increase in value by 20% with probability of 30% or fall in value by 20% with probability of 70%. The annual risk-free interest rate is 2%. No dividends are paid on any of the underlying securities in the index.
a. find out the value of a European call option on the index with an exercise price of $50 by using one-period binomial model
b. Suppose that the market price of the call option considered in problem a is $11. Do you have an arbitrage opportunity in this market? If yes, then find an arbitrage strategy (that is find your positions in an underlying stock, T-bills and call option)