You are given the following information concerning a stock denoted by St
(1) Current value =102.
(2) Annual volatility = 30%.
(3) You are also given the spot rate r = 50%, which is known to constant during the next 3 months
It is hoped that the dynamic behavior of St can be approximated reasonably well by a binomial process if one assumes observation intervals of length 1 month
(a) Consider a European call option written on St. the call has a strike price K = 120 and expiration of 3 months. Using St and the risk-free borrowing and lending, Bi, construct a portfolio that replicates the option.
(b) Using the replicating portfolio price this call
(c) Suppose you sell, over-the-counter, 100 such calls to your customers. How would you hedge this position? Be precise.
(d) Suppose the market price of this call is 5. How would you form an arbitrage portfolio?