Problem 1.1. You own a stock trading at $50. The stock does not pay any dividend. You are worried about the risk of stock price movement but cannot sell or short the stock. You want to reduce your exposure to stock price movement but do not want to incur any cash expense for doing so. Use a collar so that the value of your hedged stock after six months will lie within a range. That is, lock a price range between A and B such that your positions value will be A if stock price after six months is less than A, B if stock price after six months exceeds B, and equal to the stock price if stock price after six months is between A and B. What collar strategy will provide you a $20 range (that is, B - A = 20) at zero cost? Ignore commissions or transaction costs. The risk-free rate is 4% per annum with continuous compounding and the volatility of the stock is 30%. Structure the collar using European options. Assume option prices are given by Black-Scholes formulas.