Black–Scholes and Collar Cost An investor is said to take a position in a “collar”

if she buys the asset, buys an out-of-the-money put option on the asset, and sells an out-of-the-money call option on the asset. The two options should have the same time to expiration. Suppose Marie wishes to purchase a collar on Hollywood, Inc., a non-dividend–paying common stock, with six months until expiration. She would like the put to have a strike price of $55 and the call to have a strike price of $95. The current price of Hollywood’s stock is $70 per share. Marie can borrow and lend at the continuously compounded risk-free rate of 7 percent per annum, and the annual standard deviation of the stock’s return is 50 percent. Use the Black–Scholes model to calculate the total cost of the collar that Marie is interested in buying. What is the effect of the collar?