Question

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 Riggs, Inc., a non-dividend-paying common stock, with six months until expiration. She would like the put to have a strike price of $34 and the call to have a strike price of $63. The current price of the stock is $45 per share. Marie can borrow and lend at the continuously compounded risk-free rate of 5 percent per year 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. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

	Cost of collar

Note* answer is not -.4628

Answer 1

Total cost of collar = Cost to buy the asset + Cost to buy an out-of-the-money put option on the asset - proceeds from selling an out-of-the-money call option on the asset = S + P - C

We will use Black Scholes Model to Value the Call and Put option values, C & P respectively.

And the value of the put option is given by:

Hence, the cost of collar = S + P - C = 45 + 1.4520 - 1.9148 = $ 44.54