1. You are evaluating a stock that is currently selling for $45 per share. Over the period, you think that the stock price might go down 15% or go up 15%. There is a call option available on the stock with an exercise price of $50. Answer the following questions about hedging your position in the stock. Assume that you will hold one share, and the risk-free rate is 5%.
A) What is the hedge ratio? How much would you borrow to purchase the stock? What is the amount of your net investment in the stock?
B) Complete the table below to show the value of your stock portfolio at the end of the holding period.
Scenario Low Stock Price High Stock Price
Value of Stock at Year End
Repayment of Loan
Value of Call Position
C) How many call options will you combine with the stock to construct the perfect hedge? Will you buy the calls or sell the calls?
D) What must the price of one call option be? And put ?
2. Use the Black-Scholes to find the value of a call option on the following stock.
Time to expiration 2-month
Standard deviation 30% per year
Exercise price $40
Stock price $45
Interest rate 4%
What is the value of the put with the same strike price?