final_review_fall23 (1)

11. Current prices of call options on Furniture City Inc stock are given in the table below. Identify two apparent pricing discrepancies in the table. Identify which of the basic option pricing relationships each discrepancy violates. Expiration month Stock price Exercise price June July August September $119.50 $110 $9 $12.50 $15 $18 $119.50 $120 $1.50 $3.75 $3 $4.50 $119.50 $130 $1 $2.25 $2.75 $5 12. The following is a list of prices of zero coupon bonds with different maturities and par value of $1,000. Time to Maturity Price 1 $943.40 2 $881.68 3 $808.88 4 $742.09 Calculate the following: (a) yield to maturity for each zero coupon bond (b) forward rates for each of the next 4 years 13. What is the modified duration of a seven-year bond which has a coupon rate of 9% and sells at par? 14. Bond A is an 8% coupon bond with 20 years to maturity selling at par (face) value. Bond B is an 8% coupon bond, with 20 years to maturity selling below par (face) value. Which of the two bonds has a longer duration? 15. The common stock of CALL Corporation has been trading in a narrow range around $50 per share for months, and you are convinced that it is going to stay in that range for the next three months. The price of a 3-month put option with an exercise price of $50 is $4. The stock will pay no dividends for the next three months. (a) if the risk-free rate is 10% per year, what must be the price of a 3-month call option on CALL stock with an exercise price of $50 if it is in the money? (b) what would be a simple options strategy using a put and a call to exploit your conviction about the stock price’s future movement? What is the most money you can make on this position? How far can the stock price move in either direction before you lose money? (c) how can you create a position using a put, a call, and risk-free lending that would have the same payoff structure as the stock at expiration? How much will it cost you to establish this position? 16. A vertical combination is the purchase of a call with exercise price X 2 and a put with exercise price X 1 , with X 2 greater than X 1 . Graph the payoff to this strategy. 17. Prove that the portfolio variance formula in the case of two perfectly negatively correlated assets simplifies to σ P 2 =( w 1 σ 1 − w 2 σ 2 ) 2 . 3