FE1 Bonus Test

1. This test is 45 minutes long and there are 6 questions. The test will be taken down after 46 minutes. 2. Each question carries 2.5 points. 3. Answer All questions 4. Students who attempts the test twice will be given zero credit. 1

The price of a stock is $50. The stock pays a dividend of $5 in 3 months. A 6-month European put option on the stock has a strike price of $48 and a premium of $4.38. The continuously compounded interest rate is 8%. Calculate the premium for a 6-month European call option on the stock with a strike price of $48. * A 1.02

* B 3.36

* C 3.46

* D 4.38

* E 5.40

2

1. An “exchange call option” gives the owner of the option the right to give up one share of Stock A in exchange for receiving one share of Stock B. Stock A currently has a price of $56 and Stock B has a current price of $52. The continuously compounded risk-free rate of interest is 5% and the price of a one-year European exchange call option is $7. Suppose that neither Stock A nor Stock B pays any dividends. Find the price of a European exchange put option expiring in one year which gives the owner the right to give up one share of Stock B in exchange for receiving one share of Stock A. * A) $3

* B) $5

* C) $7

* D) $9

* E) $11

3.

The price of a 6-month dollar-denominated call option on the euro with a $0.90 strike is $0.0404. The price of an otherwise equivalent put option is

$0.0141. The annual continuously compounded dollar interest rate is 5%. If the euro-denominated annual continuously compounded interest rate is 3.5%, what is the spot exchange rate? * (A) $0.98

* (B) $0.92

* (C) $0.90

* (D) $0.87

* (E) $0.84

4.

Consider a European put option on a stock XYZ. You are given: • The current price of the stock is $50. • The present value of the dividends that the stock pays within next 3 years is $1.50. • The call option currently sells for $0.20 more than the put option. • Both the put option and call option will expire in 3 years. • Both the put option and call option have a strike price of $60. Calculate the continuously compounded risk-free interest rate. * A 0.032

* B 0.042

* C 0.052

* D 0.062

* E 0.072

5.

Call options with strikes of $30, $35, and $40 have option premiums of $1.50, $1.70, and $2.00, respectively. Using strike price convexity, which option premium, if any, is not possible? * A. C (30)

* B. C (35)

* C. C (40)

* D. All are possible

6.

The current exchange rate is $0.80 per Swiss franc. The risk-free continuously compounded interest rate for dollars is 4%. The risk-free continuously compounded interest rate for francs is 6%. A franc-denominated European call option on one dollar has a strike price of 1.15 francs. The franc-denominated European call option expires in 1 year and has a premium of 0.127 francs. Calculate the value of a franc-denominated European put option on one dollar that has a strike price of 1.15 francs and expires in 1 year. * A $0.007

* B $0.009

* C $0.011

* D $0.055

* E $0.552