6. Assuming other things constant, bonds of equal maturity will still have different DV01 per USD 100 Face Value. Their DV01 per USD 100 Face Value will be in the following sequence of Highest Value to Lowest Value:

A. Zero Coupon Bonds, Par Bonds, Premium Bonds

B. Premium Bonds, Par Bonds,  Zero Coupon Bonds

C. Premium Bonds, Zero Coupon Bonds, Par Bonds

D. Zero Coupon Bonds, Premium Bonds, Par Bonds

7. Jeff is an arbitrage trader, and he wants to calculate the implied dividend yield on a stock while looking at the over-the-counter price of a 5-year put and call (both European-style) on that same stock. He has the following data:

l            Initial stock price = USD 85

l            Strike price = USD 90

l            Continuous risk-free rate = 5%

l            Underlying stock volatility = unknown

l            Call price = USD 10

l            Put price = USD 15

What is the continuous implied dividend yield of that stock?

A. 2.48%

B. 4.69%

C. 5.34%

D. 7.71%

8. A zero-coupon bond with a maturity of 10 years has an annual effective yield of 10%. What is the closest value for its modified duration?

A. 9

B. 10

C. 100

D. Insufficient Information

9. You are given the following information about a call option:

l            Time to maturity = 2 years

l            Continuous risk-free rate = 4%

l            Continuous dividend yield = 1%

l            N(d1) = 0.64

Calculate the delta of this option.

A. -0.64

B. 0.36

C. 0.63

D. 0.64

10. Which of the following statements about American options is false?

A. American options can be exercised at any time until maturity

B. American options are always worth at least as much as European options

C. American options can easily be valued with Monte Carlo simulation

D. American options can be valued with binomial trees

6. Assuming other things constant, bonds of equal maturity will still have different DV01 per USD 100 Face Value. Their DV01 per USD 100 Face Value will be in the following sequence of Highest Value to Lowest Value:

A. Zero Coupon Bonds, Par Bonds, Premium Bonds

B. Premium Bonds, Par Bonds,  Zero Coupon Bonds

C. Premium Bonds, Zero Coupon Bonds, Par Bonds

D. Zero Coupon Bonds, Premium Bonds, Par Bonds

Correct answer is B

A is incorrect. Premium Bond will have a higher Base Price and hence higher DV01 than that of Zero Coupon Bond. fficeffice" />

B is correct.  DV01 is certain multiple of Dirty Price (which includes Coupons) and not Clean Price. Thus, it is proportional to Base Price, which is Dirty Price.  Ordinarily, Premium Bond will have the highest (dirty) price followed by Par Bond and with the least price of Zero Coupon Bond. Hence, DV01 of Premium Bond is the highest while that of Zero Coupon Bonds is the lowest. C is incorrect. Base Price of Par Bond is higher than that of Zero Coupon Bond and hence, its DV01 cannot be less than that of Zero Coupon Bond. 

D is incorrect. DV01 per USD 100 Face Value is an Absolute Amount of USD based on actual Base Price Change. Ordinarily, Base Price of a Zero Coupon Bond will be lower than that of Par & Premium Bond. Hence, DV01 of Zero Coupon Bond is less than that of Premium Bond of same maturity. 

Reference Tuckman, Fixed Income Securities, Chapter 5.

7. Jeff is an arbitrage trader, and he wants to calculate the implied dividend yield on a stock while looking at the over-the-counter price of a 5-year put and call (both European-style) on that same stock. He has the following data:

l            Initial stock price = USD 85

l            Strike price = USD 90

l            Continuous risk-free rate = 5%

l            Underlying stock volatility = unknown

l            Call price = USD 10

l            Put price = USD 15

What is the continuous implied dividend yield of that stock?

ffice:smarttags" />A. 2.48%

B. 4.69%

C. 5.34%

D. 7.71%

Correct answer is C

We can use the Put-Call parity here to easily solve for the continuous dividend yield.  We have C - P = S 0e-q*T - Ke-r*T, so 10 - 15 = 85e-q*5 - 90e-0.05*5.  Solving for q, we get 5.34%.

A is incorrect because C and P where inverted in the formula.

B is incorrect because C and P where inverted in the formula, and S and K where also inverted in the formula.

C is correct because the above formula was used correctly, C - P = S0e-q*T - Ke-r*T.

D is incorrect because S and K where inverted in the formula.

Reference: Options, Futures and Other Derivatives, John C. Hull, 6th edition, Prentice Hall, 2006, Chapter 13.

8. A zero-coupon bond with a maturity of 10 years has an annual effective yield of 10%. What is the closest value for its modified duration?

A. 9

B. 10

C. 100

D. Insufficient Information

Correct answer is A

You must first recall that the Macauley duration of a zero-coupon bond is equal to its maturity.  Then, the modified duration of a zero-coupon bond is: Macauley duration / 1+ i = 10 / 1.10 = 9.09.

A is correct because the above formula was used correctly, Dmod = Macauley duration / 1+ i.

B is incorrect because it corresponds to the Macauley duration, not the Modified duration.

C is incorrect because the denominator used in the formula was i instead of 1+i.

D is incorrect because all the necessary information is in there.

Reference: Options, Futures and Other Derivatives, John C. Hull, 6th edition, Prentice Hall, 2006, Chapter 6.

9. You are given the following information about a call option:

l            Time to maturity = 2 years

l            Continuous risk-free rate = 4%

l            Continuous dividend yield = 1%

l            N(d1) = 0.64

Calculate the delta of this option.

A. -0.64

B. 0.36

C. 0.63

D. 0.64

Correct answer is C

The delta of a call option with a continuous dividend yield is given by the following formula:

Delta= N(d1)*e-qT, where q is the continuous dividend yield, and T is the time to maturity.

So, Delta = 0.64*e-0.01*2 = 0.63. 

A is incorrect because the delta of a call is not equal to -N(d font face='Arial Sub'>1).

B is incorrect because the delta of a call is not equal to 1-N(d font face='Arial Sub'>1).

C is correct because the above formula was used correctly, N(d font face='Arial Sub'>1)*e-qT.

D is incorrect because the delta of a call with dividend yield is not equal to N(d font face='Arial Sub'>1), the q was not used in the above formula.

Reference:Options, Futures and Other Derivatives, John C. Hull, 6th edition, Prentice Hall, 2006, Chapter 15

10. Which of the following statements about American options is false?

A. American options can be exercised at any time until maturity

B. American options are always worth at least as much as European options

C. American options can easily be valued with Monte Carlo simulation

D. American options can be valued with binomial trees

Correct answer is C

C is the right answer:

A is TRUE because American options can be exercise at any time.

B is TRUE because American options can be exercise at any time vs only at maturity for European option, which make American option more valuable.

C is FALSE because it is very difficult to apply Monte Carlo retrospectively.

D is TRUE because we can value American options at each node of the binomial tree as if it could be different exercise dates.

Reference:Options, Futures and Other Derivatives, John C. Hull, 6th edition, Prentice Hall, 2006, Chapter 24.