Question 1

Which of the following statements is INCORRECT? A binomial model may be used for valuing:

Accepted Answer

A)   European options in the presence of known dollar dividends
B)   European options in the presence of a known dividend yield
C)   an exotic option whose payoff depends on some function of the current stock price and the strike price
D)   a European option in an incomplete market
E)   an American option D

Question 2

Today's price of an American put option is:

Accepted Answer

A)   $8.41
B)   $9.05
C)   $9.12
D)   $10.03
E)   None of these answers are correct. B

Question 3

Use the following data for a two-period binomial model to answer the questions that follow.
- The stock's price S is $100.After three months,it either goes up and gets multiplied by the factor U =1.13847256,or it goes down and gets multiplied by the factor D = 0.88664332.
- Options mature after T = 0.5 year and have a strike price of K = $105.
- The continuously compounded risk-free interest rate r is 5 percent per year.
- Today's European call price is c and the put price is p.Call prices after one period are denoted by cS1U1B1US1U1B0 in the up node and cS1U1B1DS1U1B0 in the down node.Call prices after two periods are denoted by cS1U1B1UDS1U1B0 in the "up,and then down node" and so on.Put prices are similarly defined.
-Call prices (in dollars)are given by:

Accepted Answer

A)   c = 8.81,cU=17.84,cUU = 36.11,and zero at other nodes
B)   c = 7.68,cU =15.09,cD = 0.47,cUU =29.61,cUD = 0.94,cDD = 0
C)   c =4.78,cU = 9.69,cUU = 19.61,and zero at other nodes
D)   c = 6.00,cU =12.16,cUU =24.61,and zero at other nodes
E)   None of these answers are correct. D

Question 4

Consider the following exotic option whose payoff at maturity is given by the square root of the stock price less the strike price if it has a positive value,zero otherwise,that is: max[$\surd$S(2)- K,0].
Using the above data except for assuming a new strike price is $5,today's arbitrage-free price of this exotic option is:

Accepted Answer

A)   $0.21
B)   $0.29
C)   $0.36
D)   $0.70
E)   None of these answers are correct.

Question 5

Use the following data for an eight-period binomial model to answer the questions that follow.
- The stock's price S is $100.The stock price evolves according to an eight-period binomial model.
- Options mature after T = 1 year and have a strike price of K = $70.
- The continuously compounded risk-free interest rate r is 5 percent per year.
- The annualized volatility of stock price returns $\sigma$ = 0.25 or 25 percent per year.
-Today's price of a European put in this eight-period binomial model is:

Accepted Answer

A)   $0.1107
B)   $0.3719
C)   $0.3910
D)   $1.2798
E)   None of these answers are correct.

Question 6

Use the following data for a two-period binomial model to answer the questions that follow.
- The stock's price S is $100.After three months,it either goes up and gets multiplied by the factor U = 1.13847256,or it goes down and gets multiplied by the factor
D = 0.88664332.
- Options mature after T = 0.5 year and have a strike price of K = $105.
- The continuously compounded risk-free interest rate r is 5 percent per year.
-If the stock pays a $1 dividend just before the end of the first three months,then today's price of a European call is:

Accepted Answer

A)   $4.86
B)   $5.73
C)   $6.00
D)   $11.59
E)   None of these answers are correct.

Question 7

Which of the following statements about option pricing in a multiperiod framework using synthetic construction is INCORRECT?

Accepted Answer

A)   The two assets,a stock and a money market account,dynamically complete the market by matching all possible option values at maturity.
B)   The replicating portfolio is self-financing.
C)   The replicating portfolio is arbitrage-free.
D)   Option prices obtained for different period setups are different.
E)   The pricing model estimates real-world probabilities and uses them for the expected payoff computations.

Question 8

Use the following data for a two-period binomial model to answer the questions that follow.
- The stock's price S is $100.After three months,it either goes up and gets multiplied by the factor U = 1.13847256,or it goes down and gets multiplied by the factor
D = 0.88664332.
- Options mature after T = 0.5 year and have a strike price of K = $105.
- The continuously compounded risk-free interest rate r is 5 percent per year.
-If the stock pays a $1 dividend just before the end of the first three months,then today's price of a European put is:

Accepted Answer

A)   $2.44
B)   $5.73
C)   $9.12
D)   $16.03
E)   None of these answers are correct.

Question 9

For a stock price following a binomial process,the up factor U = 1.1,the down factor D= 0.9,the dollar return (1 +R)= 1.05 percent (per period),and the initial stock price is 100.The probability that the stock will have 18 up movements and 2 down movements is:

Accepted Answer

A)   0.0556
B)   0.0669
C)   0.075
D)   0.10
E)   None of these answers are correct.

Question 10

Use the following data for an eight-period binomial model to answer the questions that follow.
- The stock's price S is $100.The stock price evolves according to an eight-period binomial model.
- Options mature after T = 1 year and have a strike price of K = $70.
- The continuously compounded risk-free interest rate r is 5 percent per year.
- The annualized volatility of stock price returns $\sigma$ = 0.25 or 25 percent per year.
-Today's price of a European call in this eight-period binomial model is:

Accepted Answer

A)   $11.7628
B)   $33.4139
C)   $33.7858
D)   $36.4527
E)   None of these answers are correct.

Question 11

To create the arbitrage-free synthetic put after one period (in the down state)you need to:

Accepted Answer

A)   short sell 1 share of the stock and buy 103.70 units of the money market account
B)   short sell 0.14 shares of the stock and buy 18.12 units of the money market account
C)   buy 0.48 shares of the stock and short sell 42.2642 units of the money market account
D)   buy 0.9343 shares of the stock and short sell 93.2677 units of the money market account
E)   None of these answers are correct.

Question 12

The formula for pricing options by repeated application of risk-neutral pricing is given by which of the following formulas,where  $\pi$ = [(1 + R)- D]/(U - D);U and D are the up and down factors,respectively; (1 + R)is the dollar return;optionU is the option price at the next node in the up state;and optionD is the option price at the next node in the down state?

Accepted Answer

A)   option price= [  π\piπ  * option U + (1 -  π\piπ ) * optionD] * (1 + R) 
B)   option price = [  π\piπ * option U + (1 -   π\piπ ) * optionD] / R
C)   option price = [  π\piπ * option U +(1 -  π\piπ ) *optionD] / (1 +R) 
D)   option price = [  π\piπ 2 * option U + (1 - π\piπ ) 2*optionD] * (1 +R) 
E)   None of these answers are correct.

Question 13

Use the following data for a two-period binomial model to answer the questions that follow.
- The stock's price S is $100.After three months,it either goes up and gets multiplied by the factor U = 1.13847256,or it goes down and gets multiplied by the factor
D = 0.88664332.
- Options mature after T = 0.5 year and have a strike price of K = $105.
- The continuously compounded risk-free interest rate r is 5 percent per year.
-If the stock pays a 1 percent dividend just before the end of the first three months,then today's price of a European put is:

Accepted Answer

A)   $8.41
B)   $9.09
C)   $9.12
D)   $10.03
E)   None of these answers are correct.

Question 14

Which set of arbitrage-free put prices (in dollars)is correct?

Accepted Answer

A)   p = 2.00,pU = 0,and pD = 4.06
B)   p = 8.41,pU = 2.00,and pD = 15.03
C)   p =15.03,pU = 4.06,and pD = 26.39
D)   p = 8.41,pU F=0,and pD = 26.39
E)   None of these answers are correct.

Question 15

Which of the following statements about the multiperiod binomial option pricing model is INCORRECT?

Accepted Answer

A)   The pricing technique is described as forward induction.
B)   The pricing technique is described as backward induction.
C)   When the model's parameters are properly set and the model is run over many small intervals,then it gives an answer that approaches the Black-Scholes-Merton model value.
D)   The binomial model can be used to price exotic options.
E)   Strictly speaking,the binomial model is not a separate model but an approximation method.

Question 16

Use the following data for a two-period binomial model to answer the questions that follow.
- The stock's price S is $100.After three months,it either goes up and gets multiplied by the factor U = 1.13847256,or it goes down and gets multiplied by the factor
D = 0.88664332.
- Options mature after T = 0.5 year and have a strike price of K = $105.
- The continuously compounded risk-free interest rate r is 5 percent per year.
-If the stock pays a 1 percent dividend just before the end of the first three months,then today's price of a European call is:

Accepted Answer

A)   $5.69
B)   $5.73
C)   $6.00
D)   $7.96
E)   None of these answers are correct.

Question 17

Suppose a trader quotes a call price of $4.50.Then,you can make an immediate arbitrage profit of:

Accepted Answer

A)   $1.50 by buying the synthetic call and selling the market-quoted call
B)   $1.50 by selling the synthetic call and buying the market-quoted call
C)   $7.66 by buying the synthetic call and selling the market-quoted call
D)   $7.66 by selling the synthetic call and buying the market-quoted call
E)   None of these answers are correct.

Question 18

To create the arbitrage-free synthetic put today,you need to:

Accepted Answer

A)   buy 0.48 shares of the stock and short sell 42.2642 units of the money market account
B)   short sell 1 share of the stock and buy 103.70 units of the money market account
C)   short sell 0.14 shares of the stock and buy 18.12 units of the money market account
D)   short sell 0.52 shares of the stock and buy 60.14 units of the money market account
E)   None of these answers are correct.

Question 19

To create the arbitrage-free synthetic call after one period (in the up state)you need to:

Accepted Answer

A)   buy 0.8585 shares of the stock and short sell 85.5777 units of the money market account
B)   buy 0.4827 shares of the stock and short sell 42.2642 units of the money market account
C)   buy 0.8585 shares of the stock and short sell 42.2642 units of the money market account
D)   buy 0.9343 shares of the stock and short sell 93.2677 units of the money market account
E)   None of these answers are correct.

Question 20

Today's price of an American call option is:

Accepted Answer

A)   $4.86
B)   $5.73
C)   $6.00
D)   $11.59
E)   None of these answers are correct.

Exam 18: Multiperiod Binomial Model

Which of the following statements is INCORRECT? A binomial model may be used for valuing:

Today's price of an American put option is:

Which of the following statements about option pricing in a multiperiod framework using synthetic construction is INCORRECT?

For a stock price following a binomial process,the up factor U = 1.1,the down factor D= 0.9,the dollar return (1 +R) = 1.05 percent (per period) ,and the initial stock price is 100.The probability that the stock will have 18 up movements and 2 down movements is:

To create the arbitrage-free synthetic put after one period (in the down state) you need to:

Which set of arbitrage-free put prices (in dollars) is correct?

Which of the following statements about the multiperiod binomial option pricing model is INCORRECT?

Suppose a trader quotes a call price of $4.50.Then,you can make an immediate arbitrage profit of:

To create the arbitrage-free synthetic put today,you need to:

To create the arbitrage-free synthetic call after one period (in the up state) you need to:

Today's price of an American call option is: