Question 1

Which of the following is true when the stock price follows geometric Brownian motion

Accepted Answer

A)   The future stock price has a normal distribution
B)   The future stock price has a lognormal distribution
C)   The future stock price has geometric distribution
D)   The future stock price has a truncated normal distribution

Question 2

If a variable x follows the process dx = b dz where dz is a Wiener process,which of the following is the process followed by y = exp(x) .

Accepted Answer

A)   dy = by dz
B)   dy = 0.5b2y dt+by dz
C)   dy = (y+0.5b2y)  dt+by dz
D)   dy = 0.5b2y dt+b dz

Question 3

If e is a random sample from a standard normal distribution,which of the following is the change in a Wiener process in time dt .

Accepted Answer

A)   e times the square root of dt
B)   e times dt
C)   dt times the square root of e
D)   The square root of e times the square root of dt

Question 4

Which of the following defines an Ito process?

Accepted Answer

A)   A process where the drift is non-constant and can be stochastic
B)   A process where the coefficient of dz is non-constant and can be stochastic
C)   A process where either the drift or the coefficient of dz or both are non-constant and can be stochastic
D)   A process where proportional changes follow a generalized Wiener process C

Question 5

If a stock price follows a Markov process which of the following could be true

Accepted Answer

A)   Whenever the stock price has gone up for four successive days it has a 70% chance of going up on the fifth day.
B)   Whenever the stock price has gone up for four successive days there is almost certain to be a correction on the fifth day.
C)   The way the stock price moves on a day is unaffected by how it moved on the previous four days.
D)   Bad years for stock price returns are usually followed by good years. C

Question 6

When a stock price,S,follows geometric Brownian motion with mean return m and volatility s what is the process follows by X where X = ln S.

Accepted Answer

A)   dX = m dt + s dz
B)   dX = (m−r)  dt + s dz
C)   dX = (m −s2)  dt + s dz
D)   dX = (m − s2/2)  dt + s dz

Question 7

A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz
Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What the standard deviation of the value of the variable at the end of 5 years

Accepted Answer

A)   6.2
B)   6.7
C)   7.2
D)   7.7

Question 8

For what value of the correlation between two Wiener processes is the sum of the processes also a Wiener process?

Accepted Answer

A)   0.5
B)   −0.5
C)   0
D)   1

Question 9

The process followed by a variable X is dX = mX dt+sX dz
What is the coefficient of dz in the process for the square of X.

Accepted Answer

A)   sX
B)   sX2
C)   2sX2
D)   msX C

Question 10

A stock price is $20.It has an expected return of 12% and a volatility of 25%.What is the standard deviation of the change in the price in one day.(For this question assume that there are 365 days in the year.)

Accepted Answer

A)   $0.20
B)   $0.23
C)   $0.26
D)   $0.29

Question 11

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz
Where time is measured in years.If a = 3 and b =4 what is the standard deviation of the value in 4 years?

Accepted Answer

A)   4
B)   8
C)   12
D)   16

Question 12

A stock price is $20.It has an expected return of 12% and a volatility of 25%.What is the stock price that has a 2.5% chance of being exceeded in one day? (For this question assume that there are 365 days in the year.)

Accepted Answer

A)   $20.41
B)   $20.51
C)   $20.61
D)   $20.71

Question 13

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz
If a = 3 and b =4 what is the standard deviation of the value in three months?

Accepted Answer

A)   1
B)   2
C)   3
D)   4

Question 14

The variance of a Wiener process in time t is

Accepted Answer

A)   t
B)   t squared
C)   the square root of t
D)   t to the power of 4

Question 15

If the risk-free rate is r and price of a nondividend paying stock grows at rate m with volatility s,at what rate does a forward price of the stock grow for a forward contract maturing at a future time T.

Accepted Answer

A)   m
B)   m−s2/2
C)   m−r
D)   r−s2/2

Question 16

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz
Where time is measured in years.If a = 2 and b =3 what is the expected value after 3 years?

Accepted Answer

A)   12
B)   14
C)   16
D)   18

Question 17

A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz
Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What is the expected value of the variable at the end of 5 years

Accepted Answer

A)   16
B)   20
C)   24
D)   30

Question 18

The process followed by a variable X is dX = mX dt+sX dz
What is the coefficient of dt in the process for the square of X.

Accepted Answer

A)   2mX2+s2X2
B)   2mX2
C)   mX2+2s2X2
D)   mX2+s2X2

Question 19

Which of the following gives a random sample from a standard normal distribution in Excel?

Accepted Answer

A)   =NORMSINV() 
B)   =NORMSINV(RAND() ) 
C)   =RND(NORMSINV() ) 
D)   =RAND()

Exam 14: Wiener Processes and Itos Lemma

Which of the following is true when the stock price follows geometric Brownian motion

Correct Answer
verified

If a variable x follows the process dx = b dz where dz is a Wiener process,which of the following is the process followed by y = exp(x) .

Correct Answer
verified

If e is a random sample from a standard normal distribution,which of the following is the change in a Wiener process in time dt .

Correct Answer
verified

Which of the following defines an Ito process?

Correct Answer
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C

If a stock price follows a Markov process which of the following could be true

Correct Answer
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C

When a stock price,S,follows geometric Brownian motion with mean return m and volatility s what is the process follows by X where X = ln S.

Correct Answer
verified

A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What the standard deviation of the value of the variable at the end of 5 years

Correct Answer
verified

For what value of the correlation between two Wiener processes is the sum of the processes also a Wiener process?

Correct Answer
verified

The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dz in the process for the square of X.

Correct Answer
verified
C

A stock price is $20.It has an expected return of 12% and a volatility of 25%.What is the standard deviation of the change in the price in one day.(For this question assume that there are 365 days in the year.)

Correct Answer
verified

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.If a = 3 and b =4 what is the standard deviation of the value in 4 years?

Correct Answer
verified

A stock price is $20.It has an expected return of 12% and a volatility of 25%.What is the stock price that has a 2.5% chance of being exceeded in one day? (For this question assume that there are 365 days in the year.)

Correct Answer
verified

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz If a = 3 and b =4 what is the standard deviation of the value in three months?

Correct Answer
verified

The variance of a Wiener process in time t is

Correct Answer
verified

If the risk-free rate is r and price of a nondividend paying stock grows at rate m with volatility s,at what rate does a forward price of the stock grow for a forward contract maturing at a future time T.

Correct Answer
verified

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.If a = 2 and b =3 what is the expected value after 3 years?

Correct Answer
verified

A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What is the expected value of the variable at the end of 5 years

Correct Answer
verified

The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dt in the process for the square of X.

Correct Answer
verified

Which of the following gives a random sample from a standard normal distribution in Excel?

Correct Answer
verified

Exam 14: Wiener Processes and Itos Lemma

Which of the following is true when the stock price follows geometric Brownian motion

Correct AnswerverifiedShow Answer

If a variable x follows the process dx = b dz where dz is a Wiener process,which of the following is the process followed by y = exp(x) .

Correct AnswerverifiedShow Answer

If e is a random sample from a standard normal distribution,which of the following is the change in a Wiener process in time dt .

Correct AnswerverifiedShow Answer

Which of the following defines an Ito process?

Correct AnswerverifiedC

If a stock price follows a Markov process which of the following could be true

Correct AnswerverifiedC

When a stock price,S,follows geometric Brownian motion with mean return m and volatility s what is the process follows by X where X = ln S.

Correct AnswerverifiedShow Answer

A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What the standard deviation of the value of the variable at the end of 5 years

Correct AnswerverifiedShow Answer

For what value of the correlation between two Wiener processes is the sum of the processes also a Wiener process?

Correct AnswerverifiedShow Answer

The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dz in the process for the square of X.

Correct AnswerverifiedC

A stock price is $20.It has an expected return of 12% and a volatility of 25%.What is the standard deviation of the change in the price in one day.(For this question assume that there are 365 days in the year.)

Correct AnswerverifiedShow Answer

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.If a = 3 and b =4 what is the standard deviation of the value in 4 years?

Correct AnswerverifiedShow Answer

A stock price is $20.It has an expected return of 12% and a volatility of 25%.What is the stock price that has a 2.5% chance of being exceeded in one day? (For this question assume that there are 365 days in the year.)

Correct AnswerverifiedShow Answer

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz If a = 3 and b =4 what is the standard deviation of the value in three months?

Correct AnswerverifiedShow Answer

The variance of a Wiener process in time t is

Correct AnswerverifiedShow Answer

If the risk-free rate is r and price of a nondividend paying stock grows at rate m with volatility s,at what rate does a forward price of the stock grow for a forward contract maturing at a future time T.

Correct AnswerverifiedShow Answer

A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.If a = 2 and b =3 what is the expected value after 3 years?

Correct AnswerverifiedShow Answer

A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What is the expected value of the variable at the end of 5 years

Correct AnswerverifiedShow Answer

The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dt in the process for the square of X.

Correct AnswerverifiedShow Answer

Which of the following gives a random sample from a standard normal distribution in Excel?

Correct AnswerverifiedShow Answer

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C

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C

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C

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