[OFOD10e14] Wiener Processes and Ito’s Lemma

* 基本信息：

* 1.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?

* 2.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?

* 3.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?

* 4.The variance of a Wiener process in time t is

* 5.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.

* 6.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.

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

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

* 9.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

* 10.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

* 11.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).

* 12.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.

* 13.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.

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

* 15.Which of the following defines an Ito process?

* 16.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.)

* 17. 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.)

* 18.Which of the following is NOT a property of a Wiener process?

* 19. 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 .

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