Exam 13: Implementing the Binomial Model

Suppose returns on a stock are lognormally distributed with expected (annualized) mean of of 0.10 and standard deviation of 0.20. What is the expected simple return on the stock for one month?

Suppose that the stock price is stochastic (say, lognormal) with constant volatility, and that the interest rate, though not stochastic changes from period to period on the tree. Which of the following statements is valid?

If $x$ is normally distributed with mean $\mu$ and variance $\sigma ^ { 2 }$ , then $y = e ^ { x }$ is

Suppose returns on a stock are lognormally distributed with expected (annualized) mean of of 0.10 and standard deviation of 0.20. What is the expected continuously compounded return on the stock for one month?

Suppose returns on a stock are lognormally distributed with expected (annualized) mean of of 0.10 and standard deviation of 0.20. What is the standard deviation of simple return on the stock for one month?

Stock ABC is currently trading at 100. The stock has lognormal returns with with $\mu = 0$ and $\sigma = 0.40$ . What is the 95% confidence interval for the stock price in 3 months?

Consider a binomial tree in which the stock moves up by a factor $2 i$ and down by a factor $d$ , respectively with probabilities $p$ and $1 - p$ . The variance of log-returns per time step is given by the following formula:

While stock returns are commonly modeled as lognormal, bond returns are less ideally modeled as lognormal because

Suppose the returns on a stock are lognormally distributed with $\mu = 0$ and $\sigma = 0.2$ . The expected three-month simple returns on the stock are

As the number of steps in the CRR binomial tree increases (keeping maturity fixed), the solution "converges" to a limit result. Which of the following statements characterizes this convergence best?

Suppose you are modeling the price evolution of a stock on a tree using a general version of the CRR model. The stock price is stochastic (lognormal), but the rate of interest each time step may not be the same, and the time step itself may be different across periods. The following is sufficient for a binomial tree representation of the stock price process to be recombining:

Suppose returns on a stock are lognormally distributed with expected (annualized) mean of of 0.10 and standard deviation of 0.20. What is the standard deviation of the continuously compounded return on the stock for one month?

In the Jarrow-Rudd (JR) binomial model, the volatility is given as $\sigma = 0.2$ . The risk-free rate of interest is 2%. What is the risk-neutral probability of an up move on a binomial tree with a time step of one month?

Which of the following statements is most valid for the recursive programming of a binomial tree for pricing options?

If $\ln x$ is normally distributed with mean $\mu$ and variance $\sigma ^ { 2 }$ , then $x$ is

Assume that a stock has lognormal returns with mean $\mu = 0.10$ and standard deviation $\sigma = 0.20$ . The current stock price is $50. What is a 95% confidence interval for the stock price in six months?

Let $S _ { T }$ denote the time- $T$ price of a stock and $S _ { 0 }$ its current price. Suppose that for any $T$ , $\ln \left( \frac { S _ { T } } { S _ { 0 } } \right) : N \left( \mu _ { T } , \sigma ^ { 2 } T \right)$ for constant annual parameters $\mu$ and $\sigma$ . What does this imply about the returns process? Pick the most accurate of the following alternatives:

In the Cox-Ross-Rubinstein (CRR) binomial model, the volatility is given as $\sigma = 0.2$ . The risk-free rate of interest is 2%. What is the risk-neutral probability of an up move on a binomial tree with a time step of one month?