Module 6.1 - Lognormal Distribution & Simulation Techniques Flashcards
(23 cards)
What is the lognormal distribution generated by?
The function ex, where x is normally distributed.
Why are the logarithms of lognormally distributed random variables normally distributed?
Because the natural logarithm, ln, of ex is x.
What is the formula for asset price at time T?
PT = P0e^r0,T
In the formula PT = P0e^r0,T, what does P0 represent?
Asset price at time 0 (today).
What does r0,T stand for in the asset pricing formula?
Continuously compounded return on the asset from time 0 to time T.
What property allows us to state that r0,T is normally distributed?
The central limit theorem.
If returns are independently distributed, what does that imply?
Past returns are not useful for predicting future returns.
When returns are identically distributed what is the importance of stationarity in time series modeling?
Mean and variance do not change over time.
What is Monte Carlo simulation based on?
The repeated generation of one or more risk factors.
What must the analyst specify for each risk factor in Monte Carlo simulation?
The parameters of the probability distribution that the risk factor is assumed to follow.
What is the purpose of generating random values for each risk factor in Monte Carlo simulation?
To value the security using a pricing model.
What can Monte Carlo simulation help estimate regarding a portfolio of assets?
Value at risk (VaR).
What is one advantage of Monte Carlo simulation?
Its inputs are not limited to the range of historical data.
What is a limitation of Monte Carlo simulation?
It is fairly complex and relies on the assumptions about the distributions of risk factors.
What is resampling used for in simulations?
Generating data inputs when population data is unavailable.
What is bootstrap resampling?
Drawing repeated samples of size n from the full dataset with replacement.
What can be inferred from bootstrap resampling?
Parameters for the population, such as mean and variance.
How does simulation using bootstrap resampling differ from Monte Carlo simulation?
The source and scope of the data.
For a lognormal distribution, the probability of a negative outcome is _______.
Zero
If random variable Y follows a lognormal distribution then the natural log of Y must be:
Normally distributed
One of the major limitations of Monte Carlo simulation is that it______.
Cannot provide the insight that analytical methods can.
If a random variable X is lognormally distributed then ln(X) is ______.
Normally distributed
Lognormal distribution returns are used for asset pricing models because ______.
This will not result in asset returns of less than -100%.
