CS422: Stochastic Models and Monte Carlo Quiz

• Continuous random variable

• Discrete random variable

• Mixed random variable

• Deterministic variable

Which of the following best describes a stochastic process?

• A process that always produces the same output given the same input

• A collection of random variables indexed by time or space

• A deterministic mathematical function with no uncertainty

• A process that only applies to financial models

In a Monte Carlo simulation, what is the primary purpose of generating a large number of random samples?

• To eliminate all uncertainty from the model

• To approximate the probability distribution of an outcome through repeated random sampling

• To find the exact analytical solution to a problem

• To reduce the number of variables in the model

• Normal distribution

• Poisson distribution

• Binomial distribution

• Exponential distribution

In a Monte Carlo simulation, increasing the number of iterations from 1,000 to 1,000,000 will generally:

• Increase the bias of the estimate

• Decrease the variance of the estimate and improve accuracy

• Have no effect on the accuracy of the simulation

• Make the simulation deterministic

Which of the following statements correctly describes the Central Limit Theorem in the context of Monte Carlo simulations?

• The sum of random variables always follows a uniform distribution

• As the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the original distribution

• The variance of a simulation always decreases to zero as sample size increases

• Monte Carlo simulations only work when the underlying distribution is normal

A stochastic model is used to simulate stock prices. The model assumes that daily returns are independent and identically distributed. A financial analyst notices that during market crashes, returns are highly correlated. This observation suggests:

• The model is perfectly accurate

• The independence assumption of the model is violated during extreme market conditions

• The model should use a Poisson distribution instead

• The number of simulations needs to be reduced