Monte Carlo Simulation & VaR Flashcards
7 cards from real CRA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Monte Carlo Simulation & VaR flashcards as text
Which variance reduction technique in Monte Carlo simulation uses pairs of random numbers that are negatively correlated to reduce estimation error?
Answer: Antithetic variates
Antithetic variates generates pairs of random numbers (u, 1-u) that are negatively correlated, averaging their outcomes to reduce variance in the estimate.
A 10-day 99% VaR of $5 million means there is a 1% probability that losses will exceed $5 million over:
Answer: A 10-trading-day period
The time horizon is explicitly stated in the VaR definition — a 10-day 99% VaR refers to losses over a 10-trading-day holding period.
In Monte Carlo VaR, which distribution assumption is most commonly used to model daily equity returns as a starting point?
Answer: Lognormal distribution
Equity prices are typically modeled as lognormal, meaning daily log-returns follow a normal distribution, which is the standard starting point in Monte Carlo equity VaR models.
What is the primary purpose of using a Cholesky decomposition in a multi-asset Monte Carlo simulation?
Answer: To incorporate correlation structure between assets
Cholesky decomposition of the correlation matrix is used to generate correlated random variables, ensuring simulated asset returns reflect observed correlations.
Expected Shortfall (ES) at the 99% confidence level is best described as:
Answer: The average loss in the worst 1% of scenarios
ES (also called CVaR) is the conditional expectation of losses given that the loss exceeds the VaR threshold — i.e., the average of the worst 1% of outcomes.
Which of the following is a key advantage of Monte Carlo VaR over Historical Simulation VaR?
Answer: It can model complex, path-dependent instruments
Monte Carlo simulation can price path-dependent derivatives (e.g., Asian options, barrier options) by generating full price paths, which Historical Simulation cannot easily handle.
If a firm scales its 1-day VaR to a 10-day VaR using the square-root-of-time rule, which critical assumption is being made?
Answer: Daily returns are i.i.d. (independent and identically distributed)
The square-root-of-time scaling rule is valid only when daily returns are i.i.d., so that variance scales linearly with time.