QFC Quantitative Finance Risk & Derivatives 2 — Questions and Answers
Question 1: A portfolio has a 1-day 99% VaR of $1 million. Under the square-root-of-time rule, what is the approximate 10-day 99% VaR?
- $3.16 million (Correct answer)
- $10 million
- $1.41 million
- $7.07 million
Correct answer: $3.16 million
The 10-day VaR scales by √10 ≈ 3.162, so $1M × 3.162 ≈ $3.16 million.
Question 2: Which Greeks measure an option's sensitivity to the passage of time?
- Delta
- Gamma
- Theta (Correct answer)
- Vega
Correct answer: Theta
Theta measures the rate of decline in an option's value as time passes, often called time decay.
Question 3: In the Black-Scholes model, increasing implied volatility has what effect on both call and put option prices?
- Increases both (Correct answer)
- Decreases both
- Increases calls, decreases puts
- Decreases calls, increases puts
Correct answer: Increases both
Higher volatility increases the probability of large moves in either direction, raising the value of both calls and puts.
Question 4: A credit default swap (CDS) provides protection to the buyer by:
- Paying a premium stream to the protection seller
- Receiving par value from the seller if a credit event occurs (Correct answer)
- Exchanging fixed for floating interest rate payments
- Delivering equity shares upon default
Correct answer: Receiving par value from the seller if a credit event occurs
Upon a qualifying credit event, the CDS protection seller pays the buyer the difference between par and recovery value (or delivers par in exchange for the defaulted bond).
Question 5: Expected Shortfall (ES) at the 95% confidence level is best described as:
- The loss at exactly the 95th percentile
- The average loss in the worst 5% of scenarios (Correct answer)
- The maximum possible loss
- The median loss across all scenarios
Correct answer: The average loss in the worst 5% of scenarios
ES (also called CVaR) equals the conditional expected loss given that the loss exceeds the VaR threshold, i.e., the mean of the tail beyond the confidence level.
Question 6: A 'protective put' strategy involves:
- Buying a put and shorting the underlying stock
- Buying a put on a stock you already own long (Correct answer)
- Selling a put against a long call position
- Writing a covered put on a short stock position
Correct answer: Buying a put on a stock you already own long
A protective put combines a long stock position with a long put, providing downside insurance while retaining upside participation.
Question 7: Under the CIR (Cox-Ingersoll-Ross) model, what feature prevents interest rates from becoming negative?
- A cap imposed on the drift term
- The square root of the rate in the diffusion coefficient (Correct answer)
- A reflecting boundary at zero volatility
- Mean reversion toward a negative long-run level
Correct answer: The square root of the rate in the diffusion coefficient
The CIR model uses √r in the diffusion term, so as rates approach zero the stochastic shock also approaches zero, preventing rates from going negative.
QFC Quantitative Finance Risk & Derivatives 2
A portfolio has a 1-day 99% VaR of $1 million.
Under the square-root-of-time rule, what is the approximate 10-day 99% VaR?