QFC Quantitative Finance Risk & Derivatives 3 — Questions and Answers
Question 1: What does a negative convexity in a bond's price-yield relationship typically indicate?
- The bond benefits more from yield decreases than it loses from yield increases
- Price increases slow down as yields fall, as with callable bonds (Correct answer)
- Duration is zero at all yield levels
- The bond is priced at a premium to par
Correct answer: Price increases slow down as yields fall, as with callable bonds
Negative convexity, common in callable bonds, means price appreciation is limited as yields fall because the issuer is likely to call the bond.
Question 2: In a plain vanilla interest rate swap, the fixed-rate payer is effectively:
- Long a fixed-rate bond and short a floating-rate bond
- Short a fixed-rate bond and long a floating-rate bond (Correct answer)
- Long both a fixed and a floating bond
- Neutral to interest rate movements
Correct answer: Short a fixed-rate bond and long a floating-rate bond
Paying fixed and receiving floating is economically equivalent to shorting a fixed-rate bond and being long a floating-rate note.
Question 3: Model risk in quantitative finance primarily refers to:
- The risk that market prices move against a position
- Losses due to incorrect or misapplied financial models (Correct answer)
- Counterparty default on OTC derivatives
- Liquidity risk in emerging market securities
Correct answer: Losses due to incorrect or misapplied financial models
Model risk arises when a pricing or risk model is misspecified, incorrectly calibrated, or used outside its valid assumptions, leading to flawed valuations or hedges.
Question 4: The risk-neutral measure Q differs from the real-world measure P in that under Q:
- Investors demand a positive risk premium
- All assets are expected to earn the risk-free rate (Correct answer)
- Volatility is set to its historical estimate
- Dividends are excluded from asset pricing
Correct answer: All assets are expected to earn the risk-free rate
Under the risk-neutral (pricing) measure, discounted asset prices are martingales and assets are priced as if investors require no risk premium beyond the risk-free rate.
Question 5: A 'bull call spread' is constructed by:
- Buying a lower-strike call and selling a higher-strike call with the same expiry (Correct answer)
- Buying both a call and a put with the same strike and expiry
- Selling a lower-strike call and buying a higher-strike call
- Buying a call and shorting the underlying stock
Correct answer: Buying a lower-strike call and selling a higher-strike call with the same expiry
A bull call spread profits from a moderate rise in the underlying by buying a lower-strike call and selling a higher-strike call, capping both potential gain and net cost.
Question 6: Which of the following best defines 'liquidity risk' in derivatives markets?
- The risk that a counterparty defaults on its obligations
- The risk that a position cannot be exited at a fair price without significant market impact (Correct answer)
- The risk that settlement systems fail to process trades
- The risk that interest rates change unexpectedly
Correct answer: The risk that a position cannot be exited at a fair price without significant market impact
Liquidity risk in derivatives refers to the difficulty of unwinding or hedging a position without incurring large bid-ask spreads or moving the market adversely.
Question 7: In Monte Carlo simulation for option pricing, increasing the number of simulated paths primarily:
- Eliminates bias from the discretization scheme
- Reduces the standard error of the price estimate (Correct answer)
- Increases the speed of convergence exponentially
- Removes the need for variance reduction techniques
Correct answer: Reduces the standard error of the price estimate
Standard error of a Monte Carlo estimator decreases as 1/√N, so more paths reduce estimation uncertainty but do not eliminate discretization bias.
QFC Quantitative Finance Risk & Derivatives 3
What does a negative convexity in a bond's price-yield relationship typically indicate?