QFC Quantitative Finance Modeling & Valuation 3 β Questions and Answers
Question 1: In the Black-Scholes model, which parameter directly measures the market's expectation of future price variability of the underlying asset?
- Implied volatility (Ο) (Correct answer)
- Delta (Ξ)
- The risk-free rate (r)
- Time to expiry (T)
Correct answer: Implied volatility (Ο)
Implied volatility, backed out from market option prices, reflects the market's consensus forecast of future realized volatility.
Question 2: A company's WACC is 10% and its after-tax cost of debt is 5%. If the firm is 40% debt-financed, what is its cost of equity?
- 13.33% (Correct answer)
- 10.00%
- 8.33%
- 15.00%
Correct answer: 13.33%
WACC = 0.4Γ5% + 0.6ΓKe β 10% = 2% + 0.6ΓKe β Ke = 8%/0.6 = 13.33%.
Question 3: Which of the following is an assumption of the Modigliani-Miller theorem in a world with no taxes?
- Capital structure does not affect firm value (Correct answer)
- Debt always increases firm value via the tax shield
- Equity is always cheaper than debt
- Dividend policy determines firm value
Correct answer: Capital structure does not affect firm value
In a perfect market with no taxes, MM Proposition I states that firm value is independent of its capital structure.
Question 4: A forward contract on a non-dividend-paying stock is priced as F = S Γ e^(rT). What does this formula prevent?
- Risk-free arbitrage (Correct answer)
- Market illiquidity
- Credit risk exposure
- Volatility clustering
Correct answer: Risk-free arbitrage
The cost-of-carry formula ensures the forward price equals the cost of owning the stock through maturity, eliminating riskless profit opportunities.
Question 5: Which numerical method is most appropriate for pricing American options that cannot be handled analytically by Black-Scholes?
- Binomial lattice or finite difference method (Correct answer)
- Fourier transform
- Monte Carlo simulation with variance reduction
- Newton-Raphson root finding
Correct answer: Binomial lattice or finite difference method
Lattice and PDE/finite-difference methods can enforce early-exercise constraints at each node, unlike the closed-form Black-Scholes formula.
Question 6: Enterprise Value (EV) equals market capitalization plus total debt minus what?
- Cash and cash equivalents (Correct answer)
- Goodwill and intangibles
- Capital expenditures
- Retained earnings
Correct answer: Cash and cash equivalents
EV = Market Cap + Debt β Cash, because cash can immediately repay debt and is thus not a core operating asset.
Question 7: In a Monte Carlo simulation for option pricing, increasing the number of simulation paths primarily improves which quality of the estimate?
- Statistical precision (reduces standard error) (Correct answer)
- Model accuracy by correcting for fat tails
- Speed of computation
- Accuracy of the implied volatility estimate
Correct answer: Statistical precision (reduces standard error)
By the law of large numbers, more paths reduce the standard error of the estimated expected payoff, improving statistical precision.
QFC Quantitative Finance Modeling & Valuation 3
In the Black-Scholes model, which parameter directly measures the market's expectation of future price variability of the underlying asset?