QFC Quantitative Finance Modeling & Valuation 3

Question 1

In the Black-Scholes model, which parameter directly measures the market's expectation of future price variability of the underlying asset?

Accepted Answer

Implied volatility (σ)

Answer

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?

Accepted Answer

13.33%

Answer

WACC = 0.4×5% + 0.6×Ke → 10% = 2% + 0.6×Ke → 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?

Accepted Answer

Capital structure does not affect firm value

Answer

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 × e^(rT). What does this formula prevent?

Accepted Answer

Risk-free arbitrage

Answer

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?

Accepted Answer

Binomial lattice or finite difference method

Answer

Lattice and PDE/finite-difference methods can enforce early-exercise constraints at each node, unlike the closed-form Black-Scholes formula.

(QFC) Quantitative Finance Certification Practice Test