QFC Quantitative Finance Modeling & Valuation 2

Question 1

In a binomial option pricing model, what happens to the option price as the number of time steps approaches infinity?

Accepted Answer

It approaches the Black-Scholes price

Answer

As the number of binomial steps increases, the discrete binomial model converges to the continuous Black-Scholes model.

Question 2

The Gordon Growth Model (GGM) values a stock as D1 / (r - g). Which condition must hold for this formula to be valid?

Accepted Answer

The growth rate g must be less than the discount rate r

Answer

GGM requires r > g; if g ≥ r, the denominator is non-positive and the model produces a nonsensical or infinite value.

Question 3

Which sensitivity measure captures the rate of change of an option's delta with respect to the underlying asset price?

Accepted Answer

Gamma

Answer

Gamma (Γ) is the second derivative of the option price with respect to the underlying price, measuring how fast delta changes.

Question 4

In discounted cash flow (DCF) valuation, the terminal value using the perpetuity growth method is most sensitive to which input?

Accepted Answer

The assumed long-run growth rate

Answer

Small changes in the perpetuity growth rate dramatically alter terminal value because it appears in the denominator (WACC – g).

Question 5

A zero-coupon bond with a face value of $1,000 matures in 5 years. If the continuously compounded rate is 4%, what is its present value?

Accepted Answer

$818.73

Answer

PV = 1000 × e^(−0.04×5) = 1000 × e^(−0.20) ≈ $818.73 under continuous compounding.

(QFC) Quantitative Finance Certification Practice Test