Free CFA Level II Derivatives Practice Questions (2026)

Sample Questions

Question 1 Easy

In options trading, implied volatility is best described as:

Solution

C is correct.

Volatility is the only BSM input that is not directly observable. Traders therefore invert the model: they take the market price as given and solve for the volatility that reproduces it. That value is the implied volatility, and it is used as a common metric for quoting and comparing option prices across strikes and maturities, and for judging whether an option looks rich or cheap relative to a trader's own volatility forecast.

Question 2 Medium

An FRA described as a 6x12 FRA covers a borrowing period that:

Solution

B is correct.

An FRA described as 'AxB' (e.g., 6x12) means:
- The FRA settlement date is in A months (6 months from today).
- The underlying loan period ends in B months (12 months from today).
- The FRA covers the period from month 6 to month 12 (a 6-month borrowing period).

So a 6x12 FRA is a forward agreement on the 6-month interest rate, starting 6 months from now.

Question 3 Hard

Using the Black model, the value of the payer swaption described in the vignette is closest to:

Solution

A is correct.

The Black model value for a payer swaption is:

V_{\text{payer}} = \text{Notional} \times A \times [F \cdot N(d_1) - K \cdot N(d_2)]

where

F = 0.0520

(forward swap rate),

K = 0.0450

(strike rate),

A = 2.6085

(annuity factor),

\sigma = 0.18

T = 1

year. Step 1 — Compute

d_1

and

d_2

d_1 = \frac{\ln(F/K) + \frac{1}{2}\sigma^2 T}{\sigma\sqrt{T}} = \frac{\ln(0.052/0.045) + 0.5 \times 0.0324}{0.18} = \frac{0.14539 + 0.0162}{0.18} = \frac{0.16159}{0.18} = 0.8933

d_2 = d_1 - \sigma\sqrt{T} = 0.8933 - 0.18 = 0.7133

Step 2 — Standard normal CDF values:

N(0.8933) \approx 0.8141

N(0.7133) \approx 0.7622

. Step 3 — Swaption value:

V = 100{,}000{,}000 \times 2.6085 \times [0.052 \times 0.8141 - 0.045 \times 0.7622]

= 100{,}000{,}000 \times 2.6085 \times [0.042333 - 0.034299]

= 100{,}000{,}000 \times 2.6085 \times 0.008034

= 100{,}000{,}000 \times 0.020955 \approx 2{,}097{,}000

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