Derivatives

CFA® Level II, published weight 5–10%. Forward commitments and contingent claims — binomial, BSM, the Greeks.

What the outline covers

Pricing and Valuation of Forward Commitments
Valuation of Contingent Claims

Sample questions

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Question 1

Three months after inception, the forward price on a contract has risen from $50 to $53. With six months remaining and a risk-free rate of 4%, the value to the long is closest to:

F₀ = $50 · Fₜ = $53 · T − t = 0.5 · r = 4%

A. $2.94
B. $3.00
C. $3.06
D. $0.00

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A. V = (Fₜ − F₀)/(1 + r)^(T−t) = 3/(1.04)^0.5 = 3/1.0198 = $2.94. The value is the discounted difference between forward prices.

Reading: Derivatives — Pricing and Valuation of Forward Commitments, LOS 1.c

Question 2

In the Black–Scholes–Merton model, N(d₂) is best interpreted as:

A. The delta of the call
B. The risk-neutral probability the option finishes in the money
C. The actual probability the option finishes in the money
D. The present value factor applied to the strike

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B. N(d₂) is the risk-neutral probability of exercise. N(d₁) is the option’s delta, and the actual probability is not used in the model at all.

Reading: Derivatives — Valuation of Contingent Claims, LOS 2.d

Question 3

A dealer is short gamma and rebalances a delta hedge only weekly. A large move in the underlying in either direction will most likely produce:

A. A hedging gain
B. A hedging loss
C. No effect, because the book is delta neutral
D. A gain only if the move is upward

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B. A short gamma position loses on large moves in either direction because the delta hedge is systematically wrong between rebalancing dates.

Reading: Derivatives — Valuation of Contingent Claims, LOS 2.h

Question 4

An increase in the volatility of the underlying will, all else equal:

A. Increase call values and decrease put values
B. Decrease call values and increase put values
C. Increase both call and put values
D. Leave both unchanged

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C. Higher volatility raises the value of optionality on both sides, because the downside is truncated by the option structure while the upside is not.

Reading: Derivatives — Valuation of Contingent Claims, LOS 2.f

Question 5

Two months after inception of a plain vanilla interest rate swap, market rates have fallen. The value of the swap to the fixed-rate payer is:

A. Positive
B. Negative
C. Zero
D. Positive only if the swap is collateralised

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B. The fixed payer is locked into paying an above-market rate while receiving less floating. The swap has negative value to that side.

Reading: Derivatives — Pricing and Valuation of Forward Commitments, LOS 1.f

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