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A portfolio loses its delta neutrality if the delta of the portfolio changes but the underlying hedge is unchanged. The portfolio that will require the most rebalancing will be one whose delta changes by larger amounts in response to a given change in the price of the underlying. The sensitivity of the changes in delta in response to changes in the price of the underlying is measured by gamma. The higher the gamma, the more the portfolio will go out of delta neutrality given a change in the price of the underlying. Therefore Choice 'b' is the correct answer.

A portfolio with a low gamma will maintain its delta over a larger price range for the underlying, and is therefore likely to require less frequent rebalancing. The absolute level of the delta itself does not matter, what matters is the gamma. Vega is irrelevant to the delta hedging decision. Therefore the other choices are incorrect.

Futures contracts carry no gamma. Only options have gamma. Choice 'a' is the correct answer. Any instrument whose price varies in a linear fashion with respect to the underlying will have gamma equal to zero.

To solve this question, we need to revisit how delta is calculated in a single step binomial model:

Consider a portfolio with just two positions: 1 Long Call option, and Δ Short Stock. We do not know what Δ (Delta) is.

Now if the current price of the stock is P, which can take the value P2 (higher value) and P1 (lower value) in the future at time T, then Δ needs to be such that the value of the portfolio is equal in both the cases. If the price goes up, the value of the option will be $1 (given) and the value of the short stock will be -Δ P2. If the price goes down, the value of the option will be $0, and the value of the stock will be -Δ P1.

Therefore, $1 - Δ P2 = $0 - Δ P1.

Solving for Δ, we get Δ = $1 /(P2 - P1) = $1 / ($102-$98) = 1/4.

The crack spread is the difference between the price of refined products and crude oil. An option on the crack spread can protect a refiner from both a fall in the price of its output and a rise in the price of its inputs. Calendar spreads are options with different maturities. Crude oil futures and swaps only protect against an adverse change in the price of crude, and not that of refined products. Choice 'b' is the correct answer.