To determine the correct forward rate curve, we need to apply the mathematical relationship between spot rates and forward rates.

The correct answer is C.

The Core Concept

The forward rate represents the "marginal" rate for a specific future period. There are three mathematical rules that govern the relationship between the spot rate curve ($S$) and the forward rate curve ($F$):

1. Rising Spot Curve: When the spot rate curve is increasing, the forward rate must be above the spot rate ($F > S$).
2. Flat Spot Curve: When the spot rate curve reaches its peak (the slope is zero), the forward rate intersects the spot rate ($F = S$).
3. Falling Spot Curve: When the spot rate curve is decreasing, the forward rate must be below the spot rate ($F < S$).

Step-by-Step Analysis of the Provided Graphs

1. Identify the Trend of the Spot Rate

In the original chart, the spot rate curve:

• Increases from Year 1 to roughly Year 7.5.
• Peaks at roughly Year 8.
• Decreases from Year 8 to Year 10.

2. Evaluate the Options

• Option A: Shows the forward rate curve always remaining above the spot rate curve. This would only be true if the spot rate never stopped rising. (Incorrect)

• Option B: Shows the forward rate curve staying above the spot rate even as the spot rate begins to decline at the end. (Incorrect)

• Option C: * Upward Slope: The forward rate is above the spot rate while the spot curve rises.

• The Intersection: The forward rate curve crosses the spot rate curve at the exact point where the spot rate is at its maximum (around Year 8).

• Downward Slope: Once the spot rate starts falling, the forward rate drops below it.

• This matches the mathematical requirements perfectly. (Correct)

• Option D: Shows an extreme drop in the forward rate that does not proportionally match the mild decline in the spot rate shown in the original data. (Incorrect)