Explanation

In fixed income analysis, spot rates and forward rates have a mathematical relationship where they can be derived from each other:

1. Spot rates are the yields on zero-coupon bonds for specific maturities.
2. Forward rates are implied future interest rates derived from spot rates.

Mathematical Relationship:

• Forward rates can be calculated from spot rates using the formula: $(1 + z_n)^n = (1 + z_{n-1})^{n-1} \times (1 + f_{n-1,n})$ where $z_n$ is the n-year spot rate and $f_{n-1,n}$ is the forward rate from year n-1 to n.

• Conversely, spot rates can be calculated from forward rates using the formula: $(1 + z_n)^n = (1 + f_{0,1}) \times (1 + f_{1,2}) \times ... \times (1 + f_{n-1,n})$

Therefore, both curves contain the same information and can be derived from each other. This makes option A correct: "The spot curve can be calculated from the forward curve, and the forward curve can be calculated from the spot curve."

Why other options are incorrect:

• Option B: Incorrect because forward curves CAN be calculated from spot curves.
• Option C: Incorrect because spot curves CAN be calculated from forward curves.

This relationship is fundamental in fixed income analysis for pricing bonds, calculating forward rates, and understanding the term structure of interest rates.