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FRM Part II · FRM Exam Part II · The Vasicek and Gauss+ Models

A desk hedges a long-dated bond using a two-year note, assuming a one-factor Vasicek model. The curve then moves in a steepening way, with short rates unchanged and long rates rising. What is the most likely consequence for the hedge?

The hedge leaves residual slope risk. In a one-factor Vasicek model all yields respond to the same single shock and are perfectly correlated, so the model cannot represent a steepening where short rates are flat and long rates rise. A multifactor Gauss+ model with a slope factor would capture this risk.

  1. AThe hedge performs well because Vasicek captures steepening through its mean-reversion level
  2. BThe hedge leaves residual risk because one factor implies perfectly correlated rate changes across maturities and cannot represent slope changesCorrect
  3. CThe hedge gains because mean reversion pulls long rates back to the short rate
  4. DThe hedge is unaffected because duration-matched positions are immune to curve shape changes

Explanation

In one-factor Vasicek all yield changes are driven by one shock, so they are perfectly correlated and a steepening is outside the model. A hedge calibrated to it leaves slope risk. A multifactor Gauss+ model would include a slope-like factor to hedge this. Duration matching only protects against parallel-type moves.

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