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

A desk calibrates a Gauss+ model by fitting model-implied swap rates to the market curve and fitting volatilities to historical rate changes. Why is a multi-factor Gaussian model preferable to a one-factor Vasicek model for hedging a portfolio of long and short positions across maturities?

A one-factor model makes all rates move together perfectly because they share a single shock, so it misses twists and slope changes that matter for long-short portfolios. A multi-factor Gaussian model allows imperfect correlation across maturities and gives more realistic hedge ratios.

  1. ABecause a one-factor model implies all rates across maturities are perfectly correlated, so it cannot reflect curve twists that affect a long-short portfolioCorrect
  2. BBecause multi-factor Gaussian models eliminate the possibility of negative interest rates
  3. CBecause multi-factor models require no calibration of volatility parameters
  4. DBecause a one-factor model produces higher volatility for long-maturity rates than for short-maturity rates in every case

Explanation

In a one-factor model, all rate changes are driven by the same shock, so rates are perfectly correlated and a hedge against that one factor can appear perfect even when the curve twists. Multiple factors allow imperfect correlation. Gaussian models still permit negative rates, and they still need volatility calibration.

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