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

In a one-factor Vasicek model, an analyst fits k, θ and σ to match today's prices of a set of zero-coupon bonds exactly with a single constant θ. Compared with a model that lets the drift vary with time to fit the curve exactly (Ho-Lee/Hull-White style), which statement is correct?

Constant-parameter Vasicek cannot generally match an arbitrary observed term structure because it has too few parameters. Models with a time-dependent drift add the needed flexibility to fit the curve exactly while still allowing closed-form option pricing.

  1. AConstant-parameter Vasicek generally cannot fit an arbitrary term structure exactly because it has only three parametersCorrect
  2. BConstant-parameter Vasicek fits any term structure exactly because it is arbitrage-free by construction
  3. CTime-varying drift models cannot be used for option pricing because they lack closed forms
  4. DVasicek fits exactly only when σ is set to zero for all maturities

Explanation

With three constants (plus r0) the Vasicek curve has limited shapes and cannot match an arbitrary observed curve. Time-dependent drift (Hull-White) adds enough freedom to fit exactly while retaining closed-form bond option prices. Absence of arbitrage within the model does not mean it matches market prices.

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