Financial Risk Manager Part 2

Get started today

Ultimate access to all questions.

Explanation:

Explanation

The correct answer is A because it accurately describes the cascade structure of the Gauss+ model.

Key Features of the Gauss+ Model:

Cascade Structure:
- Short-term rate mean reverts to a medium-term factor
- Medium-term factor mean reverts to a long-term factor
- Long-term factor has time-dependent drift and volatility
Why Other Options are Incorrect:
- Option B: Incorrectly attributes the model's hump-shaped volatility to Fed policy pegging, when it actually arises from the cascade structure itself
- Option C: Incorrect - in the Gauss+ model, factors are typically assumed to be independent, not correlated
- Option D: Incorrect - the model allows for different mean reversion speeds among factors, which is actually supported by empirical evidence

Mathematical Structure:

The Gauss+ model typically has the form:

Short rate: dr = κ₁(θ - r)dt + σ₁dW₁
Medium factor: dθ = κ₂(φ - θ)dt + σ₂dW₂
Long factor: dφ = μ(t)dt + σ₃(t)dW₃

This cascade approach helps capture the hump-shaped term structure of volatility observed in real markets, where medium-term rates exhibit higher volatility than both short-term and long-term rates.

Explanation:

Explanation

The correct answer is A because it accurately describes the cascade structure of the Gauss+ model.

Key Features of the Gauss+ Model:

Cascade Structure:
- Short-term rate mean reverts to a medium-term factor
- Medium-term factor mean reverts to a long-term factor
- Long-term factor has time-dependent drift and volatility
Why Other Options are Incorrect:
- Option B: Incorrectly attributes the model's hump-shaped volatility to Fed policy pegging, when it actually arises from the cascade structure itself
- Option C: Incorrect - in the Gauss+ model, factors are typically assumed to be independent, not correlated
- Option D: Incorrect - the model allows for different mean reversion speeds among factors, which is actually supported by empirical evidence

Mathematical Structure:

The Gauss+ model typically has the form:

Short rate: dr = κ₁(θ - r)dt + σ₁dW₁
Medium factor: dθ = κ₂(φ - θ)dt + σ₂dW₂
Long factor: dφ = μ(t)dt + σ₃(t)dW₃

This cascade approach helps capture the hump-shaped term structure of volatility observed in real markets, where medium-term rates exhibit higher volatility than both short-term and long-term rates.

Comments (0)

No comments yet.

Which of the following statements correctly describes the dynamics and implications of the cascade form of the Gauss+ model?

Exam-Like

Community

LLeetQuiz

Last updated: February 3, 2026 at 14:03

Under the Gauss+ model, the short-term rate mean reverts to a medium-term factor, the medium-term factor mean reverts to a long-term factor, and the long-term factor is modelled with time-dependent drift and time-dependent volatility.

54.5%

Under the Gauss+ model, the evolution of short-term rate reflects the fact that the Fed keeps the short-term policy rate pegged at a target, and this helps generate a "hump-shaped" term structure of volatility that fits the empirical data quite well.

9.1%

Under the Gauss+ model, the evolution of short-term rate and medium-term factor is modelled with a pre-specified correlation parameter, while the long-term factor is assumed to be independent of the medium-term factor.

9.1%

Under the Gauss+ model, the speed of mean reversion from short-term to medium-term is assumed to be equal to that from medium-term to long-term, while the empirical evidence suggests that the speed of mean reversion among factors is different.