Consider a one-factor interest rate model, specifically the Vasicek model, which is used to describe the evolution of interest rates over time. The model assumes that the short-term interest rate follows a mean-reverting process, with the following stochastic differential equation: dR(t) = θ(μ - R(t))dt + σdW(t) where: R(t) is the short-term interest rate at time t, θ is the speed of mean reversion, μ is the long-term mean level of the interest rate, σ is the volatility of the interest rates, and dW(t) is a Wiener process. If the parameters of the model indicate that the speed of mean reversion is high and the volatility is low, which of the following statements regarding the future behavior of interest rates is most accurate?

Exam

CFA Level 2

Section

Difficulty

Fixed Income

Vasicek Model and Interest Rates Dynamics

Hard Term Structure Dynamics Interest Rate Models

Consider a one-factor interest rate model, specifically the Vasicek model, which is used to describe the evolution of interest rates over time. The model assumes that the short-term interest rate follows a mean-reverting process, with the following stochastic differential equation:

dR(t) = θ(μ - R(t))dt + σdW(t)

where:

R(t) is the short-term interest rate at time t,
θ is the speed of mean reversion,
μ is the long-term mean level of the interest rate,
σ is the volatility of the interest rates, and
dW(t) is a Wiener process.

If the parameters of the model indicate that the speed of mean reversion is high and the volatility is low, which of the following statements regarding the future behavior of interest rates is most accurate?

Interest rates will exhibit high volatility but will quickly revert to the mean level μ.

Interest rates will fluctuate wildly around the mean level μ due to low mean reversion.

Interest rates will generally stay close to μ with small fluctuations over time.

Hint

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