Question #1
Reading: Reading 26 The Arbitrage-Free Valuation Framework
PDF File: Reading 26 The Arbitrage-Free Valuation Framework.pdf
Page: 1
Status: Correct
Correct Answer: A
Question
Jill Sebelius, editor-in-chief of a monthly interest-rate newsletter uses the following model to forecast short-term interest rates: For the current newsletter, Sebelius has issued the following expectations: a=0.40, b = 3%, r = 2%. According to the model used by Sebelius, volatility in the short-term in interest rate is most likely:
Answer Choices:
A. independent of the current level of the short-term interest rate
B. negatively related to the current level of the short-term interest rate
C. positively related to the current level of the short-term interest rate. Dan Laske, CFA, recently joined Axes Bank as a bond trader. Laske is reviewing bank's interest rate models and meets with Sheila Jensen, a senior portfolio manager at the bank. Jensen makes the following statements: Statement 1: I don't want any random noise in the short-term rate forecasts. Statement 2: I like interest models to incorporate mean reversion of rates. Statement 3: I prefer that the interest rate volatility varies with the level of interest rates. Laske finally decides on using the Gauss+ model and asks Jensen about her opinion. Jensen makes the following observations about the Gauss+ model: Observation 1: Gauss+ models are primarily used for forecasting long-term rates, while equilibrium models are used for short-term rates. Observation 2: Gauss+ models assume that the long-term rates are mean reverting, while the central bank actions determine the short-term rates. dr = a(b −r) dt + σ√rdz
Explanation
Under the Cox-Ingersoll-Ross model, the random or stochastic component incorporates
the square root of current level of interest rate. Hence the higher the current level of
interest rates, the higher the volatility of interest rates.
(Module 26.3, LOS 26.i)
Dan Laske, CFA, recently joined Axes Bank as a bond trader. Laske is reviewing bank's interest rate
models and meets with Sheila Jensen, a senior portfolio manager at the bank.
Jensen makes the following statements:
Statement 1:
I don't want any random noise in the short-term rate forecasts.
Statement 2:
I like interest models to incorporate mean reversion of rates.
Statement 3:
I prefer that the interest rate volatility varies with the level of interest
rates.
Laske finally decides on using the Gauss+ model and asks Jensen about her opinion.
Jensen makes the following observations about the Gauss+ model:
Observation 1:
Gauss+ models are primarily used for forecasting long-term rates, while
equilibrium models are used for short-term rates.
Observation 2:
Gauss+ models assume that the long-term rates are mean reverting, while
the central bank actions determine the short-term rates.
dr = a(b −r) dt + σ√rdz