ACRO of a hedge fund is asking the risk team to develop a term-structure
model that is appropriate for fitting interest rates for use in the fund’s
options pricing practice. The risk team is evaluating among several interest
rate models with time-dependent drift and time-dependent volatility functions.
Which of the following is a correct description of the specified model?
A) In the Ho-Lee model, the drift of the interest rate process is presumed to
B) In the Ho-Lee model, when the short-term rate is above its long-run
equilibrium value, the drift is presumed to be negative.
C) In the Cox-Ingersoll-Ross model, the basis-point volatility of the
short-term rate is presumed to be proportional to the square root of the rate,
and short-term rates cannot be negative.
D) In the Cox-Ingersoll-Ross model, the volatility of the short-term rate is
presumed to decline exponentially to a constant level.
解析：C is correct. In the CIR model, the basis-point volatility of the short
rate is not independent of the short rate as other simpler models assume. The
annualized basis-point volatility equals.
Analyst Barry runs a short-term interest rate simulation using Model 1, which
assume no drift. The time step in his model is one month. His Model 1 also makes
two assumptions. First, the initial or current short-term rate is equal to
4.00%. Second, the annual basis-point volatility is 200 basis points. In the
first step of his first trial, the random uniform variable is 0.8925 such that,
via inverse transformation, the associated random standard normal value is
1.240. To what level does the rate evolve in the first month?
解析：dw = 1.240 × sqrt (1/12) and dr = 2.0% × 1.240 × sqrt (1/12) = 0.7159%,
such that r = 4.7159%