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LOS 34.k: Describe modern term structure READING 34: THE TERM STRUCTURE AND
models and how they are used. INTEREST RATE DYNAMICS
MODULE 34.6: INTEREST RATE MODELS
The Vasicek Model
Also suggests interest rates are mean reverting to some long-run value.
dr = a(b − r)dt + σdz The difference with CIR model?
No interest rate (r): Implication?
Volatility does NOT
increase as the level
of interest rates increase.
The main disadvantage of the Vasicek model is that it fails to force interest rates to be non-negative.
Assume that the current short-term rate is r = 3% and the long-run value for the short-term rate is b = 8%. Also assume that the
speed of the adjustment factor is a = 0.40 and the annual volatility is σ = 2%. The Vasicek model provides the following formula
for the change in short-term interest rates, dr:
dr = 0.40(8% – r)dt + (2%)dz
The stochastic term, dz, is typically drawn from a standard normal distribution with a mean of zero and a standard
deviation of 1. Assume that a random number generator produced standard normal random error terms of 0.45, 0.18,
−0.30, and 0.25. The Vasicek model would produce the evolution of interest rates shown below:
