How does mean reversion work in the Vasicek model and what are its limitations?

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AcadiFi · Accepted Answer

The Vasicek short-rate model posits dr = a(b - r)dt + sigma dW, where a is the speed of mean reversion, b is the long-run mean rate, and sigma is volatility. When r is above b, the drift a(b - r) is negative, pulling the rate down; when below b, the drift pushes it up.

Calibration example: fit to ten years of daily Fed funds data showing a mean of 2.1%, standard deviation of 1.4%, and first-order autocorrelation of 0.995 on a daily basis. The annual mean reversion speed a equals -252 * ln(0.995) = 1.26, the long-run mean b is 2.1%, and the annualized sigma is 1.4% * sqrt(2 * 1.26) = 2.22%.

Strengths: analytic bond pricing formula P(t,T) = A(t,T) * exp(-B(t,T) * r), Gaussian distribution of future rates, and simple swaption formulas. Limitations: (1) rates can go negative, which was embarrassing pre-2014 but acceptable post-European negative rates; (2) a single factor cannot simultaneously fit short and long-end dynamics; (3) volatility is rate-independent, contradicting empirical evidence that volatility rises with rate levels. For credit-sensitive exposures, use Hull-White or CIR instead.

How does mean reversion work in the Vasicek model and what are its limitations?

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