What's the advantage of the Hull-White one-factor model over Vasicek?

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AcadiFi · Accepted Answer

Hull-White extends Vasicek by making the long-run mean time-dependent: dr = (theta(t) - a*r)dt + sigma*dW. The deterministic function theta(t) is chosen to exactly reproduce today's observed zero curve, which Vasicek cannot do with constant b. This no-arbitrage calibration to the initial curve is essential for pricing derivatives consistent with market prices.

Given the current instantaneous forward rate f(0,t) and its derivative, theta(t) = df(0,t)/dt + a*f(0,t) + sigma^2/(2a) * (1 - exp(-2at)). A trader calibrating on March 14, 2026 with a = 5% and sigma = 85 basis points backs out theta(t) from the SOFR curve, guaranteeing that the model reprices every discount bond within rounding error.

Additional flexibility includes time-dependent volatility sigma(t), enabling the model to match caplet volatility term structures. Hull-White also admits closed-form formulas for European swaptions via Jamshidian's decomposition, making it tractable for Bermudan option pricing via trees. The tradeoff: like Vasicek, rates can go negative, and single-factor dynamics imply perfectly correlated yield movements across maturities. For multi-factor realism, practitioners use two-factor Hull-White or LIBOR market models.

What's the advantage of the Hull-White one-factor model over Vasicek?

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