The Gaussian Hull-White model has pricing dynamics . Its deterministic drift function can fit the initial yield curve exactly, while its Ornstein-Uhlenbeck process part controls stochastic variation. Like the Vasicek model, it permits negative rates.
Let be the initial instantaneous forward rate curve and choose . In the Hull-White model, take . To verify the fit, write with , , and . The Gaussian exponential formula gives .
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The Hull-White model is a popular term structure model used in finance to describe the evolution of interest rates over time. Named after its creators, John Hull and Alan White, the model is particularly useful for pricing interest rate derivatives and managing interest rate risk. ### Key Features of the Hull-White Model: 1. **Single Factor Model**: The original Hull-White model is a single-factor model, meaning it relies on one state variable to describe the dynamics of interest rates.