Hull White Analytic Closed-Form Solution


In financial mathematics, the Hull-White model is a model of future interest rates and is an extension the Vasicek model.

Its an no-arbitrage model that is able to fit todays term structure of interest rates.

It assumes that the short-term rate is normally distributed and subject to mean reversion.

The stochastic differential equation describing Hull-White is:

\[\delta{r} = [\theta(t) - ar]\delta{t} + \sigma\delta{z}\]

These input parameters are:

\(\delta r\) - is the change in the short-term interest rate over a small interval

\(\theta (t)\) - is a function of time determining the average direction in which r moves (derived from yield curve)

\(a\) - the mean reversion

\(r\) - the short-term interest rate

\(\delta t\) - a small change in time

\(\sigma\) - the volatility

\(\delta z\) - is a Wiener (Random) process