Hull White Analytic Closed-Form Solution¶
Overview¶
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:
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