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:

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

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