# Hull-White Model

The Hull-White Model is an important concept in the context of financial mathematics. The Hull-White Model deals with future rates of interest. John Hull and Alan White explained the original version of Hull-White model in 1990.

The Hull-White model had been formulated by using a trinomial lattice. The Hull-White model is a supplement of the Vasicek model. However, the Hull-White model is different from the Vasicek model. The main difference lies in the nature of the mean reversion.
Description of Hull-White Model
In the Hull-White Model the interest rate for a shorter period of time is of utmost importance. Thus the Hull-White Model can also be alternatively described as No-arbitrage Yield Curve model or Short-rate model or Single-Factor model.
Equational Representation of Hull-White Model
The equational representation of the Hull-White model is dr(t) = (φ(t) – α(t)r(t))dt + σ(t)dW(t)

The details of the equational representation of the Hull-White model could be explained as below:

Sign Meaning or Representation
dr Short term interest rate change over a short period of time
dt Minor movement of time
r Rate of interest over a shorter period of time
s Short rate’s yearly standard variation
q(t) Function of time that determines the average direction of r’s movement. The function is chosen in a way that changes in the short term rate of interest tally with the yield curve of the modern zero coupon bond
dz It is a Wiener process. It is derived from a random standard normal process
a Average rate of reversion. It regulates the relationship of the long rate volatilities and short rate volatilities

Application of Hull-White Model

The Hull-White model is used to determine the value of bonds. The Hull-White model is also applied to find out the worth of derivatives.