Hull-White Model

What Is the Hull-White Model?

The Hull-White model is a single-factor interest model used to price interest rate derivatives. The Hull-White model expects that short rates have a normal distribution and that the short rates are subject to mean reversion. Volatility is hence prone to be low when short rates are close to zero, which is reflected in a bigger mean reversion in the model.

The Hull-White model broadens the Vasicek Model and Cox-Ingersoll-Ross (CIR) model.

Understanding the Hull-White Model

An interest rate derivative is a financial instrument with a value that is linked to the developments of an interest rate or rates. Interest rate derivatives are frequently utilized as hedges by institutional investors, banks, companies, and people to safeguard themselves against changes in market interest rates, yet they can likewise be utilized to increase or refine the holder's risk profile or to hypothesize on rate moves. These may incorporate interest rate caps and floors.

Investments whose values are dependent upon interest rates, like bond options and mortgage-backed securities (MBS), have filled in prominence as financial systems have become more sophisticated. Determining the value of these investments frequently involved utilizing various models, with each model having its own set of assumptions. This made it challenging to match the volatility boundaries of one model with another model, and furthermore made it hard to grasp risk across a portfolio of various investments.

Special Considerations

Like the Ho-Lee model, the Hull-White model treats interest rates as normally distributed. This makes a scenario wherein interest rates are negative, however there is a low likelihood of this happening as a model output.

The Hull-White model likewise prices the derivative as a function of the whole yield curve, instead of at a single point. Since the yield curve gauges future interest rates instead of discernible market rates, analysts will hedge against various scenarios that economic conditions could make.

Dissimilar to the Hull-White model, which utilizes the momentary short rate, or the Heath-Jarrow-Morton (HJM) model, which utilizes the prompt forward rate, the Brace Gatarek Musiela Model (BGM) model just purposes rates that are detectable; i.e., forward LIBOR rates.

Who Are Hull and White?

John C. Hull and Alan D. White are finance teachers at the Rotman School of Management at the University of Toronto. Together they developed the model in 1990. Teacher Hull is the creator of Risk Management and Financial Institutions and Fundamentals of Futures and Options Markets. Teacher White, additionally recognized universally as an authority on financial engineering, is the Associate Editor of the Journal of Financial and Quantitative Analysis and the Journal of Derivatives.

Features

• The Hull-White model is an interest rate derivatives pricing model.
• The Hull-White model works out the price of a derivative security as a function of the whole yield curve as opposed to a single rate.
• This model makes the assumption that exceptionally short-term rates are normally distributed and return to the mean.