Options & Derivatives Trading

Hull-White model

What is the Hull-White Model?

The Hull-White model is a one-factor interest rate model used to price interest rate derivatives. The Hull-White model assumes that short-term interest rates follow a normal distribution and short-term interest rates follow mean reversion. Therefore, when short-term interest rates are near zero, volatility is likely to be lower, which is reflected in the larger mean reversion in the model.

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

key takeaways

  • The Hull-White model is an interest rate derivative pricing model.
  • The model assumes that very short-term interest rates are normally distributed and revert to the mean.
  • The Hull-White model calculates the price of a derivative security as a function of the entire yield curve, not a single interest rate.

Understanding the Hull-White Model

An interest rate derivative is a financial instrument whose value is related to changes in one or more interest rates. Interest rate derivatives are often used by institutional investors, banks, companies and individuals as a hedging tool to protect themselves from changes in market interest rates, but they can also be used to increase or improve the risk profile of holders or speculate on changes in interest rates. These may include upper and lower interest rate caps.

As the financial system becomes more complex, investments whose value depends on interest rates, such as bond options and mortgage-backed securities (MBS), have grown in popularity. Determining the value of these investments often requires the use of different models, each with its own set of assumptions. This makes it difficult to match the volatility parameters of one model to another, and also to understand the risk of different portfolios.

special attention items

Like the Ho-Lee model, the Hull-White model treats interest rates as normally distributed. This creates a situation where interest rates are negative, although the probability of this happening as a model output is low.

The Hull-White model also prices derivatives as a function of the entire yield curve, rather than individual points. Because the yield curve estimates future interest rates rather than observable market rates, analysts will hedge against different scenarios that economic conditions might create.

Unlike the Hull-White model, which uses instantaneous short-term rates, or the Heath-Jarrow-Morton (HJM) model, which uses instantaneous forward rates, the Brace Gatarek Musiela Model (BGM) model uses only observable rates; that is, forward LIBOR rates.

Who are Hull and White?

John C. Hull and Alan D. White are professors of finance at the Rotman School of Management at the University of Toronto. They jointly developed the model in 1990.Professor Hull is Risk Management and Financial Institutions and Fundamentals of Futures and Options MarketsProfessor White is an internationally recognized authority on financial engineering and is an associate editor of the Journal of Financial Engineering. Journal of Finance and Quantitative Analysis and Derivatives Magazine.

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