What Is the Hull-White Model?
Let me explain the Hull-White model directly to you: it's a single-factor interest rate model that we use to price interest rate derivatives. In this model, I assume that short rates follow a normal distribution and are subject to mean reversion. This means volatility tends to be low when short rates are near zero, which the model captures through a stronger mean reversion effect.
You should know that the Hull-White model builds on and extends the Vasicek model and the Cox-Ingersoll-Ross (CIR) model, making it a more flexible tool in financial pricing.
Key Takeaways
Here's what you need to grasp about the Hull-White model: it's specifically an interest rate derivatives pricing model. It operates on the assumption that very short-term rates are normally distributed and revert to the mean over time. Importantly, when I calculate the price of a derivative security using this model, I do so as a function of the entire yield curve, not just a single rate.
Understanding the Hull-White Model
An interest rate derivative is a financial instrument whose value ties directly to the movements of interest rates. You might use these as hedges if you're an institutional investor, bank, company, or individual looking to protect against market interest rate changes. They can also help you increase or refine your risk profile or even speculate on rate movements—think interest rate caps and floors as examples.
Investments like bond options and mortgage-backed securities (MBS), which depend on interest rates, have become more popular as financial systems grow sophisticated. Valuing these often requires different models, each with its own assumptions, and that can make it tough to match volatility parameters across models or understand risks in a diverse portfolio.
Special Considerations
Similar to the Ho-Lee model, the Hull-White model treats interest rates as normally distributed, which means there's a scenario where rates could go negative, though the probability is low in the model's outputs.
What sets the Hull-White model apart is that it prices derivatives based on the entire yield curve, not just a single point. Since the yield curve estimates future interest rates rather than using observable market rates, you as an analyst would hedge against various economic scenarios.
Keep in mind, unlike the Hull-White model that uses the instantaneous short rate, or the Heath-Jarrow-Morton (HJM) model with the instantaneous forward rate, the Brace Gatarek Musiela (BGM) model sticks to observable rates like forward LIBOR rates.
Who Are Hull and White?
John C. Hull and Alan D. White are finance professors at the Rotman School of Management at the University of Toronto. They developed this model together back in 1990. Professor Hull has authored books like 'Risk Management and Financial Institutions' and 'Fundamentals of Futures and Options Markets.' Professor White is an international authority on financial engineering and serves as the Associate Editor for the Journal of Financial and Quantitative Analysis and the Journal of Derivatives.
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