"Our tree is actually a tree of the short-term interest rate. The average direction in which the short-term interest rate moves depends on the level of the rate. When the rate is very high, that direction is downward; when the rate is very low, it is upward"
About this Quote
Hull is quietly dismantling the fantasy that interest rates move like weather: random, directionless, equally likely to drift anywhere. His point is more procedural than poetic, but the subtext is sharp: if you model rates as if they’re just another stock price, you will misprice the world.
Calling it “a tree of the short-term interest rate” is a signal to practitioners. In derivatives pricing, trees are workhorses: simple, discrete models you can build and stress-test. Hull’s twist is that the tree isn’t symmetric. The “average direction” depends on where you start. High rates tend to fall; low rates tend to rise. That’s mean reversion in plain clothes, and it’s doing heavy rhetorical lifting. He’s telling you that the market and the macroeconomy have guardrails: central banks, growth constraints, and the sheer gravitational pull of what counts as “normal.”
The intent is practical: build a rate model that doesn’t blow up when you use it to value caps, floors, swaps, and bond options. The context is the Hull-White/Black-Derman-Toy tradition of interest-rate modeling, where the short rate is the state variable and calibration to today’s yield curve is non-negotiable.
There’s also an implicit warning about regime sensitivity. “Very high” and “very low” aren’t abstract; they’re historical moods. In high-inflation eras, cuts become the default trajectory. Near the zero lower bound, hikes become the plausible pull. Hull is describing a model, but he’s really describing power: policy, expectations, and the limits of extremes.
Calling it “a tree of the short-term interest rate” is a signal to practitioners. In derivatives pricing, trees are workhorses: simple, discrete models you can build and stress-test. Hull’s twist is that the tree isn’t symmetric. The “average direction” depends on where you start. High rates tend to fall; low rates tend to rise. That’s mean reversion in plain clothes, and it’s doing heavy rhetorical lifting. He’s telling you that the market and the macroeconomy have guardrails: central banks, growth constraints, and the sheer gravitational pull of what counts as “normal.”
The intent is practical: build a rate model that doesn’t blow up when you use it to value caps, floors, swaps, and bond options. The context is the Hull-White/Black-Derman-Toy tradition of interest-rate modeling, where the short rate is the state variable and calibration to today’s yield curve is non-negotiable.
There’s also an implicit warning about regime sensitivity. “Very high” and “very low” aren’t abstract; they’re historical moods. In high-inflation eras, cuts become the default trajectory. Near the zero lower bound, hikes become the plausible pull. Hull is describing a model, but he’s really describing power: policy, expectations, and the limits of extremes.
Quote Details
| Topic | Money |
|---|---|
| Source | Help us find the source |
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