Interpreting the Ho-Lee Drift During Binomial Tree Calibration

Summary

The document asks how to interpret the time-dependent drift parameter in the Ho-Lee short-rate model while calibrating a discrete interest rate tree. In the described procedure, each period's parameter is chosen so that model prices under the risk-neutral measure match market bond prices. The questioner observes that a calibrated parameter appears to shrink as further bonds are fitted using rates from earlier periods, and asks whether the drift can be understood as an underlying trend in rates.

The supplied material contains no answer, explanation, or calibration evidence, so it does not resolve whether the observed change follows from the model, the tree construction, or a possible implementation issue. It serves as a prompt about distinguishing a model's risk-neutral drift used for pricing from an intuitive forecast of future short-rate direction. No numerical example, parameter estimation guidance, or market conclusion is provided.

Key ideas

• The Ho-Lee model represents short-rate changes with a time-varying drift and a volatility term.
• The described tree calibration selects drift values to match market bond prices under risk-neutral valuation.
• A changing calibrated drift raises a question about how earlier tree rates affect later calibration steps.
• The document does not answer whether the drift represents an intuitive trend or explain the observed parameter changes.

Tags

# Ho-Lee Model Calibration: theta becomes smaller


# Ho-Lee Model Calibration: theta becomes smaller












This question is regarding the Ho-Lee model:

$$ dr_t = \theta_tdt + \sigma dW_t $$

In discrete time, we can calibrate an interest rate binomial tree by finding $\theta$ in each period to match market price with the model price (expectations under the risk-neutral measure). However, every step I proceed to calibrate the next bond on the tree, the $\theta$ in the same period becomes smaller and smaller, because I'm using the calibrated interest rates for previous periods (not sure, please correct me if I'm wrong!).

My question is: what is the intuition/explanation of the $\theta$? Can we view it as the underlying "trend" of the interest rates since $\theta$ is the drift?

Thanks!

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