Is the Ho-Lee model still relevant or just a historical stepping stone?

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AcadiFi · Accepted Answer

Ho-Lee is the simplest no-arbitrage short-rate model: dr = theta(t)*dt + sigma*dW. There is no mean reversion term, meaning the rate follows a drifted random walk with constant volatility. The function theta(t) is calibrated to the initial zero curve just like Hull-White, but once fit, rates drift away without reverting.

Practical use is limited because long-horizon simulations produce unrealistic rate dispersion. Over a thirty-year simulation with sigma = 1%, the standard deviation of terminal rates is sigma * sqrt(30) = 5.48%, implying plausible realizations from negative 15% to positive 25%. Nobody believes ten-year Treasuries can reach 25%.

Where it remains useful: (1) pedagogical introduction to no-arbitrage calibration since the math is cleanest; (2) short-horizon applications like one-year caplet pricing where mean reversion effects are negligible; (3) building intuition before moving to Hull-White or Black-Derman-Toy.

For the FRM exam, know the key facts: Ho-Lee was the first no-arbitrage short-rate model (1986), has constant volatility, no mean reversion, Gaussian rates allowing negatives, and can be implemented on a recombining binomial tree. In production, Hull-White or HJM-family models have superseded it.

Is the Ho-Lee model still relevant or just a historical stepping stone?

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