Skip to content

Why rate mean reversion matters for pricing

Question

Why is it important whether a model lets interest rates mean-revert?

Short answer

Because in rate models mean reversion survives into the pricing measure and shapes the volatility term structure. Unlike a stock, the short rate is not a traded asset, so its drift is not replaced by a fixed quantity under the risk-neutral measure. Mean reversion damps long-horizon rate moves, so long rates are less volatile than short ones and forward rates decorrelate; it changes cap, swaption and Bermudan prices and keeps rates from drifting to implausible levels.

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q4.4, p.148; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question