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.
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