How does volatility affect the value of callable and putable bonds?

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AcadiFi · Accepted Answer

Volatility is the primary non-rate driver of embedded option value. The tree's width increases with sigma — higher volatility creates larger up-moves and larger down-moves in future rates, producing a wider distribution of future bond prices. Consequences by bond type: (1) Callable bond — higher volatility increases the call option's value. More future paths will see rates fall significantly, pushing bond prices well above par, which triggers more calls. Because V_callable = V_straight - V_call, a more valuable call reduces the callable bond's price. Moving sigma from 12% to 22% might reduce a callable bond's price from 102.40 to 99.10 — a drop of 3.30 points. (2) Putable bond — higher volatility increases the put option's value similarly. More paths see rates rise, pushing bond prices below par, triggering more puts. Because V_putable = V_straight + V_put, the putable bond becomes more valuable. Moving sigma from 12% to 22% might raise a putable bond's price from 98.80 to 100.75 — up 1.95 points. (3) Straight bond — unchanged in principle since there's no option; any change in a straight bond's price from volatility in a calibrated tree indicates mis-calibration. Practical implications: when constructing OAS, you must fix a volatility assumption. Different desks using 15% versus 20% will produce materially different OAS values — by 20-40 bps for typical callable corporates. Historical volatility of short rates (measured from 1-year Treasury yield changes) serves as a baseline; option-implied volatilities from swaptions give market-consistent values. Analysts often report OAS at multiple vol assumptions for robustness, noting that callable bond returns are short volatility.

How does volatility affect the value of callable and putable bonds?

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