In an example, can someone show how when an analyst uses lower than actual volatility how that results in computed oas being too high and bond underpriced? Thanks in advance.
The higher the volatility (of interest rates, in this case), the greater the price of options: call options and put options.
The price of a callable bond is the price of the equivalent option-free bond minus the price of the call option. If the assumed volatility is too low, the price of the call option will be too low, so the price of the callable bond will be too high.
The price of a putable bond is the price of the equivalent option-free bond plus the price of the put option. If the assumed volatility is too low, the price of the put option will be too low, so the price of the putable bond will be too low.
I take it that your question concerns a putable bond; you haven’t made that clear.