My reasoning: If interest rate volatility is high, the value of the callable bond is lower, lower value means higher discount rate…
the discount rate is Ex: 100 / (1.10) + OAS
I can’t see how OAS is lower 
Cost of Option = Z-spread - OAS
Volatility goes up, cost of option goes up (this relation also holds when dealing with option contracts in derivatives). It’s easier to see this in mathematical terms first and then think about what happens in the market - in order for the left side of the equation to go up, something on the right hand side must adjust. The Z-spread is your compensation when interest rates are stable… hence, the term, zero-volatility spread. So if volatility goes up, Z-spread won’t budge. Meaning OAS must decrease.
Hope this helps.
Aether, Thanks! You’re the man!
It’s vague for me that OAS rises with greater volatility.
If Z- spread = OAS + option cost and option cost rises as a consequence of higher volatility, then so should Z-spread. OAS compensates credit risk and liquidity risk so I see no link with higher volatility that would reduce those risks (and hence force OAS to decrease).
It would seem reasonable for me that along higher volatility, we should experience a rise in Z-spread that amounts fully to the increase in option cost - with OAS unchanged. But it would not meet the definition…(Zero-volatility)
If interest rate volatility increases – so the value of the call option increases – it’s likely that the market price of the bond will drop; the market is smart enough to know that the value of the call option has increased, so the value of the callable bond (a long-straight-bond-plus-short-call-option portfolio) should decrease. This will lead to an increase in the Z-spread: you have to discount at higher interest rates to get a lower price.
Will the increase in the Z-spread match exactly the increase in the option cost, leaving the OAS unchanged? Perhaps in theory it should – the remaining risks (default, interest-rate, credit, whatever) presumably are unchanged – but in practice I suspect that the market will underestimate the increase in the option value, so the price of the bond will drop less than it should (anchoring bias?). Thus, I would expect – in practice – that the OAS will drop as interest-rate volatility increases.
You’re very fast in responding 
So it’s not true that Z-spread doesn’t move with a change in volatility - it moves but not as much as it should be because some part of it’s increase is taken back by a decrease in OAS - but not fully. Am I right?
It’s a pity that literature doesn’t clarify it well.
I’m sitting in Pearson airport in Toronto, waiting for a flight to Chicago (my earlier flight was cancelled: apparently the O’Hare control tower was flooded by all the rain), so what else do I have to do but post on Analyst Forum?
In practice, I’m sure it’s not true. I don’t know what the CFA curriculum has to say on the matter. Your understanding of what I wrote is correct.
That’s true of a great many things.
S2000magician I think you normally explain things very well, but here I feel your answer is a bit confusing since you start talking about the market reacting to the increased volatility, doing these calculations are hard enough given you should calibrate to a market price. But if you talk about the market price moving as well, given a volitility change, it becomes a moving target. I think one should consider the OAS and Z-spread given a constant market price.
See it in the light of this type of thinking: If my Vol assumption is 10% what OAS does that imply, If my Vol assumption is 20% what OAS does that imply?
Given that we can think in these simply terms: OAS gives us the value taking away the spread that represent the option part. Therefore the OAS should be lower than the spread including the Callable option on the Bond. If the Vol increase the option becomes worth more and the OAS then becomes even lower, all else equal.
Which gives us Cost of Option = Z-spread - OAS
Sorry, RobRoy. I was just trying to describe what I think happens in practice. I agree that it’s more complicated – perhaps more complicted than it needs to be – but it’s not all that much more complicated, and I believe that it’s a better representation of what really happens.
Lower.
Hi I faced the same question after 11 year :). Thank you for your explanation but I confused how to apply this formula to explain for putable bond OAS?