so when i picture it in the tree, i can see the relationship between volatility and the OAS. When volatility increases, the call will be exercised more, some cash flows capped, and the average spread across all nodes will effectively be lower. So higher volatility, lower OAS for callable bonds, i get that i think.

But when i think about the market impact, i see the opposite effect. If volatility increases, then the call gets more valuable and the value of the callable bond will decrease in the market- so if the price is decreasing, isnt the spread increasing to get to this lower price? Since z stays the same, isnt a higher OAS needed to reach this lower price? This is what im having trouble understanding. Thanks

Bear in mind that what youâ€™re describing here is an attempt to calculate the correct OAS, keeping the price fixed and varying the assumed volatility of future interest rates.

You see a different effect because youâ€™re doing something completely different.

Here, youâ€™re keeping the spread fixed and watching what happens to the price.

The effects, however, are consistent. As you know, for normal bonds, price and yield move in opposite directions. So, if interest rate volatility increases and the price of a callable bond remains unchanged, you know that OAS decreases; i.e., the yield decreases. Thatâ€™s the first case, above. If interest rate volatility increases and the OAS remains unchanged, then the yield is higher than in the first case, so the price will decrease. Thatâ€™s the case youâ€™re seeing here.