OAS and interest rate volatility

From cfa text: For a given bond price, the higher the interest rate volatility assumed, the lower OAS for a callable bond. I know the higher IR volatility, the higher the option cost, and the lower the value of callable bond, but why OAS is lower too?

The higher the interest rate volatility, the more the option cost is worth. Since OAS = Z-Spread - option cost, it follows that OAS is lower.