When interest rate volatility increases, OAS should narrow however the text says its widens.

OAS = z-spread - option cost

I find it a little counter-intuitive.

When interest rate volatility increases, OAS should narrow however the text says its widens.

OAS = z-spread - option cost

I find it a little counter-intuitive.

When interest rate volatility increases, the Z-spread will widen, as will the option value. But if the option is far out-of-the-money, then the Z-spread will increase by a lot, and the option value will increase by just a little. As a result, the OAS widens.

I thought z-spread(ZERO VOLATILITY spread) is unaffected by interest rate volatility and a bond with far out of the money option will behave like a straight bond.

Put the formula aside. When the interest rate volatility rises, the price of the bonds [usually] decreases. Price and OAS move in opposite direction, so OAS widens.