I think that generally it is incorrect to consider any type of market convention like, “callable bonds demand a premium yield to entice investors” or “OAS increases with volatility to compensate for the call risk”. While market wise these maybe correct, they distort the mathematics. Generally, a callable bond with a 6% coupon with rates at 4 has negative convexity. Under negative convexity the bond will underperform when rates rally(go down) and outperform when rates sell off(go up) due to the concave price/yield curve. The only time the bond will exhibit positive convexity is at yields greater then 6. off topic: Similarly, i always find the OAS statement from above confusing. But, the relationship Z- Option cost = OAS always stands and vol always increases option cost and always mathematically decreases OAS.