Either the owner or the contractor can obtain a builder’s risk policy, and the parties’ contract will typically specify which party buys the coverage. In my experience, it is more common for owners than contractors to purchase builder’s risk insurance―perhaps due to the AIA form contract (The A201- 2007 provides at section 11.3.1: "Unless otherwise provided, the Owner shall purchase and maintain … property insurance written on a builder’s risk ‘all risk’ or equivalent policy form … comprising total value for the entire Project…This insurance shall include interests of the Owner, the Contractor, Subcontractors and Sub-subcontractors in the Project"). If the owner hasn’t bought builder’s risk insurance, the contractor still has the option to buy it. It’s always wise to make sure up front, and not assume that the owner is obtaining builder’s risk insurance―even if the contract says the owner must procure it. That’s better than buying a lawsuit, even one the contractor is likely to win (breach of an owner’s obligation to buy the builder’s risk insurance will almost surely result in a win for the contractor if the owner sues him for damaging “the Work”).
One pitfall here is that an owner’s builder’s risk policy does not automatically protect the contractor from liability if property loss occurs as a result of the negligence of a contractor (remember, the contractor’s liability policy won’t help here). Without more, the contractor is at risk of being sued and having to pay damages―not to the insured owner, but to his insurance company who, upon paying out, is “subrogated” to the owner’ s rights.
Although an insurer acquires a right to be subrogated to any claim an insured may have against the offending party upon payment of the loss, the insurer's right to subrogation derives from the insured's right against the offending party and is limited to those rights. So, if the insured releases any claims the insured has against third parties to the extent covered by insurance―precisely what results from a “waiver of subrogation” clause such as is found in the typical AIA form―the insurer cannot chase the offending party for reimbursement of what it pays out under the policy. (Naturally, insurers aren’t thrilled about this arrangement. Some builder’s risk policies actually prohibit such waivers, in which case execution of the construction contract will violate the policy conditions and prevent recovery under the builder’s risk policy.)
The typical “waiver of subrogation” is a mutual one; each party waives rights against the other to the extent of insurance coverage. (For instance, the AIA form says “The Owner and Contractor waive all rights against each other … for damages caused by fire or other perils to the extent covered by property insurance obtained pursuant to this Paragraph 11.3 or other property insurance applicable to the Work, except such rights as the Owner and Contractor may have to the proceeds of such insurance held by the Owner as fiduciary.”) But for builder’s risk insurance purposes, it is the owner’s waiver that matters. If the owner gets paid out by builder’s risk coverage and has waived the right to chase the contractor for any loss to the extent covered by insurance, the insurer is stuck with this, and contractor is safe from both owner and insurer.