This appeal turns on whether third-party insurers can enforce a master services agreement’s defense, indemnification, and insurance obligations. We conclude that those obligations run between the two parties to the master services agreement and thus are not enforceable by the insurers.
I.
BHP Billiton Petroleum Deepwater, Inc. (“BHP”) is an energy exploration company. Prior to its bankruptcy filing, Deep Marine Technology, Inc. (“Deep Marine”) was an oilfield service company that owned and operated vessels to support offshore construction. Effective April 18, 2006, BHP and Deep Marine entered into a Master Services Agreement (“MSA”), pursuant to which Deep Marine agreed to provide construction support vessels to BHP. The MSA contained reciprocal indemnity obligations and required the parties to support their respective indemnity obligations with liability insurance, self-insurance, or a combination thereof. In addition, the MSA contained a choice of law clause, stipulating that general maritime law governs interpretation of the MSA and, to the extent general maritime law is not applicable, Texas law applies.
Glen Duval (“Duval”), an employee of Wood Group/Deepwater Specialists, Inc. (another BHP contractor), claims to have suffered injuries during an offshore personnel basket transfer from a vessel owned by Deep Marine to a tension-leg platform owned by BHP. On April 8, 2008, he filed suit against Deep Marine, alleging that the negligence of Deep Marine’s personnel aboard the vessel caused his injuries. In an amended complaint, he also asserted a claim against Dolphin Services, L.L.C., the employer of the allegedly negligent crane operator. Duval did not, and has not, alleged that BHP has any liability for his injuries. On April 25, 2008, Deep Marine sought defense, additional insured status, and indemnity from BHP under the MSA, and it tendered the defense of Du-val’s claims to BHP. BHP accepted tender on May 14, 2008.
On December 4, 2009, Deep Marine filed for Chapter 11 bankruptcy in the Southern District of Texas, and Duval’s suit was automatically stayed. On September 10, 2010, the bankruptcy court entered an order permitting Duval to proceed with his case against Deep Marine’s insurers, but permanently enjoining him from “enforcing, levying, attaching, collecting, or otherwise recovering in any matter or by any means” against Deep Marine or its estate. Pursuant to that order, the district court reopened the case. On January 4, 2012, Duval amended his complaint to name Northern Assurance Company of America and Markel American Insurance Company (“Underwriters”), the protection and indemnity insurers of Deep Marine, as additional defendants under Louisiana’s Direct Action Statute.1 On February 7, 2012, Underwriters filed a third-party complaint against BHP, seeking to be “fully protected, defended, indemnified, held harmless and provided insurance coverage” by BHP in accordance with the MSA and purport*303ing to tender BHP to Duval under Federal Rule of Civil Procedure 14(c).
Underwriters and BHP filed cross-motions for summary judgment, each disputing whether Underwriters could enforce BHP’s contractual insurance, defense, and indemnity obligations to Deep Marine after Deep Marine’s bankruptcy discharge. Following a hearing with oral argument, the district court granted BHP’s motion for summary judgment, denied Underwriters’ motion for summary judgment, and dismissed the action with prejudice.2 Underwriters timely appealed.3 We have subject matter jurisdiction pursuant to 28 U.S.C. § 1292(a)(3), which provides for interlocutory appeal from a district court’s order “determining the rights and liabilities of the parties to admiralty cases.”4
II.
We review a district court’s order granting summary judgment de novo, applying the same standards as the district court.5 “Summary judgment is warranted if the pleadings, the discovery and disclosure materials on file, and any affidavits show that there is no genuine [dispute] as to any material fact and that the movant is entitled to judgment as a matter of law.”6 When parties file cross-motions for summary judgment, “we review each party’s motion independently, viewing the evidence and inferences in the light most favorable to the nonmoving party.”7
“Interpretation of the terms of a contract, including an indemnity clause, is a matter of law, renewable de novo on appeal.”8 “[T]he obligation to indemnify is to be strictly construed,”9 and “a court should not construe an indemnity clause to impose liability for a loss neither expressly within its terms nor of such a character that the parties probably intended to exclude the loss.”10
III.
The parties dispute whether the MSA requires BHP to protect, defend, indemnify, and hold harmless Underwriters against Duval’s claim. We conclude that it does not and therefore affirm the district court’s grant of summary judgment in favor of BHP. To be clear, the parties, agree that the MSA required BHP to protect, defend, indemnify, release and hold harmless Deep Marine against Du-val’s claim. Specifically, the MSA provided:
Company [BHP] shall protect, defend, indemnify, release, and hold harmless Contractor Group from and against any and all claims arising out of, resulting from or in connection with the provision *304of the Goods and/or Services pursuant to this Contract for:
(I) any injury, death, or illness suffered by any person in Company Group; and (II) any damage to or loss of any equipment, materials, vessels, or other property of any member of Company Group....
The parties defined “Contractor Group” to include the Contractor (Deep Marine); its subsidiaries, affiliates, contractors, and subcontractors; and the “agents, representatives, servants, directors, officers, assigns, managers, members, shareholders, owners, employees and invitees of all of the foregoing.” It defined “Company Group” to include BHP, as well as its subsidiaries, affiliates, contractors, and subcontractors, and employees “of all of the foregoing.” Finally, the MSA defined “claims” to include “all claims losses, demands, causes of action, suits, proceedings, fines, penalties, judgments, obligations and liabilities of every kind and character.” Thus, Duval’s claim against Deep Marine fell within the scope of BHP’s indemnification obligation because it was a personal injury claim asserted by a person in Company Group (an employee of a BHP contractor) against a member of Contractor Group (Deep Marine). But the same is not true of Duval’s claim against Underwriters. Under the plain language of the MSA, BHP’s indemnification and defense obligations only ran to members of the “Contractor Group.” The parties could have included the Contractor’s insurers within the definition of “Contractor Group,” as parties in other cases have done,11 but they did not do so. In turn, BHP owes no duty to Underwriters, and we find Underwriters’ arguments to the contrary unpersuasive.
Underwriters argue that BHP waived any potential defenses to its contractual obligations by accepting Deep Marine’s tender of Duval’s claim and defending Deep Marine in the matter. But waiver is simply inapplicable here. Even though BHP accepted Deep Marine’s tender of Duval’s claim, it never indicated it had any obligation to Underwriters. Instead, its defense arises out of an unknowable change in factual circumstances — specifically Deep Marine’s discharge in bankruptcy, the bankruptcy court’s order permanently enjoining Duval from proceeding against Deep Marine, and Underwriters’ subsequent claim against BHP.
Underwriters also make four substantive arguments in favor of their interpretation of the MSA. First, Underwriters attack BHP’s characterization of the MSA as an indemnity agreement requiring that Deep Marine make payment to Duval before BHP’s indemnification obligation becomes enforceable.12 They argue that the *305MSA requires BHP to indemnify Deep Marine against liability, so BHP’s indemnification obligation becomes enforceable once Deep Marine’s liability is established, not when Deep Marine eventually makes payment on that liability.13 Underwriters point out that, under Louisiana’s Direct Action Statute, Deep Marine must be found liable in order for Underwriters to be held liable.14 Therefore, they contend, even though Deep Marine will never pay damages to Duval, BHP’s indemnification obligation will become enforceable once liability is established. But even assuming arguendo that the MSA requires indemnification against liability and that Deep Marine will eventually be held liable, Underwriters still cannot prevail because BHP’s indemnification obligation — whatever its scope — -runs only to Deep Marine.
Second, Underwriters contend that summary judgment in favor of BHP was improper because, upon their payment of any judgment or settlement to Duval, they will become subrogated to all of Deep Marine’s rights, including its rights against BHP under the MSA. This argument also fails to persuade. Assuming arguendo that payment by Underwriters would give rise to subrogation, Underwriters would nevertheless have no claim against BHP because “a subrogee can obtain no greater rights than its subrogor had.”15 Deep Marine would not, and could not, incur any loss in the Duval action, so Underwriters could not seek indemnification from BHP. And, because BHP has agreed to continue providing Deep Marine with a nominal defense, Underwriters would not have a breach of contract claim against BHP.
Third, Underwriters argue that BHP agreed to become Deep Marine’s primary insurer against liability to members of Company Group. They point to the MSA’s requirements (1) that BHP support its indemnification obligations with self-insurance, a liability insurance policy, or a combination thereof and (2) that the insurance coverage BHP obtains name Deep Marine as an additional insured and serve as primary insurance, without the right of contribution from any insurance policies maintained by Deep Marine. We find the argument inapplicable here because BHP chose to self-insure for claims under $1 million and the parties agree that Duval’s claim is not for more than $1 million. We conclude that the additional insured and primary insurance requirements do not apply to BHP’s self-insurance. For one, the MSA focuses on “insurance coverage” and “policies of insurance” when describing both the additional insured and primary insurance requirements, leading us to believe that those requirements only apply when BHP chooses to support its indemnity obligation with a liability insurance policy. When a company self-insures, by contrast, “there is no contract with an insurance company.”16 We find further support for our reading in Texas case law. In Hertz Corp. v. Robineau, the Texas Court of Appeals explained that “the term ‘self-insurance’ is a misnomer” because “in effect, a self-insurer does not provide insurance at all.”17 It went on to make clear that a self-insurer does not “assume[ ] all the duties and burdens of an insurer,” unless the parties have expressly *306contracted for “liability coverage.”18 “To say that a self-insurer will pay the same judgments and in the same amounts as insurance company would have had to pay is one thing; while it is obvious that to assume all the obligations that exist under a [liability policy] is quite another thing.” 19 We therefore conclude that the additional insured and primary insurance requirements do not apply BHP’s self-insurance.
Fourth, Underwriters argue that because “discharge of the debtor does not affect the liability of any other entity on, or the property of any other entity for, such debt,”20 we should enforce BHP’s contractual obligations. Otherwise, they contend, BHP will receive a windfall. This argument, too, misses the point. It is true that Deep Marine’s bankruptcy does not affect the liability of any other entity, such as Underwriters, to Duval. But Duval has not alleged that BHP has any potential liability for his claims. That makes sense because BHP’s only obligation is an indemnification obligation to Deep Marine; unlike Underwriters, it has no secondary liability to injured tort victims, like Duval.
Before concluding, we pause briefly to address Underwriters’ contention that they could tender BHP directly to Duval under Federal Rule of Civil Procedure 14(c). Such tender was improper because Duval has no claim against BHP. The MSA only obligates BHP to indemnify members of the “Contractor Group.” As an employee of Wood Group (a BHP contractor), Duval is only a member of “Company Group,” not “Contractor Group,” so BHP’s contractual obligations do not run to him. And, even if they did, because no claims have been asserted against Duval, BHP would have no obligation to indemnify and defend him.21 Moreover, as we have previously explained, Underwriters did not agree to act as the primary insurer of Deep Marine against Duval’s claim, so Duval could not bring suit directly against BHP under Louisiana’s Direct Action Statute.
IV.
For the reasons set forth above, we AFFIRM the judgment of the district court.