Certain Underwriters at Lloyd’s London and Arch Specialty Insurance Co. (collectively, “Underwriters”) appeal a summary judgment to reimburse Bruce Perraud and Thomas Raffanello for attorney’s fees and costs. We find no error and affirm.
I.
Perraud and Raffanello were employees of the Stanford Financial Group Company (“SFGC”), which was covered under a directors’ and officers’ liability policy issued by Underwriters. Following a successful defense ¿gainst federal criminal charges, Perraud and Raffanello sought reimbursement for attorney’s fees and costs under that policy. Underwriters refused to pay and sued for a declaratory judgment on the basis of a policy exclusion. On cross-motions for summary judgment on stipulated facts, the district court found that the exclusion was ambiguous and interpreted it in favor of coverage pursuant to Texas’s doctrine of contra proferentem. The court declined to apply a sophisticated-insured exception to that doctrine, concluding that even if Texas were to recognize the exception, Underwriters had presented “no evidence ... indicating that Stanford negotiated or drafted [the exclusion at issue].” Underwriters do not appeal the finding of ambiguity; they challenge only the application of the sophisticated-insured exception and the denial of them Federal Rule of Civil Procedure 59(e) motion.
II.
“On 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.”1 “Summary judgment is appropriate ‘if the movant shows that there is no genuine dispute as to any material fact and the movant is entitled to judgment as a matter of law.’ ”2
The courts that have recognized the sophisticated-insured exception have taken a variety of approaches to its application. On one end of the spectrum, some have construed it narrowly, as the district court did here, to apply only where the insured actually negotiated the particular provision at issue.3 At the opposite extreme are *631courts that broadly apply the exception any time the insured is a sophisticated business entity, regardless of whether the insured, or someone on the insured’s behalf, actually negotiated or drafted portions of the policy.4 Most courts have taken a middle ground, deeming the exception triggered where the insured — or a broker acting on the insured’s behalf— actually negotiates, drafts, or proposes portions of the policy.5
This appeal is premised on the assumption that Texas recognizes the sophisticated-insured exception in any of its varieties, yet Underwriters, as appellants, chose not to argue that issue on appeal;
Underwriters does not reargue here whether Texas recognizes the sophisticated insured exception, because it anticipates the Texas Supreme Court will resolve that question before this appeal is heard. Therefore, for purposes of this appeal, Underwriters presumes the sophisticated insured exception will be recognized.[6]
Although Underwriters thus assumed that the Supreme Court of Texas would answer the certified question from this court, the *632court found it unnecessary to do so.7 Where an appellant declines to press an issue — and especially, as here, where the appellant explicitly declines to argue it— the issue is waived.8
This court followed the doctrine of contra proferentem in a case involving the same policy at issue here, stating that “if a policy is susceptible to more than one reasonable interpretation, *[t]his Court has clearly identified that Texas law requires an insurance policy to be construed against the insurer and in favor of the insured’ — in other words, in favor of coverage.”9 Although the sophisticated-insured exception was not raised in Pendergest-Holt, Texas’s strong policy in favor of coverage informs our understanding of the evidentiary showing that Texas would require to trigger the sophisticated-insured exception, assuming — for the limited purpose of this appeal — that Texas would even recognize the exception.
There is no reason to believe that Texas would adopt an unusually broad sophisticated-insured exception to its longstanding doctrine of contra proferentem.10 No Texas court has ever recognized the exception, and the state’s highest civil court recently declined to do so on a certified question. We offer no opinion on whether Texas courts would actually rec-ognizé it;- we only assume the recognition arguendo and only for the purpose of determining whether Underwriters have offered enough evidence to create a genuine dispute of material fact as -to whether they have satisfied that exception if it did exist. Because of Texas’s doctrine of contra prof-erentem, and because we have no indication that Texas courts would recognize an extremely broad sophisticated-insured exception, we will not assume for purposes of this appeal that Texas would do so. Thus, our analysis is limited to the narrow and middle-ground variations on the doctrine.
The only summary-judgment evidence of SFGC’s bargaining power is a declaration by .Paul Sewell, the head of claims for one of Underwriters’ syndicates, that there “was a negotiation between [Underwriters] and [SFGC’s broker] in terms not only of pricing, but also terms and conditions that would have been implemented into the policy.” Sewell admitted that his contention that some negotiations occurred was not based on his actual involvement in the negotiations or on information that some*633one else had told him, but rather “through thirty years of working the industry, [he] understands the process.” Likewise, in response to a question about whether he would “just ... talk about the process, not necessarily the particulars of this file,” Se-well responded that he could not “talk about the actual negotiations, as [he] wasn’t on the underwriting side, so [he] wasn’t involved in the actual negotiation,” but was familiar with “how that process works in London” from “a global perspective.”
Sewell’s bare assertion that some negotiation occurred based on his general understanding of industry processes is insufficient to create a genuine dispute of material fact as to the exception’s applicability under the narrow or middle-ground approaches. Underwriters do not challenge the district court’s conclusion that they presented “no evidence ... that Stanford negotiated or drafted [the exclusion at issue]”; instead they maintain that the court erred by applying such a narrow version of the exception.11
But the summary-judgment evidence is also insufficient to create a genuine dispute of material fact under the middle-ground approach. Sewell admitted that he had no knowledge of the “actual negotiation,” and his reference to a general negotiation process — without any specifics as to what was actually negotiable — sheds no light on SFGC’s actual bargaining power.
Absent any information about the content of the negotiations, how the contracts were prepared, or other indicators of relative bargaining power, Underwriters did not present evidence that the insured did or could have influenced the terms of the exclusion.12 The district court did not err by declining to apply the exception even if, arguendo, it were applicable in Texas.
III.
Underwriters provided additional evidence of bargaining power in their Rule 59(e) motion, which the district court denied without “expressly or impliedly refer[ring] to the additional materials,” such that this court reviews for abuse of discretion. Templet v. HydroChem Inc., 367 F.3d 473, 477 (5th Cir.2004).13 We consider: “(1) the reasons for the moving party’s default, (2) the importance of the omitted evidence to the moving party’s case, (3) whether the evidence was available to the movant before the nonmovant filed .the summary judgment motion, and (4) the likelihood that the nonmoving party will suffer unfair prejudice if the case is reopened.”14 Those factors, however, “are simply illustrative and not exhaustive ... Rule 59(e) motions provide the district court with ‘considerable discretion.’ ”15
*634With respect to the reasons for default, Underwriters maintain that they had no reason to believe that they needed to provide additional evidence until the time of the district court’s order. Nonetheless, Underwriters would have been on notice before that order — based on the substantial nationwide caselaw applying the sophisticated-insured exception — that they needed to present evidence of SFGC’s bargaining power beyond the bare assertion that some negotiation had occurred.'
Although the first factor weighs against Underwriters, the second factor weighs in their favor because the omitted evidence is important to the applicability of the exception. Bút Underwriters do not suggest that the evidence was unavailable at the time of summary-judgment briefing, such that the third factor weighs against them. Factor four is neutral; Perraud and Raffa-nello have not shown that they would suffer unfair prejudice so long as they are given an opportunity to submit evidence of their own. In light of the factors considered together, the district court did not abuse its considerable discretion by denying the motion.
The judgment is AFFIRMED.
Pursuant to 5th Cir. R. 47.5, the court has determined that this opinion should not be published and is not precedent except under the limited circumstances set forth in 5th Cir. R. 47.5.4.
. Ford Motor Co. v. Tex. Dep't of Transp., 264 F.3d 493, 498 (5th Cir.2001) (citation omitted).
. Johnston & Johmton v. Conseco Life Ins. Co., 732 F.3d 555, 561 (5th Cir.2013) (quoting Fed. R. Civ. P. 56(a)), cert. denied, — U.S. -, 134 S.Ct. 1892, 188 L.Ed.2d 914 (2014).
. See, e.g., Commercial Union Ins. Co. v. Wal-brook Ins. Co., 7 F.3d 1047, 1053 n. 8 (1st Cir. 1993) (noting that the exception is invoked "sparingly” and suggesting that it would not apply where there is “no evidence that [the insured] participated in drafting the language at issue”); Ogden Corp. v. Travelers Indem. Co., 681 F.Supp. 169, 174 (S.D.N.Y. 1988) ("Although [the insured] did in fact negotiate with [the insurer], it cannot be said that [the insured] completely drafted the provisions in question so as to cause the Court to apply a limited exception to the general rule by construing ambiguities in favor of the insurer.”); see also McDermott Int’l, Inc. v. Lloyds Underwriters of London, 944 F.2d 1199, 1207 (5th Cir.1991) (applying the exception where the insured’s agent chose the provision at issue for inclusion in the policy). The Supreme Court of California takes an even narrower approach, holding that even where the inclusion of the provision at issue has been negotiated by a sophisticated insured, the exception is inapplicable where the language at issue has been "adopted verbatim *631from standard form policies used throughout the country.” AIU Ins. Co. v. Superior Court, 51 Cal.3d 807, 274 Cal.Rptr. 820, 799 P.2d 1253, 1265 n. 9(1990).
. See, e.g., St. Paul Mercury Ins. Co. v. Grand-Chapter of Phi Sigma Kappa, Inc., 651 F.Supp. 1042, 1045 (E.D.Pa.1987) (“Pennsylvania principles of construction require the Court to resolve an ambiguity of this kind in favor of the insured unless the parties possess equal bargaining power, such as when a large corporation, advised by counsel, is the insured.”); Owens-Illinois, Inc. v. United Ins. Co., 138 N.J. 437, 650 A.2d 974, 991 (1994) ("As the Appellate Division noted, O-I was a sophisticated insured and cannot seek refuge in the doctrine of strict construction by pretending it is the corporate equivalent of the unschooled, average consumer.” (internal quotation marks omitted)); see also Eagle Leasing Corp. v. Hartford Fire Ins. Co., 540 F.2d 1257, 1261 (5th Cir.1976) (stating that “[w]e do not feel compelled to apply ... [the doctrine of contra proferentem ] in the commercial insurance field when the insured is not an innocent but a corporation of immense size,” though noting also that the policy at issue contained provisions "confected especially for” the insured).
. See, e.g., Six Flags, Inc. v. Westchester Surplus Lines Ins. Co., 565 F.3d 948, 958 (5th Cir.2009) ("[U]nder Louisiana law, the presumption does not apply where the insured is a sophisticated commercial entity that itself drafts or utilizes its agent to secure desired policy provisions.”); Pittston Co. Ultramar Am., Ltd. v. Allianz Ins. Co., 124 F.3d 508, 521 (3d Cir.1997) (“[T]he dispositive question is not merely whether the insured is a sophisticated corporate entity, but rather whether the insurance contract is negotiated, jointly drafted or drafted by the insured.”); Northbrook Excess & Surplus Ins. Co. v. Procter & Gamble Co., 924 F.2d 633, 639 (7th Cir. 1991) (applying the exception where "significant portions of the policy’s language were customized at [the insuredl's insistence”); E. Associated Coal Corp. v. Aetna Cas. & Sur. Co., 632 F.2d 1068, 1071 (3d Cir. 1980) (applying exception where insured’s broker "selected the form, prepared the policies, and sent the policies to the insurers and underwriters for signature”); Vought Aircraft Indus., Inc. v. Falvey Cargo Underwriting, Ltd., 729 F.Supp,2d 814, 824 (N.D.Tex.2010) (“The exception is justified .where the insured contributes to the drafting of the agreement rather than adopting a contract of adhesion, the contents of the policy are in some way negotiable, and the insured is as capable as the insurer of interpreting the contract.” (footnote omitted)); Cummins, Inc. v. Atl. Mut. Ins. Co., 56 A.D.3d 288, 290, 867 N.Y.S.2d 81 (N.Y.App.Div.2008) (applying the exception where “the evidence ... shows that while defendant prepared the drafts of the agreement, the basic concept and terms originated with plaintiff, that plaintiff is sophisticated and was instrumental in crafting various parts of the agreement, and that plaintiff, while not an insurance company, had equal bargaining power and acted like an insurance company by maintaining a self-insured retention”).
.Brief for Underwriters at 22 n. 8.
. See In re Deepwater Horizon, 470 S.W.3d 452, 468-69 (Tex.2015) ("The second certified question asks whether the ambiguity rule governs interpretation of the insurance-coverage provision in the Drilling Contract, given the facts of this case. The certified question- is directed to resolving the parties' disagreement about whether the rule should apply to insurance-coverage disputes between sophisticated parties.... The ambiguity rule comes into play only if there is more than one reasonable interpretation of an insurance policy. Because that is not the situation here, we do not answer the second question.” (citations omitted)).
. Spear Marketing, Inc. v. BancorpSouth Bank, 791 F.3d 586, 602-03 (5th Cir.2015) (stating that argument not advanced in opening brief is waived).
. Pendergest-Holt v. Certain Underwriters at Lloyd's of London, 600 F.3d 562, 569 (5th Cir.2010) (alteration in original) (quoting Nat’l Union Fire Ins. Co. of Pittsburgh v. Willis, 296 F.3d 336, 339 (5th Cir.2002)).
. See Mut. Life Ins. Co. v. Simpson, 88 Tex. 333, 31 S.W. 501, 502 (1895) ("We are not unmindful of the well-recognized rules as to the construction of contracts of insurance, — ■ that forfeitures are not favored, and that generally, in cases where there is doubt or ambiguity, that construction should be adopted most favorable to the assured, — -the reasons for which 'are obvious, and need not be recounted.”).
. The court also observed that because the exclusion at issue "is found in the main body of the form policy, and not in any negotiated endorsement, it appears that the Underwriters drafted that provision.”
. Cf. Pittston, 124 F.3d at 521 (reversing summary judgment and applying the sophisticated-insured exception because "[t]he broker testified in his deposition that he prepared the initial draft of the policies and negotiated the terms with the insurers” such that the "sophisticated insured ... was heavily involved in the drafting and negotiating of the policies”).
. Underwriters acknowledge that the abuse-of-discretion standard applies. Brief for Underwriters at 17-18, 30.
. ICEE Distribs., Inc. v. J & J Snack Foods Corp., 445 F.3d 841, 848 (5th Cir.2006) (quoting Templet, 367 F.3d at 482) (internal quotation marks omitted).
. Id. (alteration in original) (quoting Tem-plet, 367 F.3d at 482) (internal quotation marks omitted).