OPINION OF THE COURT
McGuire, J.This breach of contract and declaratory judgment action commenced by plaintiff Estee Lauder Inc. against its insurer, defendant OneBeacon Insurance Group, LLC and its affiliates, arises from OneBeacon’s refusal to defend and indemnify certain environmental claims asserted against plaintiff. The resolution of this appeal turns on whether OneBeacon waived its right to disclaim coverage on the ground that plaintiff failed to give it timely notice of certain claims against plaintiff.
By a letter to counsel for Lauder dated July 24, 2002, One-Beacon rejected Lauder’s claim for defense and indemnity with respect to claims against Lauder relating to the Huntington and Blydenburgh landfills. Specifically, OneBeacon advised that it was “terminating its investigation of this matter and closing its file.” The sole ground stated for this decision was that OneBeacon “cannot locate any further evidence” of the policy under which Lauder sought coverage, a policy that Lauder could not locate, although it identified the policy, which assertedly ran from September 1968 to September 1971, by its policy number. Thereafter, by a letter dated November 1, 2002, OneBeacon denied Lauder a defense to another action, the Hickey’s Carting claim, relating to the Blydenburgh landfill. The stated ground for this decision was the same ground stated in the July 24 letter, i.e., that “OneBeacon has been unable to find any other evidence to confirm the existence and terms of th[e] . . . policy” that Lauder contended OneBeacon’s predecessor had issued. Referencing its July 24 letter and other correspondence, One-Beacon stated that it “stands by its prior disclaimers of coverage.” Neither in the July 24 nor the November 1 letter did One-Beacon ever assert that Lauder had failed to give timely notice of a claim or occurrence, let alone disclaim coverage on the ground of such a failure by Lauder.
*35An insurer’s “notice of disclaimer must promptly apprise the claimant with a high degree of specificity of the ground or grounds on which the disclaimer is predicated” (General Acc. Ins. Group v Cirucci, 46 NY2d 862, 864 [1979]). Of course, an insurer may reserve the right to disclaim on such different or alternative grounds as it may later find to be applicable (National Rests. Mgt. v Executive Risk Indem., 304 AD2d 387, 388 [2003] ). However, “[a]n insurer must give written notice of disclaimer on the ground of late notice as soon as is reasonably possible after it learns of the accident or of grounds for disclaimer of liability, and failure to do so precludes effective disclaimer” (Matter of Firemen’s Fund Ins. Co. of Newark v Hopkins, 88 NY2d 836, 837 [1996] [internal quotation marks omitted]). Because of the insurer’s duties to disclaim promptly and with specificity, “New York law establishes that an insurer is deemed, as a matter of law, to have intended to waive a defense to coverage where other defenses are asserted, and where the insurer possesses sufficient knowledge (actual or constructive) of the circumstances regarding the unasserted defense” (State of New York v AMRO Realty Corp., 936 F2d 1420, 1431 [1991]).1
As the duties to disclaim promptly and specifically are imposed by law (see Hotel des Artistes, Inc. v General Acc. Ins. Co. of Am., 9 AD3d 181, 193 [2004], lv dismissed 4 NY3d 739 [2004] ), an insurer cannot unilaterally absolve itself of these duties. Thus, an insurer cannot avoid a waiver of a defense of which it has actual or constructive knowledge (i.e., avoid its duties to disclaim promptly and with specificity on the basis of that defense) by a unilateral assertion in a disclaimer notice that it is reserving or not waiving a right to disclaim on other, unstated grounds (id. at 185, 193 [despite statement by insurer in its disclaimer letter that it was not waiving any rights or defenses under the policy not mentioned in the letter, insurer waived defense of late notice both because it failed to disclaim on this ground in the letter and because it failed to raise a defense of late notice in its answer]; see also Allstate Ins. Co. v Moon, 89 AD2d 804, 806 [1982]).2
*36On the basis of, among other things, a tolling agreement between Lauder and the Attorney General relating to the Blydenburgh landfill claim that Lauder produced to OneBeacon in April 2000 (familiarity with which OneBeacon acknowledged on July 6, 2000), a notice of potential claim relating to the Huntington landfill that Lauder provided to OneBeacon in 1987 and a notification made by Lauder to OneBeacon and other carriers in May 1999 that the Attorney General had identified it as a “potentially responsible party” in connection with the Huntington landfill, it is clear that long before its July 2002 and November 2002 letters OneBeacon had sufficient knowledge of the circumstances relating to its defense of untimely notice. Indeed, OneBeacon does not argue otherwise in its brief.
Nor did Supreme Court conclude otherwise. Rather, Supreme Court reasoned that in light of the sweeping reservation of all of its rights, “that OneBeacon possessed sufficient knowledge to assert a late-notice defense by virtue of its receipt of the [tolling agreement] ... is inconsequential.” Thus, an erroneous conclusion of law—namely, that as long as an insurer claims or reserves the right to do so, it may disclaim coverage on one ground and thereafter disclaim coverage on another ground even though it had actual or constructive knowledge of the latter ground at the time of the initial disclaimer—was the basis for Supreme Court’s conclusion that OneBeacon had not waived its right to assert a defense of late notice.3
OneBeacon is not persuasive in contending that it did not disclaim coverage in its July 2002 and November 2002 letters. As noted, in the July 2002 letter OneBeacon informed Lauder that it was “terminating its investigation of this matter and closing its file” with respect to Lauder’s tender under the disputed pre-1971 policy (Policy No. E16-40036-27) with regard to the Huntington and Blydenburgh landfills. With respect to the Hickey’s Carting claim, OneBeacon expressly referenced in *37its November 2002 letter the earlier decision to close its file and went on to state, “[p]lease be advised that OneBeacon has determined, at this time, it will not revisit its prior determination.” Even assuming that OneBeacon did not state in either letter that it was “disclaiming” coverage, both letters made clear that OneBeacon was denying coverage.4
No case cited by OneBeacon supports the proposition that an insurer disclaims coverage only if it uses a form of the word “disclaim” in the course of denying coverage. The cases that are on point are to the contrary (see e.g. Commercial Union Ins. Co. v International Flavors & Fragrances, Inc., 822 F2d 267, 270, 274 [2d Cir 1987] [construing New York law]). Moreover, to accept OneBeacon’s position would exalt form over substance and invite gamesmanship. Because we conclude that OneBeacon did disclaim coverage in the July 2002 and November 2002 letters, we need not address Lauder’s independent contentions that OneBeacon constructively waived its untimely notice defenses by failing to assert them within a reasonable time (see e.g. 151 E. 26th St. Assoc. v QBE Ins. Co., 33 AD3d 452 [2006]) and by failing to assert them with specificity in its answer to Lauder’s complaint (see e.g. Hotel des Artistes, 9 AD3d at 193).
With respect to constructive waiver, one final contention by OneBeacon should be addressed. It argues that “where, as here, the existence of coverage has not been established because the insurance policy is missing, ... an insurer cannot waive its right to disclaim coverage.” To be sure, as noted above, “where the issue is the existence or nonexistence of coverage (e.g., the *38insuring clause and exclusions), the doctrine of waiver is simply inapplicable” (Albert J. Schiff, 51 NY2d at 698). Thus, where the putative insured fails to establish coverage, it is not created by the insurer’s failure timely to disclaim coverage (id.). It does not follow, however, that when an insurer asserts that no policy was in effect during the relevant period, an untimely-notice defense to coverage need not be timely asserted.
OneBeacon’s argument would be more compelling if the duties of an insurer to disclaim coverage in a timely, specific and nonselective manner were imposed solely by the terms of the contract of insurance. As noted above, however, those duties are imposed by law. So, too, at least where the policy is silent on the subject, the conditions of reasonable notice of occurrence and reasonable notice of claim are implied into every insurance contract (see Olin Corp. v Insurance Co. of N. Am., 743 F Supp 1044, 1051 [SD NY 1990] [construing New York law], affd 929 F2d 62 [2d Cir 1991]). Thus, as Lauder argues, knowledge of the policy’s actual terms is not necessary to assert such defenses to coverage.5
Although there appears to be a paucity of precedent on the issue, OneBeacon’s position is inconsistent with Burt Rigid Box, Inc. v Travelers Prop. Cas. Corp. (302 F3d 83 [2d Cir 2002]). In that case, the insurer defended in a coverage action brought by the insured on the ground, among others, that the insured had failed to prove the existence and terms of the alleged policies and thus that it was an insured (id. at 88-90). Nonetheless, construing New York law, a panel of the Second Circuit concluded that the insurer had waived its right to assert untimely notice when, in its answer, it disclaimed coverage on a number of specific grounds without specifically listing untimely notice (id. at 95-96). Although the panel did not expressly discuss the argument pressed by the insurer in the District Court that “a dispute over whether an insurance policy was *39ever issued negates the putative insurer’s obligation to disclaim based on untimely notice of an occurrence” (126 F Supp 2d 596, 632 [WD NY 2001]), it implicitly rejected that argument.
We agree, moreover, with the reasoning of Magistrate Judge Foschio that
“[imposing the duty on the insurer to provide an early disclaimer based on late notice of an occurrence or claim, even where the insurer claims there is no policy, enables the insured to make a prompt and fully informed decision as to whether to pursue efforts to establish the existence of the policy or to better invest its resources on investigating the potential claim, and preparing a defense” (id. at 633).
Acceptance of OneBeacon’s argument that an insurer is absolved of any duty to make timely, specific and nonselective disclaimers on the basis of defenses to coverage when the insurer denies that a policy was issued would entail an extraordinary proposition: that if the insurer ultimately is found to have issued the policy—even after litigation over a period of years—the insurer nonetheless still can disclaim on the basis of defenses to coverage it could have asserted prior to or at the outset of the litigation.
Finally, although Supreme Court denied Lauder’s motion for partial summary judgment on its third and fourth causes of action, it did not discuss that motion in its decision and apparently denied it as moot given its determination that OneBeacon was entitled to summary judgment dismissing the complaint. We grant Lauder’s motion. Lauder came forward with sufficient secondary evidence of the disputed pre-1971 policy—including, specifically, a renewal policy issued to it by OneBeacon’s predecessor stating in the declaration page that the policy being renewed is the disputed policy, No. E16-40036-27, and two certificates of insurance signed by the predecessor in 1969 and 1970, both certifying, among other things, that the policy, Ño. E16-40036-27, was issued to Lauder effective September 18, 1968 with an expiration date of September 18, 1971—to establish the existence of the policy and to invoke the presumptions that the terms of the renewal policy are identical to the terms of the policy being renewed and that the policy being renewed, like the renewal policy, was a three-year policy ending on September 18, 1971 (see Century Indem. Co. v Aero-Motive Co., 254 F Supp 2d 670, 692 [WD Mich 2003] [upholding insured’s *40reliance “on the rule that unless an agreement to the contrary is shown, a renewal policy is presumed to be on the same terms, conditions, and amounts as provided in the original policy”]; Lewitt & Co., Inc. v Jewelers’ Safety Fund Socy., 249 NY 217, 222 [1928] [“Clearly, a policy which renews an old policy must renew the terms of that policy as they stood at the moment of expiration. An agreement to renew a policy[ ] implies that the terms of the existing policy are to be continued ... in the absence of evidence[ ] that a change was intended” (internal quotation marks omitted)]). As Lauder would be entitled to a defense under the duty-to-defend clause in the renewal policy, it adduced sufficient evidence on its motion to establish that it is entitled to a defense in the underlying actions that are the subject of its third and fourth causes of action.6
In its opposition, OneBeacon failed to meet its burden of coming forward with evidentiary facts sufficient to raise any material issues of fact that would require denial of Lauder’s motion (see Rotuba Extruders v Ceppos, 46 NY2d 223, 231 [1978]; S.J. Capelin Assoc. v Globe Mfg. Corp., 34 NY2d 338, 343 [1974]). As the affidavit of Lauder’s expert submitted in its reply convincingly demonstrates, OneBeacon’s expert offered only unsupported assumptions and speculation (see Aero-Motive, 254 F Supp 2d at 692-693; Batista v Rivera, 5 AD3d 308, 309 [2004]; *41Warden v Orlandi, 4 AD3d 239, 242 [2004]; Leggio v Gearhart, 294 AD2d 543, 545 [2002]). For this same reason, OneBeacon failed to raise a material issue of fact supporting its position—on which it bears the burden of proof (see Town of Massena v Healthcare Underwriters Mut. Ins. Co., 98 NY2d 435, 444 [2002])—that the disputed policy would have contained a pollution exclusion during the entire policy period.
Accordingly, the order of Supreme Court, New York County (Carol R. Edmead, J.), entered December 12, 2006, which granted defendants’ motion for summary judgment dismissing the complaint, and denied plaintiffs motion for summary judgment on its third and fourth causes of action and plaintiff’s cross motion to dismiss defendants’ defense of untimely notice, should be reversed, on the law, with costs, defendants’ motion for summary judgment should be denied, plaintiffs motion for summary judgment on its third and fourth causes of action granted, plaintiffs cross motion for summary judgment dismissing defendants’ untimely notice defense with respect to plaintiffs first and second causes of action granted, and the matter remanded to Supreme Court for further proceedings.
Tom, J.P, Saxe, Friedman and Gonzalez, JJ., concur.
Order, Supreme Court, New York County, entered December 12, 2006, reversed, on the law, with costs, defendants’ motion for summary judgment denied, plaintiffs motion for summary judgment on its third and fourth causes of action granted, plaintiff’s cross motion for summary judgment dismissing defendants’ untimely notice defense with respect to plaintiffs first and second causes of action granted, and the matter remanded to Supreme Court for further proceedings.
. However, “where the issue is the existence or nonexistence of coverage (e.g., the insuring clause and exclusions), the doctrine of waiver is simply inapplicable” (Albert J. Schiff Assoc. v Flack, 51 NY2d 692, 698 [1980]).
. We came to the same conclusion in Benjamin Shapiro Realty Co. v Agricultural Ins. Co. (287 AD2d 389 [2001]). There, we held that an insurer had *36waived the defense of untimely notice of occurrence when its disclaimer letter asserted a different lack of notice ground. Although it is not mentioned in our memorandum decision, Lauder correctly points out that the disclaimer letter in Benjamin Shapiro asserted that nothing in the letter should be construed “as a waiver of any of the terms and conditions of the policy, or of any rights or defenses provided by law, all of which are expressly reserved.”
. For this reason, Supreme Court denied Lauder’s cross motion to dismiss OneBeacon’s defense of untimely notice. For this same reason, and because Supreme Court concluded that Lauder had failed to give timely notice, Supreme Court granted OneBeacon’s motion for summary judgment dismissing the complaint.
. As noted above, the November 2002 letter also stated that OneBeacon “stands by its prior disclaimers of coverage with regard to the pre-1971 policies issued by [its predecessor]” (emphasis added). OneBeacon plausibly argues that put in context the reference to “pre-1971” policies reflects a typographical error and that the letter intended and could only have been understood to refer to other, post-1971 policies. Given our view that the substance of both letters should be controlling, we think it irrelevant that in its November 2002 letter OneBeacon may not have expressly characterized the July 2002 letter as a “disclaimer! ]” of coverage. We note, however, that a header to the November 2002 letter denominates the letter as a “SUPPLEMENTAL DISCLAIMER OF COVERAGE/RESERVATION OF RIGHTS.” We note, too, that in separate letters dated November 11, 1999 relating to the claims arising out of the Blydenburgh and Huntington landfills, OneBeacon informed Lauder that “[a]s soon as we have completed our investigation, we will notify you of our coverage determination.” Because OneBeacon stated that it was “terminating its investigation” in its July 2002 letter, Lauder argues that the November 11, 1999 letters afford an additional reason to conclude that the July 2002 and November 2002 letters constitute disclaimers, i.e., the promised “coverage determination.”
. OneBeacon does not argue that policies it issued during the period in question relieved its insureds of these duties. To the contrary, OneBeacon’s expert asserted that if the alleged policy existed, it “would have required Es-tee Lauder to notify the insurer in writing of the particulars of an ‘occurrence’ ‘as soon as practicable’ and to ‘immediately’ forward any claims made or suits brought against the insured to the insurer.” Moreover, as Lauder observes, even as OneBeacon asserted in the seventh affirmative defense of its answer that Lauder had not proven the existence and terms of the disputed policy, OneBeacon’s fourth affirmative defense asserted that it was not liable to the extent Lauder had failed to perform conditions that may be contained in the alleged policy “including, but not limited to, the notice . . . requirements.”
. The third cause of action alleges that OneBeacon breached its duty to defend Lauder in the Hickey’s Carting action and claims that Lauder is entitled to recover all posttender reasonable fees and expenses necessarily incurred in defense of that action, plus prejudgment interest accruing from the date of OneBeacon’s repudiation of its duty to defend. Although the third cause of action identifies that date as “October 2002,” that date appears to reflect a typographical error as Lauder contends only that OneBeacon disclaimed coverage in its November 1, 2002 letter. We do not understand Lauder to be claiming that it is entitled to fees and expenses in excess of the applicable policy limits. The fourth cause of action claims that with respect to any future defense costs Lauder may incur in defense of the Blydenburgh landfill claim and the Hickey’s Carting action, it is entitled to a declaration that such defense costs must be paid promptly by OneBeacon to the extent that they are reasonable and necessary. Again, we do not understand Lauder to be seeking the recovery of defense costs in excess of the applicable policy limits. The fourth cause of action also claims that Lauder is entitled to a declaration that any reasonable settlement of the Blydenburgh landfill claim and the Hickey’s Carting action must be timely indemnified by OneBeacon up to the applicable loss limits. However, Lauder does not mention this claim for indemnification in its briefs and thus we limit the declaration to the claim for defense costs. Finally, for reasons that are not explained by Lauder in its briefs, it did not move for summary judgment on its first and second causes of action, asserting breach of contract on account of OneBeacon’s failure to provide a defense to and repudiation of its obligation to indemnify with respect to, respectively, the Huntington landfill and Blydenburgh landfill cases.