JOSÉ A. CABRANES, Circuit Judge:
This is an appeal from an order granting summary judgment in favor of defendant Connecticut General Life Insurance Co. (“Connecticut General”) in the United States District Court for the Southern District of New York (Shirley Wohl Kram, Judge), reported at 851 F.Supp. 547 (S.D.N.Y.1994). The plaintiff, Adele Gallien, brought the action to obtain payment under a life insurance policy issued as part of an employer-provided group plan after Connecticut General denied coverage upon the plaintiffs husband’s death. Connecticut General claimed that the decedent, Paul Gallien, died without life insurance coverage because the employer had stopped paying premiums for Gallien three months before he died.1
The district court agreed with Connecticut General and found that the policy unambigu[880]*880ously stated that life insurance coverage for employees in Gallien’s circumstances ceased when the employer stopped- paying premiums.. The district court held further that the plaintiff could not prevail on a theory of waiver because, under New York law, “defenses relating to the issue of ... coverage ... are not waivable.” 851 F.Supp. at 555 (quoting Taft v. Equitable Life Assurance Soc’y, 173 A.D.2d 267, 269, 569 N.Y.S.2d 660 (1st Dep’t 1991)).
The group insurance policy, however, is ambiguous. It could reasonably be read to provide that cessation of premium payments did not result in irreversible termination of Gallien’s life insurance coverage, but rather afforded the insurer a unilateral right to terminate coverage. Moreover, New York law does recognize that an insurer may waive its right to terminate a policy. Although the district court correctly held that under New York law an insurer cannot waive the defense of non-coverage, New York does provide that an insurer may waive its right to claim that an insured forfeited a policy that would otherwise have afforded coverage. Because we find that the plaintiff has raised a genuine issue of material fact as to whether Connecticut General waived any right it might have had to terminate coverage, we reverse the judgment entered by the district court.
I. Background '
A. Facts
Carey Energy Corp. (“Carey”), Paul Gal-lien’s employer, entered into an insurance agreement with Connecticut General under which Carey’s employees received various types of group insurance, including accidental death, disability, medical expense, and term life insurance (collectively, the “policy” or the “group policy”). On January 20, 1989, at age 60, Gallien left “active service” with Carey and went on temporary, disability status. In July 1989, Gallien became eligible for permanent disability benefits, which he received until his death on October 25, 1989. Shortly after Gallien’s death, the plaintiff applied to Connecticut General for death benefits. Connecticut General disclaimed coverage.
Connecticut General’s contention that no death benefits were owed rested on its view that the status of Gallien’s life insurance coverage differed from that of all other kinds of coverage for all' other Carey employees because Gallien was a disabled employee age 60 or over. Carey had ceased paying premiums for its employees, including Gallien, on July 1, 1989. Despite this cessation in premium payments, Connecticut General did not cancel the group policy for all Carey employees until October 18, 1989. It continued coverage during this period despite the lack of premium, payments. Had Gallien been a typical employee, it is uncontroverted that he would have had life insurance coverage under these circumstances, even though he died a week after the policy was cancelled. Under the policy, the insurer agreed to pay death benefits to the insured’s beneficiary if the insured died within thirty-ione days after life insurance coverage ended.
Connecticut General, however, claimed that Gallien’s case posed a special circumstance. The insurer maintained that under a specific provision in the policy, life insurance benefits for disabled individuals age 60 or over ceased immediately upon the employer’s failure to pay premiums. That meant that Gallien, while eligible for all other forms of insurance until the October 18 cancellation, became ineligible for life insurance coverage in July, when Carey first failed to pay premiums.
The group policy provides:
Termination of Insurance — Employees Your insurance will cease on the earliest date below
• the date the policy is cancelled.
• the date your Active Service ends. except
as described below_
If your Active Service ends due to an Inj'ury or Siekness, your insurance will be continued while you remain totally and continuously disabled as a result of the Inj'ury or Sickness. However, your insurance will not continue past the earlier of: (a) one year from the date your Active Service ends unless your Employer obtains CG’s consent in writing to a longer period; [881]*881or (b) the date your Employer stops paying premium for you or otherwise cancels the insurance.
If you are totally disabled, your Life Insurance will terminate when you attain your normal date of retirement. If you are age 60 or over when you become disabled, your Life Insurance mil terminate at the earlier of (a) the date you attain your normal date of retirement, or (b) the date the Policyholder stops paying premium for you.
(Emphasis added). Connecticut General maintains that under the underscored exception, which indisputably applied to Gallien, his life insurance coverage ceased when Carey stopped paying premiums.
The “grace period” provision in the policy provides for a thirty-one day grace period as follows:
If a premium is not paid when due, the policy will automatically be cancelled as of the Premium Due Date, except as set forth below.
GRACE Period .... If any premium is not paid by the end of the [thirty-one day] Grace Period, the policy will automatically be cancelled at the end of the Grace Period....
Despite’ the “automatic cancellation” language of the grace period, Connecticut General provided coverage on all aspects of the group policy until October 18 — excluding Gal-Hen’s life insurance, according to Connecticut General — even . though premium payments ceased in July.
B. Procedural History
When Connecticut General disclaimed life insurance coverage for Gallien, the plaintiff filed suit against the insurer to obtain death benefits. She also sued Carey under § 409 of the Employee Retirement Income Security Act of 1974, (codified at 29 U.S.C. § 1109 (1985)), claiming that Carey, as administrator of the insurance plan, breached its fiduciary duty by failing to advise GalHen that it had ceased paying premiums and that Connecticut General had terminated coverage.2 Connecticut General cross-claimed against Carey for the recovery of allegedly unpaid premiums for the months of July through October 1989.
The plaintiff moved for summary judgment on its claim against Carey. Connecticut General moved for summary judgment on the plaintiffs claims, and for summary judgment on its cross-claims against Carey. The district judge granted the plaintiffs motion, against Carey, and she granted Connecticut General’s motion against the plaintiff. She granted Connecticut General’s summary judgment motion against Carey as to Hability, and she referred that claim to a magistrate judge for an inquest to determine the damages owed by Carey to Connecticut General. On June 10, 1994, she entered final judgment as to the plaintiffs claims, granting the plaintiff recovery against Carey, and dismissing the plaintiffs claims against Connecticut General. Inasmuch as Carey does not appeal from the plaintiffs judgment against it, we address only the summary judgment entered in favor of Connecticut General on the plaintiffs claims.
II. Discussion
A Standards for Summary Judgment
We review a district court’s grant of summary judgment de novo. Aslanidis v. United States Lines, Inc., 7 F.3d 1067, 1072 (2d Cir.1993). Summary judgment shall be granted “if the pleadings, depositions, answers to interrogatories, and admissions on file, together with the affidavits ... show that there is no genuine issue as to any material fact and that the moving party is entitled to a. judgment as a matter of law.” Fed.R.Civ.P. 56(c). “[T]he mere existence of some alleged factual dispute between the parties wiU not defeat an otherwise properly supported motion for summary judgment; the requirement is that there be no genuine [882]*882issue of material fact.” Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 247-48, 106 S.Ct. 2505, 2509-10, 91 L.Ed.2d 202 (1986). While the court must view the inferences to be drawn from the facts in the light most favorable to the party opposing the motion, Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 587, 106 S.Ct. 1348, 1356, 89 L.Ed.2d 538 (1986), a party may not “rely on mere speculation or conjecture as to the true nature of the facts to overcome a motion for summary judgment.” Knight v. U.S. Fire Ins. Co., 804 F.2d 9, 12 (2d Cir.1986), cert. denied, 480 U.S. 932, 107 S.Ct. 1570, 94 L.Ed.2d 762 (1987). The non-moving party may defeat the summary judgment motion by producing specific facts sufficient to establish that there is a genuine issue of material fact for trial. Celotex Corp. v. Catrett, 477 U.S. 317, 322, 106 S.Ct. 2548, 2552, 91 L.Ed.2d 265 (1986). Finally, “ ‘mere conclusory allegations or denials’ ” in legal memo-randa or oral argument are not evidence and cannot by themselves create a genuine issue of material fact where none would otherwise exist. Quinn v. Syracuse Model Neighborhood Corp., 613 F.2d 438, 445 (2d Cir.1980) (quoting SEC v. Research Automation Corp., 585 F.2d 31, 33 (2d Cir.1978)).
The plaintiff raises, in essence, three arguments in support of her claim that the district court erred in granting summary judgment. First, the plaintiff claims that judgment as a matter of law in Connecticut General’s favor was inappropriate because the language of the policy was ambiguous. Second, the plaintiff asserts that Connecticut General is equitably estopped from declining to provide coverage because it made misrepresentations about its coverage on which Gal-lien relied to his detriment. Finally, argues the plaintiff, Connecticut General by its conduct waived any right to claim that Gallien’s benefits were forfeited when Carey stopped paying premiums.
To evaluate the. plaintiffs claims, we first decide whether the policy unambiguously provides that life insurance coverage ended upon the cessation of premium payments, or whether the policy is ambiguous and in fact could be read as giving the insurer the option either to cancel insurance coverage for employees in Gallien’s position upon cessation of premium payments or to continue coverage.
Courts considering claims of contractual ambiguity in response to summary judgment motions typically attempt to determine both whether ambiguity exists and whether relevant extrinsic evidence of actual intent exists so that a trier of fact may resolve the ambiguity. See Mellon Bank, N.A v. United Bank Corp. of N.Y., 31 F.3d 113, 116 (2d Cir.1994). In this case, however, our inquiry is somewhat different.
Here, the question of whether the policy meant that there was no life insurance in effect at the moment premium payments ceased, or whether the policy simply gave the insurer the option to cancel, is only relevant for summary judgment purposes if the insurer’s conduct reflected an intent to continue the coverage. If the insurer’s conduct was completely consistent with an intent to disclaim coverage, then it would make no difference whether the insurer could not continue coverage, or whether it chose not to continue coverage. Eithér way there would be no coverage, and summary judgment for the insurer would be appropriate. Contractual ambiguity only becomes relevant in this case if there is evidence that the insurer intended to waive any right it had to cancel coverage. If we find that the policy is ambiguous, and that there is evidence to support waiver, then we must conclude that summary judgment was inappropriate.
B. Contractual Ambiguity
We first consider whether the insurance policy was ambiguous. Under New York law, “[a]n ambiguity in the terms of an insurance contract will generally be construed liberally m favor of the insured.” Francis v. INA Life Ins. Co. of N.Y., 809 F.2d 183, 185 (2d Cir.1987) (citing New York case law). “However, if the words are clear and unambiguous, they must be accorded their plain and ordinary meaning....” Id. Under New York law, a policy is unambiguous if “the words in the paragraphs of the policy under examination have a definite and precise meaning, unattended by danger of misconception in the purport of the policy [883]*883itself, and concerning which there is no reasonable basis for a difference of opinion.” Breed v. Insurance Co. of North Am., 46 N.Y.2d 351, 355, 413 N.Y.S.2d 352, 385 N.E.2d 1280 (1978).
The insurer argues that there was no ambiguity in the provision terminating life insurance upon cessation of premium payment. In its view, Gallien lost coverage at the moment in July when Carey stopped paying premiums — regardless of the insurer’s subsequent behavior. “[F]or employees such as Paul Gallien, the contract does not allow for continuation of life insurance beyond the date when premium payments cease,” the insurer argues. Appellee’s br. at 20 (emphasis added).3 The district court agreed with the defendant and found no ambiguity in the provision addressing termination of life insurance for disabled employees. The policy, however, is ambiguous. It could reasonably be read to provide that cessation of payments on Gallien’s behalf did not result in cancellation but instead afforded the insurer the unilateral right to cancel coverage. The language that insurance “will cease” or “will terminate” does not indicate whether termination is immediate, irreversible, and beyond the control of the contracting parties, or whether termination becomes the unilateral right of the insurer upon the occurrence of an event such as non-payment of premiums.
The insurer maintains that the latter interpretation would render the disputed provision meaningless and that it is therefore unreasonable. The policy extends life insurance coverage for employees like Gallien who leave active service due to injury or sickness. The relevant provision states:
If your Active Service ends due to an Injury or Sickness, your insurance will be continued while you remain totally and continuously disabled as a result of the Injury or Sickness. However, your insurance will not continue past the earlier of: (a) one year from the date your Active Service ends unless your Employer obtains CG’s consent in writing to a longer period; or (b) the date your Employer stops paying premium for you or otherwise cancels the insurance.
If you are totally disabled, your Life'Insurance will terminate when you attain your normal date of retirement. If you are age 60 or over when you become disabled, your Life Insurance will terminate at the earlier of (a) the date you attain your normal date of retirement, or (b) the date the Policyholder stops paying premium for you.
The insurer appears to argue that because it generally retains discretion to cancel any policy upon non-payment of premiums, it need not make special mention of that fact with regard to life insurance for disabled employees age 60 or over. That is, if the provision gave the insurer the option to cancel or to continue its coverage, then the provision would simply repeat the obvious. If the provision has any meaning, the insurer says, it must be that the insurer is not “allowed” to provide coverage upon the employer’s failure to pay premiums. Appellee’s br. at 14, 21.
We disagree. Although the defendant’s reading may be reasonable, provision “(b)” could just as easily serve another purpose: to make clear that while the policy explicitly provides for the extension of life insurance for disabled employees age 60 or over until retirement age, this extension will not necessarily remain in place if the employer stops paying premiums. That is, while the insurer is willing to extend life insurance coverage for an employee whose active service has ended, its willingness may be conditioned upon the employer’s payment of premiums.
The insurer provides no legal authority to support its construction of the contract or to dispute this alternative view. What authority we have found favors a construction that such a contract gives the insurer the right to cancel. In Hoffman v. Aetna Life Ins. Co., 60 Ohio App. 497, 14 O.O. 542, 22 N.E.2d 88 (1938), a case with strikingly similar facts, an insurance contract provided that “if any such premium is not paid when due, this policy shall cease.” 22 N.E.2d at 89. In rejecting [884]*884the same argument put forth by the insurer here, the court declined to find “that the provision of the policy that it shall cease for failure to pay premiums is self-executing, and that, as a matter of law, the policy at the time of said loss was not in force.” Id. Instead, the court recognized that “an insurance company can waive a provision of its policy in reference to ... termination,” and it affirmed a jury verdict finding waiver. 22 N.E.2d at 90. Similarly, in Chrosniak v. Metropolitan Life Ins. Co., 121 Misc. 453, 201 N.Y.S. 211 (Sup.Ct., Erie Cty.1923), aff'd, 209 A.D. 846, 204 N.Y.S. 898 (4th Dep’t 1924), the court did not reject the doctrine of. waiver where language indicated that upon termination of active employment the policy “automatically and immediately terminates.” 201 N.Y.S. at 212. These eases reflect the well-established principle that an “insurer may waive provisions of a policy placed in it for the insurer’s benefit.” 16B John A. Appleman & Jean Appleman, Insurance Law and Practice § 9081, at 498 (1981).
Having decided that the contract is ambiguous, our next question is whether these circumstances warrant our resolving this ambiguity as a matter of law. We think that they do not. Where relevant extrinsic evidence of the parties’ intent is not available, then contractual ambiguity “presents not an issue of fact, but an issue of law for the court to rule on.” Williams & Sons Erectors v. South Carolina Steel, 983 F.2d 1176, 1183-84 (2d Cir.1993). Here, however, relevant extrinsic evidence exists.
First, there is evidence that Connecticut General willingly extended the policy — with the exception, it argues, of Gallien’s life insurance — despite the cessation of premium payments. The significance of this extrinsic evidence can be understood when it is viewed in light of the Grace Period in the policy. The Grace Period provision states: “If any premium is not paid by the end of the Grace Period, the policy will automatically be can-celled at the end of the Grace Period....” Carey stopped paying premiums on July 1, which meant that the Grace Period expired in August. Yet, Connecticut General continued coverage on all forms of the group insurance — again, supposedly with the exception of Gallien’s life insurance — until October. While the “automatic cancellation” language of the Grace Period certainly gave Connecticut General the right to cancel after the Grace Period, Connecticut General, as demonstrated by its intentional continuance of coverage, was indeed “allowed” to continue coverage beyond that date. The language of automatic cancellation did not preclude continuation of coverage. The same can be said of the special life insurance provision. The policy could be interpreted to have provided Connecticut General with the right to end Gallien’s coverage after the first premiums went unpaid. It follows that Connecticut General had the discretion to waive that right and continue coverage in the absence of timely payments.
This analysis applies as well to the medical insurance clause that follows the life insurance provision. That clause also states that if “Active Service ends due to an Injury or Sickness, your [medical] insurance will be continued.... However, the insurance will not continue past the date your Employer stops paying premium for you....” Despite this language, Connecticut General did continue medical insurance for Carey’s employees after premium payments ceased. The language of its policy did not preclude it from doing so.
Finally, Connecticut General’s own records indicate that Gallien was in fact covered at the time of his death. And there appears to be a factual dispute as to whether Connecticut General initially represented to Carey that Gallien was covered.
In sum, because the contract is ambiguous, and because relevant extrinsic evidence of the parties’ intent exists, a trier of fact must resolve the ambiguity in the contract to determine whether Connecticut General enjoyed a waivable right to cancel coverage.
C. Waiver
Even though we have now decided that the contractual ambiguity here should be resolved by a trier of fact, reversal and remand based on this ambiguity would be unwarranted if the defendant had behaved consistently with an intent to disclaim. Were [885]*885it clear that the insurer disclaimed coverage for Gallien upon Carey’s cessation of premium payments, then there could be no dispute that coverage had ended. Summary judgment would have been appropriate in these circumstances, whether Connecticut General was prohibited from extending coverage, or whether it exercised its right to cease coverage.
Yet, there is evidence that the defendant did intend to waive whatever right it had to disclaim coverage. The district court does not appear to have considered this evidence, presumably because the judge thought that the doctrine of waiver did not apply to insurance contracts. The court, however, failed to recognize circumstances, such as those presented by this case, in which the , doctrine of waiver arguably applies.
The New York Court of Appeals has held that if an insured’s claim is outside the scope of coverage, then the doctrine of waiver is inapplicable. Albert J. Schiff Assocs., Inc. v. Flack, 51 N.Y.2d 692, 435 N.Y.S.2d 972, 417 N.E.2d 84 (1980). In Schiff, an insurance agency had purchased an “error and omissions” policy that provided coverage for negligent acts committed by the agency in its “professional capacity.” When the agency was sued for usurpation of a trade secret, it sought coverage, and the insurer responded with a disclaimer letter. The letter did not assert that usurpation of a trade secret was beyond the scope of coverage but relied on other grounds of exclusion'. Id. at 695-96.
The Court of Appeals held that the insurer did not waive the defense of non-coverage by failing to assert it in the disclaimer letter. Because waiver “is a voluntary and intentional relinquishment of a known right,” the court reasoned, there can be no waiver of a right to deny coverage unless “underlying coverage” exists. Id. at 698. If the rule were otherwise, courts would be able to create coverage where policies did not provide for it.
The Schiff court, however, pointed out that this reasoning does not apply when the underlying contract actually provides coverage, but the insured forfeits that coverage by some act, such as failing to give timely notice of a loss. In that circumstance, the insurer may waive its right to deny coverage,- and it may extend the policy. Id.; see also Meutsch v. Travelers Ins. Co., 198 A.D.2d 845; 612 N.Y.S.2d 710, 711 (4th Dep’t 1994) (“insurer may waive its right to assert the defense of cancellation by engaging in conduct that is inconsistent with such cancellation”). In the case at bar, it is undisputed that had premiums been timely paid, Gallien would have been entitled to life insurance pursuant to the underlying contract. Waiver, therefore, may apply.
Our next inquiry is whether “there is direct’ or circumstantial proof that the insurer intended to abandon the defense” of forfeiture upon cessation of premium payments. Schiff, 51 N.Y.2d at 698, 435 N.Y.S.2d 972, 417 N.E.2d 84. There is ample proof of such intent 'to withstand the insurer’s summary judgment motion.
The plaintiff has provided evidence that warrants submission of this claim to a trier of fact. In December 1989 Carey sent Connecticut General a cheek to cover premiums for life insurance, apparently including Gal-lien’s life insurance, and Connecticut General accepted and endorsed that check. Under New York law, acceptance of premiums may serve to waive a forfeiture defense. Divita v. New York Life Ins. Co., 244 A.D. 498, 279 N.Y.S. 900, 907-08 (4th Dep’t 1935) (inquiring whether insurer “intended to accept and retain the premium as its own property and to waive any forfeiture which may have been incurred”). Connecticut General provides no evidence that it did not in fact accept such payment. Nor does it attempt to make the argument — questionable in any case — that under some particular term of its policy, acceptance of such payment would not constitute waiver and therefore would be immaterial. Cf. American Crown Life Ins. Co. v. Dickson, 748 F.Supp. 184, 188 (S.D.N.Y.1990) (where policy provided that insured must be insurable in order for policy to be reinstated after lapse, employee of insurer lacked power to waive lapse in absence of evidence of insurability). On the basis of Carey’s purportedly accepted premium cheek alone, reversal of the summary judgment is warranted in light of the ambiguity in the contract.
The plaintiff has also provided additional evidence to support the conclusion that dis[886]*886missal was premature. She points out that Connecticut General deviated from its normal policy of sending termination notices sixty days after premiums were due and instead withheld the notice to Carey. Moreover,Connecticut General’s own records indicate that Gallien in fact was insured at the time of his death.
Connecticut General does not dispute these facts but instead insists that they are not material because Gallien’s coverage— governed by the special provision for. life insurance for disabled individuals over age 60 — was not in effect as of July, when premium payments ceased. But, as explained above, Carey’s failure to pay premiums may not have bound Connecticut General to cancel coverage; it may simply have given the insurer the right to do so. And the right to disclaim coverage based on forfeiture can be waived. “Courts do not favor forfeitures and are always prompt to seize hold of any circumstances that indicate an election to waive a lapse.” Divita, 279 N.Y.S. at 908. The circumstances described here raise a genuine issue of fact as to whether Connecticut General intended to abandon the defense of forfeiture.
III. Conclusion
In sum, we find that the policy was ambiguous as to whether life insurance coverage ceased upon the employer’s failure to pay premiums on behalf of Gallien, or whether that failure gave Connecticut General the right to disclaim coverage. Were a trier of fact to find that the latter interpretation is correct, it could also conclude, from the evidence thus far presented, that Connecticut General intended to waive that right. For these reasons, it was error to grant summary judgment. Because we reverse on grounds of ambiguity and waiver, we need not reach the plaintiffs equitable estoppel, argument.
For the reasons stated above, the judgment of the district court is reversed, and the case is remanded for further proceedings consistent with this opinion.