Plaintiff-appellant Elaine B. Gibbs, Executrix of the Estate of plaintiff-appellant Jeffrey Gibbs (“Gibbs”) appeals from the judgment of the United States District Court for the District of Connecticut (Alvin W. Thompson, Judge), entered on June 16, 2005, granting summary judgment to defendants-appellees CIGNA Corporation (“CIGNA Corp.”), Life Insurance Company of North America (“LICNA” or the “Plan Administrator”), and CIGNA Long-Term and Supplemental Disability Plans (collectively, the “Plan”) (all defendants collectively, “CIGNA”). See Gibbs v. CIGNA Corp., No. 3:01CV00320, 2005 WL 1421638 (D.Conn. June 13, 2005). Gibbs brought this action pursuant to section 502(a)(1)(B) of the Employee Retirement Income Security Act (“ERISA”), 29 U.S.C. § 1132(a)(1)(B), to recover benefits under the Plan. Specifically, Gibbs challenged CIGNA’s calculation of his “eligible earnings,” on the basis of which his disability benefits were determined.
This appeal presents two issues. First, when reviewing the administrator’s denial of benefits under an ERISA-governed long-term disability plan, to which version of the summary plan description should the District Court refer when determining the applicable standard of review: the version in effect at the time the claim is denied or the one in effect when the beneficiary became disabled? Second, did the District Court err by granting summary judgment to CIGNA on the issue of the correct calculation of the Gibbs’s disability benefits? We hold that where an ERISA plan beneficiary’s benefits have vested, the summary plan description in effect at the time the benefits vest governs for purposes of determining the standard of review. We further hold that the District Court erred in disregarding CIGNA’s admission that Gibbs was not a so-called “CFA Associate” under the Plan and that *573there were material issues of fact concerning whether he received a “salary” in 1994. We, therefore, vacate the judgment of the District Court and remand for further proceedings consistent with this opinion.
BACKGROUND
Gibbs’s Employment with CIGNA
From 1969 to 1994, Gibbs1 worked for the Connecticut General Life Insurance Company (“CGLIC”), which is a wholly owned subsidiary of CIGNA Corp. As part of his employee benefits, Gibbs participated in the Plan, which was issued by LIO-NA, also a wholly owned subsidiary of CIGNA Corp. Prior to 1994, Gibbs was the Regional Vice-President of the Springfield Agency, which was part of an organization called CIGNA Financial Advisors. During this time, Gibbs’s compensation varied and depended upon the amount of commissions he earned and other payments he received related to insurance sales generated by the Springfield Agency.
In January 1994, Gibbs became the Vice-President of New England Brokerage, which was a new business venture started by CGLIC and independent from CIGNA Financial Advisors. The parties memorialized the terms of his compensation package for his new position in a two-page written document, titled “Jeff Gibbs’[s] Compensation, Brokerage RVP” (the “Compensation Agreement”). Gibbs agreed to work for $150,000 in “minimum compensation” with the possibility of earning additional compensation based on sales. This “minimum compensation” was “[guaranteed” in “Year I.” The “$150,000, minimum compensation” was “[gjuaran-teed [in] Year II assuming objectives for Year I were achieved,” and the “$150,000, minimum compensation” was not guaranteed in Year III or beyond.
The Plan
Gibbs, as an employee of CGLIC, participated in and was a beneficiary of the Plan. Under the Plan, disabled employees are entitled to receive benefits equal to 65% of their “eligible earnings.” The central issue in this case is the amount of and method for calculating Gibbs’s “eligible earnings.”2 The terms of the Plan are expressed in two documents: the Summary Plan Description (“SPD”)3 and CIG-NA’s Group Long-Term Disability Policy (the “Policy”). The Plan divides employees into two groups for purposes of calculating eligible earnings. The first group includes employees described as “CIGNA Financial Advisor Associates and Staff People” (“CFA Associates”), whose pay consists exclusively of various forms of variable, incentive-based compensation (“variable compensation”). Although the Policy does not define the term CFA Associates, the 1995 SPD4 offers the following definition:
*574A Regular or Statutory Employee of [CGLIC] (or a Regular Employee of CIGNA Financial Advisors, Inc.) who works in the CIGNA Individual Insurance Division under a contract that authorizes the person to act as an agent for the sale of life insurance and related products underwritten by CG (formerly called an “IFSD Agent”).
A CFA Associate’s eligible earnings consist of “a three-year average of all variable compensation earned while a participant.” This average is calculated annually in July by the Plan Administrator and “includes all eligible earnings earned during the pri- or three calendar-year period.”
The second group of employees under the Plan are “[ejmployees other than CIG-NA Financial Advisor Associates and Staff People” (“Non-CFA Associates”). Eligible earnings for non-CFA Associates consist of “paid or deferred salary expressed in annual terms” which is added to a three-year average of the employee’s variable compensation.
Gibbs’s Disability Benefits
In October 1995, Gibbs became completely disabled, and on May 1, 1996, he began receiving long-term disability benefits. Prior to becoming disabled, Gibbs received a statement from CIGNA indicating that his eligible earnings for purposes of calculating his disability benefits were $342,073.5 Towards the end of 1996, Gibbs realized that his benefits were not being calculated on the basis of $342,073 in eligible earnings. Through counsel, Gibbs brought this to the attention of the Plan Administrator. CIGNA responded that Gibbs’s eligible earnings were $200,082.71,6 which was the average of his variable compensation for the years 1991-93. CGLIC’s human resources department calculated Gibbs’s eligible earnings. In correspondence to LICNA officials and during a deposition, CGLIC’s representative asserted that as an “IFSD,” Gibbs received only variable compensation and that, therefore, his benefits were calculated using only the three-year average of his variable compensation.
After extensive correspondence between Gibbs and CIGNA on the issue, on January 16, 1998, Gibbs wrote CIGNA’s Vice-President of Employee Benefits requesting a definitive answer on the calculation of his eligible earnings. On March 6, 1998, Gibbs received a final letter from the Plan Administrator denying his claim for additional benefits. CIGNA’s Director of Employee Benefits wrote on behalf of the Plan Administrator, and stated that Gibbs’s $150,000 “minimum compensation” in 1994 was an advance draw against his future commissions and not a salary to be added to a three-year average of his variable compensation. This advance draw was provided to him to “allow[] him an even flow of income during the year.”
Procedural History
On February 27, 2001, Gibbs filed this action under ERISA section 502, alleging that his benefits should be calculated on the basis of eligible earnings of $350,083 (his $150,000 salary in 1994 plus the previous three-year average of his variable compensation). Section 502 of ERISA provides that “a participant or beneficiary” of an ERISA Plan may bring a civil action ■ “to recover benefits due to him under the terms of his plan, to enforce his rights under the terms of the plan, or to clarify *575his rights to future benefits under the terms of the plan.” 29 U.S.C. § 1132(a)(1)(B).
CIGNA answered the complaint, admitting, inter alia, that Gibbs was not a CFA Associate, but disputing that Gibbs’s eligible earnings were $350,083. Following discovery, CIGNA moved for summary judgment on the ground that there were no genuine issues of material fact that Gibbs was receiving the correct amount of disability benefits. The District Court declined to specify the applicable standard of review because it found that even under the less deferential standard advanced by Gibbs—de novo review of the Plan Administrator’s decision—CIGNA was entitled to summary judgment. Specifically, the District Court held that (1) the Compensation Agreement established that Gibbs was not receiving salary-based compensation in his position as Vice-President of New England Brokerage; and (2) even assuming that he was receiving a salary, he was a “CFA Associate” under the SPD and subject to the CFA Associate Method for calculating his benefits.
Gibbs filed a timely notice of appeal.
DISCUSSION
We review a district court’s decision to grant summary judgment de novo, Wachovia Bank, N.A. v. Burke, 414 F.3d 305, 311 (2d Cir.2005), and examine the evidence in the light most favorable to the non-mov-ant, Garcia Ramos v. 1199 Health Care Employees Pension Fund, 413 F.3d 234, 237 (2d Cir.2005). Summary judgment is appropriate only in cases where, “there is no genuine issue as to any material fact and ... the moving party is entitled to judgment as a matter of law.” Fed. R.Civ.P. 56(c).
I. Standard of Review of a Denial of Benefits
We must first decide what standard of review the District Court should have applied when examining CIGNA’s calculation of Gibbs’s eligible earnings. Unlike the District Court, we find the standard of review to be highly relevant and indeed dispositive of this appeal.
In an action brought pursuant to section 502(a)(1)(B) of ERISA, a district court reviews a plan administrator’s denial of benefits “under a de novo standard unless the benefit plan gives the administrator or fiduciary discretionary authority to determine eligibility for benefits or to construe the terms of the plan.” Kinstler v. First Reliance Standard Life Ins. Co., 181 F.3d 243, 249 (2d Cir.1999) (quoting Firestone Tire & Rubber Co. v. Bruch, 489 U.S. 101, 115, 109 S.Ct. 948, 103 L.Ed.2d 80 (1989)). Where the plan reserves discretionary authority for the administrator, however, “denials are subject to the more deferential arbitrary and capricious standard, and may be overturned only if the decision is without reason, unsupported by substantial evidence or erroneous as a matter of law.” Kinstler, 181 F.3d at 249 (quoting Pagan v. NYNEX Pension Plan, 52 F.3d 438, 442 (2d Cir.1995) (internal quotation marks omitted)). CIGNA, as the party arguing for the more deferential standard of review, “bears the burden of proving that the arbitrary and capricious standard of review applies.” Kinstler, 181 F.3d at 249.
Gibbs and CIGNA disagree on whether the plan provides discretionary authority to the Plan Administrator. Each position finds support in a different version of the SPD.7 CIGNA claims that the *5761997 SPD, which contains language vesting “sole discretion” in the Plan Administrator “to determine whether [a participant is] eligible for benefits ... and the amount of any benefit” controls because it was in effect at the time when Gibbs’s claim for additional benefits was denied. Gibbs contends that the 1995 SPD, which does not provide the Plan Administrator with discretion, applies because it was in effect at the time he became disabled. For the reasons set forth below, we agree with Gibbs that the amendment to the SPD granting discretionary authority to the Plan Administrator does not apply to Gibbs’s claim because his right to disability benefits vested prior to CIGNA’s amendment of the Plan.
The issue of which version of the SPD applies when determining the standard of review of an administrator’s denial of disability benefits is one of first impression in our Circuit. Long-term disability plans fall within ERISA’s definition of an “employee welfare benefit plan.” 29 U.S.C. § 1002(1); Kunstenaar v. Connecticut General Life Ins. Co., 902 F.2d 181, 181 (2d Cir.1990). It is well settled that “ ‘ERISA does not create any substantive entitlement to employer-provided health benefits or any other kind of welfare benefits. Employers or other plan sponsors are generally free under ERISA, for any reason at any time, to adopt, modify, or terminate welfare plans.’ ” Devlin v. Empire Blue Cross and Blue Shield, 274 F.3d 76, 82 (2d Cir.2001) (quoting Curtiss-Wright Corp. v. Schoonejongen, 514 U.S. 73, 78, 115 S.Ct. 1223, 131 L.Ed.2d 94 (1995)). “Under the principle that an employee benefit plan is effectively a unilateral contract, a benefit becomes ‘vested’ if the employer has promised not to amend or terminate it, and the employee has accepted this offer by beginning or continuing in employment.” Feifer v. Prudential Ins. Co. of Am., 306 F.3d 1202, 1211 (2d Cir.2002).8 In short, “if an employer promises vested benefits, [under ERISA] that promise will be enforced.” Am. Fed. of Grain Millers v. Int’l Multifoods Corp., 116 F.3d 976, 980 (2d Cir.1997) (emphasis added). Once the employee’s rights have vested, an employer’s “subsequent unilateral adoption of an amendment which is then used to defeat or diminish the [employee’s] fully vested rights ... is ... ineffective.” Feifer, 306 F.3d at 1211 (quoting Kemmerer v. ICI Americas Inc., 70 F.3d 281, 287 (3d Cir.1995) (internal quotation marks omitted)); cf. Frommert v. Conkright, 433 F.3d 254, 264 (2d Cir.2006) (holding that an amendment to an employee pension benefit plan was ineffective because “a later-adopted plan cannot be applied to reduce already-earned pension benefits”).
Whether an employee’s benefits have vested under an ERISA welfare plan is a matter of contract interpretation. Feifer, 306 F.3d at 1211. Disability plans are treated somewhat differently than other welfare plans for purposes of vesting. In Feifer, we held “as a matter of law that, absent explicit language to the contrary, a plan document providing for disability benefits promises that these benefits vest with respect to an employee no later than the time that the employee becomes disabled.” Feifer, 306 F.3d at 1212. The holding in Feifer flows from both the fact that ambiguity in a plan “should be construed against the interests of the party that *577drafted the language” and from the nature of disability benefits. Id.• (internal quotation marks omitted); see also id. (noting that disabled employees neither can reject the terms offered by their employers and secure work elsewhere, nor predict the date of separation from their employer and plan accordingly).
In this case, the 1995 SPD does not contain “explicit language” reserving CIG-NA’s right to terminate or alter a disabled employee’s benefits. Indeed, the 1995 SPD states quite the contrary: “Any modification or termination will not affect your right to benefits from a covered disability that occurred before the termination or modification” (emphasis added). Without an explicit reservation of CIGNA’s right to alter disability benefits after a beneficiary became disabled, Gibbs’s right to benefits vested when he became disabled. Therefore, CIGNA’s attempt to alter the terms of the SPD was ineffective with respect to Gibbs’s benefits.
CIGNA, relying on the Third Circuit’s decision in Smathers v. Multi-Tool, Inc./Multi-Plastics, Inc. Employee Health and Welfare Plan, argues that the grant of discretion to the Plan Administrator only alters a procedural provision of the Plan and did not affect Gibbs’s “coverage under the plan or substance of [his] benefits or his entitlement to them.” 298 F.3d 191, 195 (3d Cir.2002); see also id. at 196 (holding that the amendment granting the administrator discretion was only “a signal to the district court ... as to how it is to review the administrator’s decision” and not a substantive change to benefits). We find this argument unavailing. Unlike the plaintiff in Smathers, see id. (holding that employee’s motorcycle accident did not created a vested right to healthcare benefits), Gibbs was vested in his right to disability benefits prior to the amendment of the Plan.9
Moreover, we respectfully disagree with a basic premise of the Smathers decision that granting the Plan Administrator sole discretion to determine benefits — thus altering the District Court’s standard of review — does not “affect” the substance of Gibbs’s benefits. See Smathers, 298 F.3d at 195 (stating that granting discretion to the administrator “did not change the coverage under the plan or substance of Smathers’ benefits or his entitlement to them”). As the Seventh Circuit explained in the context of holding that the plan language must clearly confer discretion in order to trigger deferential review under Firestone: “The very existence of ‘rights’ under such plans depends on the degree of discretion lodged in the administrator. The broader that discretion, the less solid an entitlement the employee has and the more important it may be to him, therefore, to supplement his ERISA plan with other forms of insurance.” Herzberger v. Standard Ins. Co., 205 F.3d 327, 331 (7th *578Cir.2000); see also Johnson v. Allsteel, Inc., 259 F.3d 885, 888 (7th Cir.2001) (“An increased amount of discretion opens up to the administrator administering the plan a greater range of permissible choices. This expanded range renders ‘less solid’ the participant’s benefits by shifting risk to the participant.”). There is no doubt in our minds that a right that may be denied by an administrator’s incorrect, but not arbitrary, interpretation of the plan is substantively diminished as compared with one not subject to erroneous decisions.
Thus, we hold that the grant of discretion to the Plan Administrator in the 1997 SPD would “affect” Gibbs’s vested right to benefits, and therefore cannot be applied to Gibbs’s claim.
II. The Calculation of Gibbs’s Eligible Earnings
We must next determine whether the District Court erred in holding that there were no genuine issues of material fact regarding (1) whether Gibbs was a “CFA Associate” in 1994, and (2), even assuming that he was not a CFA Associate, whether he received a “salary.”
A. Gibbs’s Classification as a CFA Associate
We need not determine whether Gibbs falls under the definition of a CFA Associate in the 1995 SPD because CIGNA admitted in its answer that Gibbs was not a CFA Associate. Facts admitted in an answer, as in any pleading, are judicial admissions that bind the defendant throughout this litigation. See Bellefonte Re Ins. Co. v. Argonaut Ins. Co., 757 F.2d 523, 528 (2d Cir.1985); see also Western World Ins. Co. v. Stack Oil, Inc., 922 F.2d 118, 121-22 (2d Cir.1990) (holding that a fact admitted by the defendant in its amended answer was thereby conclusively established against the defendant). “Having agreed on a set of facts, the parties [who adopted the stipulation], and this Court, must be bound by them; we are not free to pick and choose at will.” PPX Enters., Inc. v. Audiofidelity, Inc., 746 F.2d 120, 123 (2d Cir.1984) (quoting Stanley Works v. FTC, 469 F.2d 498, 506 (2d Cir.1972) (alteration in original)).
The District Court, therefore, erred by disregarding this admission and relying on contrary evidence to determine whether Gibbs was a CFA Associate. CIGNA’s argument that its admission was limited to the fact that Gibbs did not work for CIG-NA Financial Advisors is belied by the definition of the term “CFA Associates” in paragraph 20 of the complaint as those employees whose benefits are determined under the “CIGNA Financial Advisors Associates and Staff People” method for calculating eligible earnings. Therefore, it has been conclusively established that Gibbs is not a CFA Associate under the policy, and the District Court erred by concluding to the contrary.10
B. Interpretation of “Guaranteed” “Minimum Compensation” in the Compensation Agreement
The application of the non-CFA Associate formula to Gibbs does not necessarily mean that the $150,000 “[gjuaran-teed” “minimum compensation” was a “salary.” An ERISA-regulated plan is construed in accordance with federal common law. Critchlow v. First UNUM Life Ins. Co. of Am., 378 F.3d 246, 255-56 (2d Cir.2004). “[U]nambiguous language in an ERISA plan must be interpreted and en*579forced in accordance with its plain meaning. Language is ambiguous when it is capable of more than one meaning when viewed objectively by a reasonably intelligent person who has examined the context of the entire integrated agreement.” Aramony v. United Way Replacement Benefit Plan, 191 F.3d 140, 149 (2d Cir.1999) (quoting O’Neil v. Ret. Plan for Salaried Employees of RKO General, Inc., 37 F.3d 55, 59 (2d Cir.1994)) (internal citations omitted).
The meaning of the term “salary” in the non-CFA Associate formula is straightforward. A salary is a “fixed compensation paid regularly ... for services.” Webster’s Third New International Dictionary 2003 (1961). But the term “[guaranteed” “minimum compensation” in the Compensation Agreement could indicate either a salary or a guaranteed draw against commissions earned. Therefore, whether Gibbs and CIGNA intended that he would receive a “salary” should be left to the trier of fact to determine from extrinsic evidence. See Devlin, 274 F.3d at 90 (vacating and remanding district court’s grant of summary judgment to allow the presentation of extrinsic evidence to clarify the ambiguous terms of an ERISA welfare plan). As we find there is sufficient evidence supporting each side’s interpretation of “[g]uaranteed” “minimum compensation” to create a genuine issue of material fact, the grant of summary judgment was inappropriate.
CONCLUSION
For the foregoing reasons, we hereby Vacate the judgment of the District Court and Remand the case to allow the District Court to determine, in appropriate proceedings consistent with this opinion, whether the $150,000 in “[guaranteed” “minimum compensation” was intended by the parties to be a salary or a draw on future commissions earned.
. Jeffrey Gibbs died while the motion for summary judgment was pending before the District Court, and Elaine Gibbs, his wife and representative, was substituted as the plaintiff pursuant to Federal Rule of Civil Procedure 25(a)(1).
. The parties do not dispute the District Court's determination that the term "covered earnings” used in the Policy and "eligible earnings” used in the Summary Plan Description are synonymous. Gibbs, 2005 WL 1421638, at *2 n. 3. For the sake of consistency, we will use the latter term exclusively.
. As discussed in Part I, infra, the parties do not agree on which version of the SPD applies to Gibbs’s claim for benefits. Gibbs contends that the 1995 SPD governs and CIGNA claims that the 1997 SPD is the controlling document.
. Neither party has offered a different definition of a CFA Associate. The 1991 SPD used the term "IFSD” or incentive-based field associate. Some of CIGNA's employees still use "IFSD,” which is included in the term CFA Associates in the 1995 SPD.
. CIGNA contends that this statement was sent to Gibbs in error as the result of a computer glitch. Based on this statement, however, Gibbs elected to continue his coverage under the Plan and paid an annual premium of $1,026. CIGNA has since refunded the excess premiums paid by Gibbs.
. It is undisputed that the Policy does not contain a clause granting discretion to the Plan Administrator. This fact, however, is not fatal to CIGNA's argument because when the SPD conflicts with the Policy, the SPD controls. Heidgerd v. Olin Corp., 906 F.2d 903, 907-08 (2d Cir.1990).
. The parties agree that this is the correct calculation of Gibbs’s average variable compensation for the years 1991-1993.
. Although this might seem to conflict with our holding in Reichelt v. Emhart Corp., 921 F.2d 425, 432 (2d Cir.1990), as we noted in Devlin, our decision in Reichelt concerns the preemptive scope of ERISA and rejects the assertion of an independent contract law claim for benefits. See Devlin, 274 F.3d at 84 n. 4. Reichelt does not apply to a claim under section 502(a)(1)(B), which we apply contract law principles to resolve. Id.
. Similarly, the other cases relied on by CIG-NA, the Seventh Circuit's decision in Hackett v. Xerox Corp. Long-Term Disability Inc. Income Plan, 315 F.3d 771 (7th Cir.2003) and the Ninth Circuit's in Grosz-Salomon v. Paul Revere Life Ins. Co., 237 F.3d 1154 (9th Cir.2001), are inapposite. Both cases hold that the controlling plan is the one in effect at the time the participant's claims are denied by the plan administrator. Hackett, 315 F.3d at 774; Grosz-Salomon, 237 F.3d at 1160-61. These cases are inapplicable because, as in Smathers, the plaintiffs in both cases were not vested in their right to benefits. Hackett, 315 F.3d at 774 (holding employees disability benefits did not vest in perpetuity when he became disabled); Grosz-Salomon, 237 F.3d at 1160 (holding that employee's rights were not vested when she retired). In this respect, Smathers, Hackett, and Grosz-Salomon are all inconsistent with our holding in Feifer that disability benefits vest, absent explicit language to the contrary, when the plan participant becomes disabled. See Feifer, 306 F.3d at 1212.
. While the admission that Gibbs is not a CFA Associate is binding throughout the litigation, it is possible that CIGNA might be allowed to amend its answer or withdraw its admission in further proceedings before the District Court. We take no position on whether such an amendment or withdrawal is permissible.