
985 A.2d 1076 (2010)
118 Conn.App. 757
Catherine FARRELL, et al.
v.
TWENTY-FIRST CENTURY INSURANCE COMPANY.
No. 30236.
Appellate Court of Connecticut.
Argued October 16, 2009.
Decided January 12, 2010.
*1077 Campbell D. Barrett, with whom were Jon T. Kukucka, Hartford and, on the *1078 brief, Felicia C. Hunt, certified legal intern, for the appellants (plaintiffs).
Andrew M. McPherson, with whom, on the brief, was Dennis M. Laccavole, Bridgeport, for the appellee (defendant).
BISHOP, ALVORD and DUPONT, Js.
ALVORD, J.
In this action to compel arbitration, the plaintiffs, Catherine Farrell and Olivia Farrell, appeal from the summary judgment rendered in favor of the defendant, Twenty-First Century Insurance Company. We affirm the judgment of the trial court.
The following facts and procedural history are relevant to the plaintiffs' appeal. John Farrell, Catherine Farrell, Olivia Farrell and Colm Farrell were allegedly involved in a car accident with the defendant's insured on December 20, 2000. On February 25, 2002, the Farrells filed an action against the defendant, claiming personal injury. During a pretrial conference held in February, 2005, the parties agreed to settle the claims of John Farrell and Colm Farrell and agreed, in principle, to arbitrate the claims of Catherine Farrell and Olivia Farrell. In February, 2008, the plaintiffs filed a complaint seeking a court order to compel arbitration. The defendant filed a motion for summary judgment claiming that no written agreement to arbitrate existed between the parties.[1] The plaintiffs opposed the defendant's motion and, in opposition, submitted fourteen letters exchanged between the plaintiffs' attorney and the defendant's attorney from January, 2005, to February, 2007, as well as an affidavit of the plaintiffs' attorney. They claimed that, cumulatively, the letters constituted an enforceable agreement to arbitrate. The court concluded that there was no genuine issue of material fact and no written agreement to arbitrate. It granted the defendant's motion for summary judgment. On appeal, the plaintiffs claim that the existence of an arbitration agreement is a question of fact, and as a result, the court's summary judgment was improper.
"Summary judgment is appropriate where the pleadings, affidavits and any other proof submitted show that there is no genuine issue as to any material fact and that the moving party is entitled to judgment as a matter of law. . . . A material fact is a fact that will make a difference in the result of the case." (Citations omitted; internal quotation marks omitted.) Tuccio Development, Inc. v. Neumann, 114 Conn.App. 123, 126, 968 A.2d 956 (2009). "Although the party seeking summary judgment has the burden of showing the nonexistence of any material fact . . . it [is nevertheless] incumbent upon the party opposing summary judgment to establish a factual predicate from which it can be determined, as a matter of law, that a genuine issue of material fact exists." (Internal quotation marks omitted.) Levine v. Advest, Inc., 244 Conn. 732, 759, 714 A.2d 649 (1998). "[T]he existence of [a] genuine issue of material fact must be demonstrated by counteraffidavits and concrete evidence. . . . If the affidavits and the other supporting documents are inadequate, then the court is justified in granting the summary judgment, assuming that the movant has met [its] burden of proof." (Internal quotation marks omitted.) Little v. Yale University, 92 Conn.App. 232, 235, 884 A.2d 427 (2005), cert. denied, 276 Conn. 936, 891 A.2d 1 (2006). "Our review of the trial court's decision to grant [a] defendant's motion for summary judgment is plenary." *1079 (Internal quotation marks omitted.) Double G.G. Leasing, LLC v. Underwriters at Lloyd's, London, 116 Conn.App. 417, 427, 978 A.2d 83, cert. denied, 294 Conn. 908, 982 A.2d 1082 (2009).
"Arbitration is a creature of contract." (Internal quotation marks omitted.) Marinos v. Building Rehabilitations, LLC, 67 Conn.App. 86, 88, 787 A.2d 46 (2001). Therefore, "[t]he authority for arbitration must be derived from the agreement of the parties. . . ." (Internal quotation marks omitted.) Id. "[A] person can be compelled to arbitrate a dispute only if, to the extent that, and in the manner which, he has agreed to do so. . . . No one can be forced to arbitrate a contract dispute who has not previously agreed to do so." (Internal quotation marks omitted.) Id.
Arbitration agreements are strictly construed. Wesleyan University v. Rissil Construction Associates, Inc., 1 Conn.App. 351, 355, 472 A.2d 23, cert. denied, 193 Conn. 802, 474 A.2d 1259 (1984). "An agreement to arbitrate must be clear and direct and not depend on implication." Harry Skolnick & Sons v. Heyman, 7 Conn.App. 175, 179, 508 A.2d 64, cert. denied, 200 Conn. 803, 510 A.2d 191 (1986). It must also be in writing.[2] The writing requirement of General Statutes § 52-408 is strictly enforced. Bennett v. Meader, 208 Conn. 352, 362, 545 A.2d 553 (1988); see also id., at 362 n. 8, 545 A.2d 553 ("only written arbitration agreements are enforceable and all others are void").
Although "[t]he existence of a contract is a question of fact to be determined by the trier on the basis of all the evidence"; (internal quotation marks omitted) Marinos v. Building Rehabilitations, LLC, supra, 67 Conn.App. at 89, 787 A.2d 46; to withstand a motion for summary judgment, the plaintiffs in this case bear the burden of providing concrete evidence that raises a genuine issue as to the existence of a written contract to arbitrate. They fail to do so.
The parties' correspondence, viewed in the light most favorable to the plaintiffs, indicates that the parties had an informal agreement to arbitrate, but they never agreed on any of the terms for arbitration, including the parameters for both plaintiffs' claims, how the expense of arbitration should be allocated, when the arbitration would take place or who would preside as arbitrator.
The plaintiffs nevertheless claim that a failure to agree to arbitration parameters is not detrimental to their claim. They argue that the terms of arbitration are not essential to satisfy § 52-408 and maintain that the parameters of arbitration can be defined though parol evidence. We agree that documentary parol evidence may be relevant to establishing the existence of a written agreement to arbitrate.[3] The plaintiffs, *1080 however, failed to present the essential documentary evidence.[4] Moreover, the defendant never manifested an intent to be bound by the parties' informal plan to arbitrate. From January, 2005, to September, 2006, the defendant sent eleven letters, including two draft arbitration agreements, to the plaintiffs seeking to define reasonable parameters for arbitration and to reduce an agreement to writing. For almost two years, the defendant urged the plaintiffs to "execute a binding arbitration agreement," to submit a "proposal in writing," and to work with the defendant to "get a signed arbitration agreement." The plaintiffs rarely responded and did not return or comment in writing on either of the draft arbitration agreements. Finally, in a February, 2007 letter, the defendant concluded that "no arrangements to arbitrate . . . were ever made. . . ."
The plaintiffs also argue that the court could compel unrestricted arbitration.[5] The authority for arbitration, however, must be derived from the agreement of the parties; see Marinos v. Building Rehabilitations, LLC, supra, 67 Conn. App. at 88, 787 A.2d 46; and, in this case, both parties expressed, in writing, a desire to establish high and low award limits.
Finally, the plaintiffs claim that the parties did agree, in writing, to a high figure of $100,000 for Catherine Farrell. Their claim is not supported by the evidence. In a letter dated March 28, 2005, the defendant proposed the policy limit of $100,000 as the high figure for Catherine Farrell's claim, but the plaintiffs never agreed to the defendant's proposal in writing.
The judgment is affirmed.
In this opinion the other judges concurred.
NOTES
[1]  In support of its motion, the defendant submitted an affidavit of its authorized representative that stated the same.
[2]  General Statutes § 52-408 states in pertinent part: "[A]n agreement in writing between two or more persons to submit to arbitration any controversy existing between them at the time of the agreement to submit . . . shall be valid, irrevocable and enforceable, except when there exists sufficient cause at law or in equity for the avoidance of written contracts generally."
[3]  See Bennett v. Meader, supra, 208 Conn. at 363, 545 A.2d 553 ("[B]ecause the parties must memorialize their agreement to arbitrate, it also is likely that they will establish, either separately or within the agreement to arbitrate, a written submission setting forth the arbitrable issues. It is from the submission alone that the arbitrator receives his or her authority. . . . [Emphasis added.]").

In contrast, oral parol evidence is irrelevant absent the written agreement required by § 52-408. See id., at 360 n. 7, 545 A.2d 553 (if the arbitration agreement is not in writing, "there is no legally cognizable bargain to be enforced").
[4]  The affidavit submitted by the plaintiffs in support of their motion does not further their cause. It merely states that the parties agreed to resolve the plaintiffs' claims through arbitration. It does not provide any indication that a written agreement to arbitrate ever existed.
[5]  "A submission is unrestricted when . . . the parties' arbitration agreement contains no language restricting the breadth of issues, reserving explicit rights, or conditioning the award on court review." (Internal quotation marks omitted.) Cianbro Corp. v. National Eastern Corp., 102 Conn.App. 61, 65 n. 2, 924 A.2d 160 (2007). As a result, "the arbitrators' decision is considered final and binding . . . courts will not review the evidence considered by the arbitrators nor will they review the award for errors of law or fact." (Internal quotation marks omitted.) Id., at 68, 924 A.2d 160.
