JOHN M. WALKER, JR., Circuit Judge:
Plaintiff-Appellant Donna Ann Gabriele Cheehele appeals from the judgment of the United States District Court for the Southern District of New York (Paul A. Crotty, Judge) granting insider Defendants-Ap-pellees’ motion to dismiss her short-swing trading complaint. Specifically, the district court found that the requirements of a claim under section 16(b) of the Securities Exchange Act of 1934 (“Exchange Act”), mandating disgorgement of short-swing profits by statutory insiders, had not been satisfied. We agree and affirm the district court’s judgment.
BACKGROUND
Appellant Cheehele is a shareholder of Apollo Group, Inc. (“Apollo”). Appellees John and Peter Sperling, father and son, are the Executive Chairman and Vice Chairman of Apollo’s Board of Directors, respectively. Cheehele sued the Sperlings under section 16(b) of the Exchange Act, 15 U.S.C. § 78p(b), seeking disgorgement of alleged short-swing profits. Short-swing profits are realized under section 16(b) when an insider buys and sells stock of his company within a six-month period. It is undisputed that the 29 Sperlings are insiders for the purposes of section 16(b).
As insiders, John and Peter Sperling had considerable holdings of Apollo stock. In order to convert some of their shares of Apollo Class A common stock into cash, in 2006 and 2007, John Sperling entered into two prepaid variable forward contracts (“PVFCs”) and Peter Sperling entered into three PVFCs. The terms of each PVFC were contained in three documents: (1) a Master Agreement, (2) a Pledge Agreement, and (3) a Transaction Confirmation.
The Master Agreements provided the general framework for the PVFC transactions.1 On the “Payment Date,” the banks would pay John and Peter an agreed-upon amount of cash. In exchange, the Sper-lings promised to deliver to the banks, on a pre-determined “Settlement Date,” some number of Apollo shares, or their cash equivalent. The number of shares to be delivered varied with the market closing price of Apollo stock three days prior to the Settlement Date according to a formula provided in each agreement.
Additionally, on the Payment Date, the Sperlings pledged as collateral the maximum number of shares that could be delivered under the agreement to secure the banks’ interest in the shares. In the meantime, however, the Sperlings retained ownership of the shares until delivery on the Settlement Date; they continued to have the right to exercise the shares’ voting rights and receive cash dividends.
The particulars of each PVFC transaction, including the Payment Date, upfront cash payment amount, number of pledged shares, Settlement Date, and settlement formula, were all set forth in the Transac*466tion Confirmation. For example, John Sperling’s July 11, 2007 Transaction Confirmation called for him to pledge one million shares on July 16, 2007 (the Payment Date) in return for approximately $52.4 million from Bank of America. The Settlement Date occurred approximately eighteen months later, on January 12, 2009.
Under the settlement formula in this transaction, if the share price three trading days prior to settlement (the “Maturity Date”) fell below $60.2235 (the “floor price”), John was required to deliver all of the pledged shares or a cash equivalent. The floor price protected John from a decline in the stock price because he was required to deliver one million shares (or the cash equivalent) regardless of how much below the floor price the share price fell.
But if the share price at the Maturity Date was between the floor price and $78.2906 (the “ceiling price”), the number of shares to be delivered would decline as the share price rose above the floor price according to a formula that maintained a constant cash equivalent value. John would keep any undelivered shares.
If the share price at the Maturity Date was above the ceiling price, however, the number of shares to be delivered would increase according to a formula under which John had to deliver more shares as the stock price rose. But, no matter how high the stock price climbed, John never had to deliver more than the one million originally pledged shares.2
The transaction could be viewed as a bet on whether the share price would be above the ceiling price (bank’s bet) or below the floor price (John’s bet) on the Maturity Date. John would “win the bet” if the settlement price was below the floor, because he would be satisfying his obligation to the bank with relatively inexpensive shares. The bank would “win the bet” if the settlement price was above the ceiling, because it would receive an increasing number of shares of increasing value. For settlement prices in between the floor and ceiling, the transaction resembled a loan; John borrowed $52.4 million from the bank on the Payment Date and was obligated to pay the bank back approximately $62 million (the $52.4 million he borrowed plus the implied financing cost of the loan).
On January 9, 2009, the share price was $85.3300 — -above the ceiling — so the bank “won” the bet and John had to deliver some, but not all, of the pledged shares on January 12.
All five PVFC transactions were settled by delivery of shares rather than the cash equivalent. The following charts summarize their terms.
John Sperling
Trade Maturity Pledged Floor Ceiling Settlement Delivered Undelivered
Date Date Shares Price Price Price Shares Shares
7/11/07 1/9/09 1,000,000 60.2235 78.2906 85.3300 788,300 211,700
4/24/06 4/24/09 500,000 53.3780 80.0670 61.1450 436,500 63,500
*467Peter Sperling
Trade Maturity Pledged Floor Ceiling Settlement Delivered Undelivered
Date Date Shares Price Price Price Shares Shares
7/11/07 1/9/09 1,000,000 60.2235 78.2906 85.3300 788,300 211,7 00
4/24/06 4/24/09 500,000 53.3780 80.0670 61.1450 436,500 63,500
1/19/06 1/20/09 315,000 55.3064 71.8983 86.5400 254,606 60,394
THE CLAIM IN THE DISTRICT COURT
Within six months of the settlement of the PVFC transactions at issue, the Sper-lings sold some of their Apollo stock on the open market. Chechele alleges that those sales, in light of the PVFC settlement, violated section 16(b). According to her theory of the case, the Sperlings sold the shares they pledged to the banks on the Payment Dates of the PVFCs, but then “repurchased” the undelivered shares on the Settlement Dates. She claims that their subsequent sales of company stock on the open market — less than six months after the PVFC’s settled — can be matched to the “purchase” that occurred at settlement. If she is correct, any profits made from the later sales must be disgorged as short-swing profits under section 16(b).
The district court concluded that because the “Sperlings’ rights ‘became fixed and irrevocable’ at the time they entered into the [PVFCs] ... the repurchases of the [Sperlings’] retained shares on the settlement date did not constitute a ‘purchase’ under Section 16(b).” Chechele v. Sper-ling, No. 11 Civ. 0146, 2012 WL 1038653, at *5 (S.D.N.Y. Mar. 29, 2012).
DISCUSSION
Chechele raises only one issue on appeal: whether the Sperlings’ retention of a portion of the shares that were pledged but not delivered to the banks constituted a “purchase” of company stock within the meaning of section 16(b) of the Securities Exchange Act. We review de novo the district court’s grant of a motion to dismiss under Federal Rule of Procedure 12(b)(6), Anschutz Corp. v. Merrill Lynch & Co., 690 F.3d 98, 107 (2d Cir.2012), and conclude that the Sperlings’ ultimate retention of shares pledged to the banks in the various PVFC transactions did not constitute “purchases” under section 16(b).
In relevant part, section 16(b) states:
[A]ny profit realized by [a corporate insider] from any purchase and sale, or any sale and purchase, of any equity security ... within any period of less than six months ... shall inure to and be recoverable by the issuer, irrespective of any intention on the part of [the insider].
15 U.S.C. § 78p(b). We have explained that “liability under Section 16(b) does not attach unless the plaintiff proves that there was (1) a purchase and (2) a sale of securities (3) by an [insider] (4) within a six-month period.” Gwozdzinsky v. Zell/Chilmark Fund, L.P., 156 F.3d 305, 308 (2d Cir.1998).3 The only element at issue here is element one: whether a “purchase” occurred when the PVFCs settled and the Sperlings retained some of their pledged shares.4
*468A. PVFCs are a form of complex derivatives
The PVFCs at issue here are complex derivatives.5 On the day the contracts were written, the Sperlings obtained the equivalent of a right to sell a maximum number of shares to the banks, which they would exercise if the share price fell below a floor. Because the value of the Sper-lings’ right to sell shares would increase as the price of the stock decreased, the right is a “put equivalent position.” 17 C.F.R. § 240.16a-l(h).6 In exchange for this put equivalent position, the Sperlings granted the banks a right to receive additional shares as the Apollo stock price rose above the PVFC ceiling price. Because the value of the banks’ right to receive the pledged shares would increase as the stock price increased, the right is a “call equivalent position.” 17 C.F.R. § 240.16a-l(b).7
For purposes of our analysis, the initial pledge of shares as collateral is irrelevant; the pledge agreement merely protected the bank against the sale or encumbrance of the shares at risk in the PVFC until the settlement date. And the fact that the transaction resembled a loan at settlement prices between the floor and the ceiling is also irrelevant. Even though no shares changed hands on the Payment Date, rights to an equity security were still bought and sold at the time of the contract.8
*469Were we to confíne our focus to the loan aspects of the PVFC, to the exclusion of its option-equivalent elements, we would not only contravene the SEC rules, but also create a new vehicle for insider trading. Suppose an insider anticipated a temporary dip in his company’s stock price. The insider could enter into a PVFC with a settlement date during the expected price dip. The insider could then settle in cash, paying the price of the now devalued shares, but retaining the shares themselves for the anticipated upswing in the stock price. When the stock price returned to normal, the insider would have kept his shares and profited by the difference between the up-front payment (based on the normal stock value) and the settlement price (based on the stock value during the market dip).
In this hypothetical, if the PVFC is treated as a loan, section 16(b) was not violated. No shares changed hands, and there was no “purchase” or “sale” to trigger section 16(b). Viewing the PVFC as a derivative, however, the potential for abuse becomes clear: the insider offered the PVFC “call option” as consideration for the “put option,” knowing that the call option would never be exercised. In other words, he used his informational advantage to sell something he knew to be worthless.
Precisely to prevent what would happen in our hypothetical, we have held that “for purposes of Section 16(b), the expiration of a call option within six months of its writing is to be deemed a ‘purchase’ by the option writer to be matched against the ‘sale’ deemed to occur when that option was written.” Roth v. Goldman Sachs Grp., Inc., 740 F.3d 865, 872 (2d Cir.2014); see also 17 C.F.R. § 240.16b-6(d). This rule prevents an insider from profiting by selling call options with expiration dates within six months, while knowing, by virtue of his inside information, that the stock price would not rise above the strike price and the option would never be exercised. We think this rule should apply here as well. We therefore hold that a PVFC is akin to the “sale” of a call option (and purchase of a put) by the insider, and this sale should be matched to a “purchase” at the settlement date, should the call option expire. Thus for purposes of section 16 liability, the Sperlings “sold” call options to the banks on the day they signed the contract, and any matching “purchases” would occur — if at all — on the settlement date if these options went unexercised.
Viewing the instant transactions in this manner, it becomes clear why the Sperlings did not violate section 16(b). First, for the transactions that settled above the ceiling, nothing of significance occurred on the settlement date. The bank merely exercised its call options, which is neither a purchase nor a sale under section 16(b). The exercise of a traditional derivative security (as opposed to its expiration) is a “non-event” for section 16(b) purposes. Magma Power Co. v. Dow Chem. Co., 136 F.3d 316, 322 (2d Cir.1998). Second, even if the banks’ call options had expired — as they did in several cases — the expiration of an option can only be matched to its own writing for section 16 purposes, not to another unrelated sale of stock. Allaire Corp. v. Okumus, 433 F.3d 248, 254 (2d Cir.2006). Since the Sperlings’ subsequent stock purchases were not part of the PFVC derivative transaction, the two could never have been matched.
B. PVFCs are not “hybrid derivatives”
Although Chechele would agree with our conclusion that the PVFCs at issue here are a species of derivative, she attempts to *470analyze these contracts under our emerging “hybrid derivatives” case law governing options without a fixed exercise price. This is the incorrect mode of analysis.
In Analytical Surveys, Inc. v. Tonga Partners, L.P., 684 F.3d 36, 49-50 (2d Cir.2012), we held that a hybrid derivative — a derivative without a fixed exercise price — is not “purchased” until the price becomes fixed because only then is “the extent of the profit opportunity defined!.]” 9 Our hybrid derivative cases, however, have all dealt with contracts where one of the parties controlled the timing, and thus the price, at which the option would be exercised. See Analytical Surveys, 684 F.3d at 41; At Home Corp. v. Cox Commc’ns Inc., 446 F.3d 403, 405 (2d Cir.2006); Magma Power, 136 F.3d at 319. This is critical.
Because one of the parties controls the timing of the exercise, hybrids present two opportunities to use inside information, once at the writing of the contract and again at their exercise. In Analytical Surveys, we emphasized that the “insider’s additional opportunity to rely on inside information to time the date of exercise” presented an additional danger. 684 F.3d at 50. This is why we held that the “purchase” for section 16(b) purposes occurs when the price is fixed. The time the price is fixed is when the last opportunity to use inside information occurs, and when the six-month clock for a matching sale should start. See id. at 49-50.
The PVFCs at issue here, however, do not present the same risk of manipulation at the time of their settlement that hybrids do at the time of their exercise. It is true that with these PVFCs, as with the securities in our hybrid cases, the number of shares that may be called and the price of those shares is not known at the time the contract is written. Nonetheless, with these PVFCs the price was set by a predetermined formula. There is thus no opportunity for additional manipulation after the contract is signed.10 Because the parties are bound to the formula and dates from the time of contracting, the prices of these PVFC options were fixed at the time they entered the contract even if they are not known.
Viewing these PVFCs as traditional rather than hybrid derivatives also comports with SEC regulations. A related SEC rule provides:
[I]f [an insider’s] increase or decrease [in a derivative position] occurs as a result of the fixing of the exercise price of a right initially issued without a fixed price, where the date the price is fixed is not known in advance and is outside the control of the recipient, the increase or decrease shall be exempt from section 16(b)[.]
17 C.F.R. § 240.16b-6(a). The purpose of this regulation is to avoid “the unfairness of subjecting insiders to liability under Section 16(b) who engage in a purchase or sale and then have an offsetting sale or purchase thrust upon them thereafter by *471events ‘not known in advance’ and ‘outside the[ir] control.’ ” Magma Power, 136 F.3d at 322.
Still, because there is some risk of manipulation, as we discussed above, PVFCs do not — and should not — get the benefit of a total section 16(b) exemption. Nonetheless, treating PVFCs as hybrid derivatives could produce the same “unfairness” that prompted the issuance of 17 C.F.R. § 240.16b-6(a). If the “purchase” or “sale” of the derivative does not occur until the price is “fixed” in the sense of being determined, every PVFC could subject the insider to section 16(b) liability. This is because under a hybrid derivative analysis a “sale” will always occur shortly before settlement, when the value to be delivered is determined. Because, under Roth, an expiration of the bank’s call option is a “purchase” (by the insider) to be matched with this “sale,” section 16 liability would result whenever a PVFC settles below the floor and the bank’s call option expires. This does not make sense.
Viewing the PVFCs as traditional derivatives, however, avoids this odd result. The transactions to be matched are not the “fixing” of the price shortly before settlement and the settlement itself, but the writing of the contract and the settlement. As long contract date, there is no risk of any short-swing profit.
In short, the Sperlings did not violate section 16(b). First, nothing of significance occurred on the Settlement Dates. The banks simply exercised their call options, which is neither a purchase nor a sale under section 16(b). The exercise of a traditional derivative security is a “nonevent” for section 16(b) purposes. Magma Power, 136 F.3d at 322. Therefore the Sperlings’ subsequent sale of stock after settlement did not trigger liability. Second, even if the banks’ call options had expired, under SEC Rule 16b-6(a) “the expiration of an option, when matched against any transaction other than its own •writing, is not [a transaction].” Allaire Corp., 433 F.3d at 254. Furthermore, as mentioned earlier, the expiration of the banks’ call options is “deemed a ‘purchase’ by the option writer to be matched against the ‘sale’ deemed to occur when that option was written.” Roth, 740 F.3d at 872. And third, the PVFC transaction was a sale of stock; both the rights the Sperlings granted and received are “put .equivalent positions” deemed to be “sale[s] of the underlying securities for purposes of section 16(b)[J” 17 C.F.R. § 240.16b-6(a). To trigger section 16(b) liability there must be both a purchase and a sale, not two sales. See Roth, 740 F.3d at 870.
To sum up, the PVFCs in this case are properly analyzed under traditional, and not hybrid, derivatives analysis. When that is done, it becomes evident that no “purchase” occurred against which a “sale” could be matched for section 16(b) purposes.
CONCLUSION
For the foregoing reasons, the district court’s judgment is AFFIRMED.
