Abstract:
An enhanced system and method for executing options trades are disclosed. The order book and quote book are maintained separately to make quote and order processing more efficient, but the order book and quote book are integrated, as needed, to determine the marketability of incoming quotes and, where necessary, so that incoming quotes can execute against resting quotes or orders.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority from and claims the benefit of U.S. Provisional Application No. 60/834,327, filed Jul. 28, 2006, entitled “Electronic Equity Options Order Execution and Routing System,” which is hereby incorporated by reference. 
    
    
     BACKGROUND 
     In the past, when all options trades were transacted on the floor, order processing and quote processing were completely separate manual processes. Individual quotes were manually maintained in an automated system which displayed one quotation for the entire pit, representing the best price but without an associated size. Orders, on the other hand, were maintained on one or more separate order books. A best bid and offer was calculated for quotations and professional orders, while a separate best bid and offer was calculated for the limit order book. 
     With the widespread adoption of multiple listings, exchanges began to increasingly integrate their systems and to execute orders and quotes completely electronically. As a result, some market centers now consolidate all active nonmarketable orders and nonmarketable quotes and maintain them together in the same book memory. For electronic systems that algorithmically allocate trades among orders and quotes, there are advantages to storing both in the same book. 
     In addition to storing orders and quotes in the same book, some systems also allow orders and quotes to be submitted to a market center using the same data pipeline, requiring a “thicker” telecom link to handle both, as an order message generally requires more data elements than a quote message does. While the ability to use one pipeline for both orders and quotes has some operational advantages, and having both orders and quotes already integrated on a single book makes it easier to execute and allocate trades, such business strategies may be less than optimal from a performance standpoint due to the high volume of options quotations compared to the much lower volume of options orders. 
     The options marketplace has historically been a quote-driven market, in contrast to the equities marketplace, which is generally perceived to be more of an order-driven market. On the options marketplace, a single stock can be the underlying for a hundred or more different strike prices and expiration dates. When the underlying stock is very active, market makers may need to update their quotations in dozens of options series simultaneously in response to the fluctuations of the underlying stock price. 
     The popularity of options trading has increased dramatically over the past few years. As a result, the quote traffic has required ever-increasing bandwidth. In recent years, the quotation rates have become so excessive that the SEC has requested that the options market centers propose quote mitigation strategies to reduce quote traffic. This issue is only being exacerbated further with the roll out of penny pricing in options. While penny increments can tighten the spread, especially in the most actively traded products, the downside is that quotes move around more in a penny environment, due to more pricing levels. 
     Accordingly, there is a need for a system and method that minimizes the impact of market maker quote traffic on the other components of the system, especially in regard to the ability to display and execute orders and quotes with maximum speed and efficiency. 
     SUMMARY 
     According to one aspect of the present invention, a method for enhancing quote and order integration includes providing a market center which lists a plurality of options series, wherein the market center has an order book for each option series and a quote book for each option series, wherein the order book for a series is separate from the quote book for a series. The method further includes receiving a quote for a specified option series on the market center, analyzing the received quote to determine if the quote is marketable and, wherein if the quote is marketable, generating a system alert. Further, according to this aspect, wherein, in response to the system alert, the method retrieves the order book and the quote book for the specified option series, and simultaneously, reviews the retrieved order book and quote book to determine if at least one quote or order on the retrieved quote or order book can execute against the received quote. If a retrieved order can execute against the received quote, the method generates a pseudo-order to represent the received quote and executes the generated pseudo-order against the retrieved marketable order. According to another aspect of the present invention, if a retrieved quote can execute against the received quote, the method generates a pseudo-order to represent the received quote and generates a pseudo-order to represent the retrieved quote and executes the generated pseudo-orders against each other. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       These and other features, aspects and advantages of the present invention will become better understood with regard to the following description, appended claims and accompanying drawings where: 
         FIG. 1  is a block diagram illustrating the trading environment in which an embodiment of the present invention operates; 
         FIG. 2  is a block diagram illustrating an overview of the architecture involved in the enhanced quote and order integration process; 
         FIGS. 3A-3B  are flow diagrams illustrating processes for receiving market maker bids and offers in an embodiment of the present invention; 
         FIG. 4A  is a flow diagram illustrating a process in an embodiment of the present invention, wherein an order matching engine reacts to a received “wake up” alert message; 
         FIG. 4B  is an exemplary depiction of the generation of a virtual consolidated order and quote list of the present invention; and 
         FIG. 5  is a flow diagram illustrating a process in an embodiment of the present invention, wherein a market maker quote engine receives an executed quote message. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 , a trading environment in which an embodiment of the system and method of the present invention operates is depicted. The examples discussed herein describe the use and application of the present invention in an equity options market center environment, but it should be understood that the present invention could be used in any type of financial instrument market center environment (e.g., equities, futures, bonds, etc.). This embodiment of the invention describes the use of multiply listed single-leg equity options in the invention environment, wherein contracts for a specified underlying security can be bought (if the option type is a call) or sold (if the option type is a put) at a specific strike price prior to a specific exercise date. The functionality described herein is generally applicable to all standard options products (including near-term options and LEAPs) in all underlying securities, including but not limited to exchange-listed stocks, Exchange-Traded Funds (ETFs), Holding Company Depositary Receipts (HOLDRs), American Depositary Receipts (ADRs), and commonly traded indices. 
     The trading environment of this embodiment includes a market center  20  which interacts with a number of other market centers  24  (i.e., away markets) and traders at order sending firms  26  and market makers  31 . The trading environment of this invention supports a market maker interface  32  and market maker quotes data structure  33 . It should also be understood that the market center  20  referred to herein refers to a computing system having sufficient processing and memory capabilities and does not refer to a specific physical location. In fact, in certain embodiments, the computing system may be distributed over several physical locations. It should also be understood that any number of traders  26  or market makers  31  or away market centers  24  can interact with the market center  20 . The market center  20  is the market center on which a specific trader  26  posts a specific order, and on which a specific market maker  31  posts a specific quote. The market center  20  includes an order matching engine  21 , which validates, maintains, ranks, executes and/or routes all orders on the market center  20 , and which executes marketable quotes on the market center  20 . In this embodiment, the code for the order matching engine  21  is stored in the market center&#39;s memory. 
     The market center  20  may also include a quote and last sale interface  23  that interacts with the away market centers  24  to capture quote and last sale information. This information is stored to a best bids and offers and last sales data structure  25 . This data structure  25  is where the market best bid and offer information is stored. This data structure  25  is also where the market trade reports (prints) are stored. Some issues may be traded exclusively on the market center  20 , and accordingly away market quotes may not exist. The market center  20  may also include an order and trade parameters data structure  27 . The order and trade parameters data structure  27  stores pre-defined trading parameters and rules that are used by the order matching engine  21  in matching orders and executing trades. The market center  20  may also include an order and execution interface  28  which interacts with the traders  26 , the market makers  31 , the away market centers  24  and the order matching engine  21  in the order execution process. 
     The market center  20  may also include an order information data structure  29  where order information is stored and a trade information data structure  30  where completed trade information is stored. The market center  20  may also include a market maker interface  32  that interacts with market makers  31  to capture market maker bids and offers in assigned issues. These bids and offers are logically and physically depicted in a market maker quotes structure  33  in this illustration. 
     Throughout the discussion herein, it should be understood that the details regarding the operating environment, data structures, and other technological elements surrounding the market center  20  are by way of example and that the present invention may be implemented in various differing forms. For example, the data structures referred to herein may be implemented using any appropriate structure, data storage, or retrieval methodology (e.g., local or remote data storage in data bases, tables, internal arrays, etc.). Furthermore, a market center of the type described herein may support any type of suitable interface on any suitable computer system. 
     Referring to  FIG. 2 , a trading environment in which order sending firms  26  and market makers  31  send orders and quotes is depicted. As shown in  FIG. 2 , in this embodiment, order sending firms  26  send only orders, while market maker firms  31  send both orders and quotes. Orders sent by order sending firms  26  are transmitted to the order and execution interface  28  using what is referred to herein as a “thick” pipeline that is able to accommodate all the data that must generally be specified on an incoming order using one or more established third-party message protocols, such as FIX, which generally requires a significant amount of housekeeping information to be included in its order messages. The order and execution interface  28  includes a customer gateway routine  28   a , which, when executed, invokes a process that determines whether and by what means a specific order sending firm  26  is eligible to send orders to the market center  20 , and also includes an order validation routine  28   b  which, when executed, invokes a process that determines whether the specific order meets all the business requirements of the market center  20 . If an order is determined to be valid, then the order and execution interface  28  releases the order to the order matching engine  21  for further processing. Marketable orders are executed immediately, whereas nonmarketable orders that can execute later are posted to an order book  29   a  on the order data structure  29 . The order book  29   a  includes all active nonmarketable orders resident on the market center  20 , including fully displayed orders, partially displayed orders and nondisplayed orders. 
     As illustrated in  FIG. 2 , orders sent by market makers  31  use a pipeline that is referred to herein as a somewhat “thinner” pipeline than the one used by order sending firms  26 . Market marker orders can be sent on this somewhat thinner pipeline because orders sent by market maker firms  31  are transmitted using a direct connection, so some information such as the identity of the sender is available directly from the TCP/IP connection. If a market maker order is determined to be valid, as with an order sending firm order, then the order and execution interface  28  releases the order to the order matching engine  21  for further processing. Marketable orders are executed immediately, whereas nonmarketable orders from market makers  31  are posted to the same order book  29   a  as are orders from order sending firms  26 . 
     In contrast to orders, in this embodiment, market maker quotes are transmitted to the market maker interface  32  using what is referred to herein as a very “thin” pipeline. This is possible due to the fact that, generally speaking, a quote transmitted via a validated direct TCP/IP connection is extremely lean and does not require as much overhead as an order sent using a third-party message protocol. With a TCP/IP connection, the market center  20  already knows the identity of the firm sending the quote and the message type being transmitted. With one TCP/IP Write message, a market maker can send quotes in up to 200 different series, and with one TCP/IP Read message, the market center  20  can unload the quotes into a large array in the market maker quotes data structure  33 . Also, as market makers are only allowed to send one bid and one offer per option series according to the business rules of the market center  20  in this embodiment, there is no need to transmit information for the purpose of distinguishing between multiple quotes for any given market maker in a given option series. As each incoming quote automatically overwrites a prior quote, there is no need for the identification required by a cancel/replace message, reducing quote traffic and functional complexity. It should also be noted that in this embodiment, auto-quoting is not supported. All market maker quotes are generated by the market makers, and all depleted quotes are replenished by the market makers. 
     The market maker interface  32  includes a market maker direct connect routine  32   a , and also includes a market maker quote engine  32   b , which, when executed, initiates a process that receives and analyzes market maker quotes. Specifically, when the process receives a new market maker quote, it stores the quote in a market maker quote book  33   a . It also checks the price of the new market maker quote against resting contra-side market maker quotes, resting contra-side market center orders and optionally the contra-side away market center quotes. If the process determines that the new market maker quote may be marketable, i.e., the new market maker quote touches (i.e., equals or overlaps with) the price of any prior order or market maker quote, then the process generates a “wake up” alert message and sends it to the order matching engine  21 , identifying the potentially marketable series. The order matching engine  21 , in response, as discussed in detail below, retrieves and combines the quote and order books as a virtual list  42  and reads the combined books simultaneously, i.e. “walks” the list, to determine matching opportunities. 
     Orders and quotes in this embodiment of the invention are transmitted using separate pipelines, are stored and maintained in separate data structures and are kept separate until they need to be commingled and integrated for analysis and potential execution purposes. This results in optimized throughput because the quote pipeline is much “thinner” than the order pipeline, and the quote activity level is much higher than the order activity level. By isolating the market maker quote book, which needs to be updated much more often than the order book, the order matching engine  21  does not need to thrash unnecessarily to constantly update a combined book of quotes and orders. In this embodiment, away market best bid and offer (“BBO”) quotes  25   a  are maintained in another data structure  25 , further optimizing performance. 
     Receiving an Incoming Market Maker Bid 
     Referring to  FIG. 3A , at step  100 , the market maker quote engine  32   b  receives an incoming market maker bid, and the market maker quote engine process is initiated. At step  102 , the process retrieves the market maker quote book  33   a  for this option series from the market maker quote data structure  33 . At step  104 , the process checks whether the market maker that sent the bid already has a bid in this option series. If the market maker does not already have a bid in this series, then the process continues to step  106 , where it adds the incoming bid to the market maker quote book  33   a  in price/time priority and proceeds to step  109 . If, however, at step  104 , the process determines that the market maker does already have a bid in this series, then the process continues to step  108 , where it replaces the prior bid with the incoming bid, and re-ranks the quote according to its new price/time priority. By way of explanation, according to the business rules of the market center in this embodiment, a market maker is only allowed to publish one bid per option series. 
     The process continues to step  109 , where it checks if the new market maker bid locks or crosses the best market maker offer. If it does, then the process proceeds to step  114 , where the process generates a “wake up” message for the order matching engine  21 . It should be noted that the locked/crossed best bid and offer (BBO) is not disseminated publicly. The “wake up” message in this embodiment includes a pointer to the option series so that the order matching engine  21  immediately knows which series to evaluate. The process then terminates in step  116  as indicated. 
     Returning to step  109 , if, however, the new market maker bid does not overlap with the best market maker offer, then the process continues to step  110 , where it retrieves the order book  29   a  for this option series from the order book data structure  29 . Then, at step  112 , the process checks if the price of the new market maker bid is greater than or equal to the best sell order. If the price of the new bid is inferior, then the process terminates as indicated at step  116 . 
     If, however, the price of the new market maker bid is greater than or equal to the best sell order, then the process continues to step  114 , where, as before, it generates a “wake up” message with a pointer to the option series so that the order matching engine  21  immediately knows which series to evaluate. The locked/crossed BBO is not disseminated publicly. The process then terminates as indicated at step  116 . 
     Receiving an Incoming Market Maker Offer 
     Referring to  FIG. 3B , similar to the process for receiving an incoming market maker bid, at step  200 , the market maker quote engine  32   b  receives an incoming market maker offer, and the market maker quote engine process is initiated. At step  202 , the process retrieves the market maker quote book  33   a  for this option series from the market maker quote data structure  33 . At step  204 , the process checks whether the market maker that sent the offer already has an offer in this option series. If the market maker does not already have an offer in this series, then the process continues to step  206 , where it adds the incoming offer to the market maker quote book  33   a  in price/time priority and proceeds to step  209 . If, however, at step  204 , the process determines that the market maker does already have an offer in this series, then the process continues to step  208 , where it replaces the prior offer with the incoming offer, and re-ranks the quote according to its new price/time priority. By way of explanation, according to the business rules of the market center in this embodiment, a market maker is only allowed to publish one offer per option series. 
     The process continues to step  209 , where it checks if the new market maker offer locks or crosses the best market maker bid. If it does, then the process proceeds to step  214 , where the process generates a “wake up” message for the order matching engine  21 . As described above, it should be noted that the locked/crossed best bid and offer (BBO) is not disseminated publicly. The “wake up” message in this embodiment includes a pointer to the option series so that the order matching engine  21  immediately knows which series to evaluate. The process then terminates as indicated at step  216 . 
     Returning to step  209 , if, however, the new market maker offer does not overlap with the best market maker bid, then the process continues to step  210 , where it retrieves the order book  29   a  for this option series from the order book data structure  29 . Then, at step  212 , the process checks if the price of the new market maker offer is less than or equal to the best buy order. If the price of the new offer is inferior, then the process terminates as indicated at step  216 . 
     If, however, the price of the new market maker offer is less than or equal to the best buy order, then the process continues to step  214 , where, as before, it generates a “wake up” message with a pointer to the option series so that the order matching engine  21  immediately knows which series to evaluate. The locked/crossed BBO is not disseminated publicly. The process then terminates as indicated at step  216 . 
     Order Matching Engine Receives “Wake Up” Message 
     Referring to  FIGS. 4A and 4B , the order matching engine  21  receives a “wake up” message from the market maker quote engine  32   b , as described above, alerting it to a possible execution opportunity in a specific option series, as indicated at step  300 . The order matching engine  21  in response, and as described below, evaluates the orders and quotes, executes them if a match is possible, and notifies the market maker quote engine  32   b  if any quotes need to be decremented or canceled due to the executions. 
     At step  304  in  FIG. 4A  and as depicted in  FIG. 4B , the process retrieves the order book  29   a  for the designated option series. At step  306  in  FIG. 4A  and as depicted in  FIG. 4B , the process retrieves a snapshot of the market maker quote book  33   a  for the designated option series, and a snapshot of the away market BBO book  25   a  for the designated option series. At step  307 , the process combines the retrieved order book  29   a , the retrieved market maker quote book  33   a  and the retrieved away market BBO book  25   a  to create a virtual consolidated order and quote list  42 . The virtual consolidated order and quote list  42  is a temporary, virtual list and is not maintained as a separate, standing order and quote book in this embodiment. The underlying orders and quotes are maintained in their separate data structures. The virtual consolidated order and quote list  42  is assembled so that the order matching engine  21  can “walk” the list  42  as described below. 
     Specifically, at step  308 , after the virtual consolidated order and quote list  42  is generated, the process then “walks” both sides of the virtual consolidated order and quote list  42  simultaneously, starting with the highest-ranked bid and the highest-ranked offer to determine if there is an overlap between the best bid prices and the best offer prices. The process then proceeds to step  310  to determine if the new market maker quote can execute. If the new market maker quote can execute, then, at step  312 , the process checks the active market maker quote book  33   a  again to determine if it is still executable, specifically to ensure that the new market maker quote has not been changed to an inferior price during the brief interval in which the order matching engine  21  was “walking” the list  42 , i.e. the quote price in the snapshot is not stale. If, at step  312 , the process determines that the market maker quote is no longer marketable, then the process terminates as indicated at step  314 . 
     If, however, the current market maker quote is still marketable, then the process continues to step  318 , where it generates an immediate-or-cancel (“IOC”) pseudo-order on behalf of the underlying executable market maker quote. At step  320 , the process then executes the generated pseudo-order against any resting orders and/or resting market maker quotes whose prices overlap with the pseudo-order, in the sequence of their ranking. It should be noted that in this embodiment, market makers are responsible for transmitting their own linkage orders to other market centers if a market maker quote locks or crosses an away market quote. As such, pseudo-orders are not routed to away market quotes. In this embodiment, the resting orders and/or quotes are executed according to price/time priority, but with a preference for displayed interest over nondisplayed (“working”) order types. Accordingly, if any non-displayed, order types are executable against the pseudo-order, then the non-displayed order types are executed only after all displayed orders and quotes at the same price execute first. 
     If any resting market maker quotes are executable against the pseudo-order created on behalf of the new market maker quote, then the process also generates an IOC pseudo-order on behalf of each resting market maker quote that can execute. As indicated at step  322 , the process decrements or removes the executed quotes from local memory. It should be noted that in this embodiment, at this point in the process, the quotes are depleted or decremented in the order matching engine&#39;s local memory only and do not affect the published quotes yet. 
     At step  324 , for each market maker quote that executed, the process sends an “executed quote” message to the market maker quote engine  32   b  informing it of the quantity of contracts executed and the quantity remaining, if any. The process, as indicated at step  325 , also sends the resulting trade information to the order and execution interface  28 , which in turn sends the fills to the order sending firms  26  and the market maker firms  31 . The process then terminates in step  326  as indicated. 
     Market Maker Quote Engine Receives an Executed Quote Message from the Order Matching Engine 
     Referring to  FIG. 5 , at step  400 , the market maker quote engine  32   b  receives an executed quote message from the order matching engine  21 , and the process is initiated. At step  404 , the process retrieves the market maker quote book  33   a  for the option series. At step  408 , the process checks if the price of the executed quote is the same as the price of the current quote. If the prices are different, then the process terminates as indicated at step  414 . If, however, the prices are equal, then the process continues to step  410 , where it checks if the remaining quote size reported on the message is less than the current quote size. If the remaining quote size is indeed lower, then the process continues to step  412 , where it decrements the current quote size to the remaining quote size specified on the executed quote message. The process then terminates as indicated at step  414 . 
     Returning to step  410 , if, however, the remaining quote size reported on the message is greater than or equal to the current quote size, then the process does not replace the current quote, and terminates as indicated at step  414 . Accordingly, the process automatically decreases (but does not automatically increase) the size of a current quote. 
     DETAILED EXAMPLES 
     Examples of how quotes and orders are processed in a preferred embodiment of the invention are provided below. It should be understood that the order and quote prices and sizes discussed in these examples are by way of example only to illustrate how the process of an embodiment of the invention operates. Quote and order processing is not limited to these examples. 
     In the examples below, the option series has three appointed market makers: LMM, MM 2 , and MM 3 . In the first example, market maker MM 2  sends a new nonmarketable bid, which simply replaces its current bid. In the second example, market maker MM 3  sends a new offer, whose price is marketable against a posted buy order and is also marketable against the bid from market maker MM 2 . As illustrated in these examples, the order matching engine  21  is not notified of the nonmarketable quote update, and is only notified of the marketable quote update. 
     At the start of these examples, the various books appear as shown below. 
     →The NBBO is 2.00 to 2.05 (50×240) 
     For ease of illustration, the quotes from only two away market centers  24  are shown. The away market BBO book  25   a  looks like this: 
     
       
         
               
               
             
           
               
                   
               
               
                 Away Market Bids 
                 Away Market Offers 
               
               
                   
               
             
             
               
                 Away Market A: Bid 30 @ 2.00 (10:00:03) 
                 Away Market B: 
               
               
                   
                 Offer 40 @ 2.05 (10:01:02) 
               
               
                 Away Market B: Bid 60 @ 1.95 (09:59:57) 
                 Away Market A: 
               
               
                   
                 Offer 50 @ 2.10 (10:00:30) 
               
               
                   
               
             
          
         
       
     
     The market maker quote book  33   a  looks like this: 
     
       
         
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                 LMM: Bid 40 @ 1.95 (10:03:09) 
                 LMM: Offer 70 @ 2.05 (10:00:27) 
               
               
                 MM2: Bid 50 @ 1.95 (10:03:15) 
                 MM3: Offer 60 @ 2.05 (10:02:05) 
               
               
                 MM3: Bid 80 @ 1.95 (10:03:50) 
                 MM2: Offer 50 @ 2.10 (10:00:36) 
               
               
                   
               
             
          
         
       
     
     The order book  29   a  looks like this: 
                                             Buy Orders   Sell Orders                           Order A: Buy 20 @ 2.00 (10:02:07)   Order E: Sell 30 @ 2.05               (10:01:20)           Order G: Buy 10 @ 1.95 (10:02:45)   Order B: Sell 40 @ 2.05               (10:02:37)           Order F: Buy 30 @ 1.90 (09:57:10)   Order H: Sell 60 @ 2.10               (10:03:43)           Order D: Buy 50 @ 1.90 (10:04:03)   Order C: Sell 40 @ 2.15               (09:58:04)                        
→The market center BBO is 2.00 to 2.05 (20×200)
 
     The public order book looks like this: 
                                             Bids   Offers                           20 @ 2.00   200 @ 2.05           180 @ 1.95    110 @ 2.10           80 @ 1.90    40 @ 2.15                        
Market Maker MM 2  Sends a Nonmarketable Bid
 
     Referring to  FIG. 3A , at step  100  in this example, the market maker quote engine  32   b  receives the following bid from market maker MM 2 :
         Bid  50 @2.00       

     At step  102 , the initiated process retrieves the market maker quote book  33   a  for this series. At step  104 , the process checks if MM 2  already has a bid in this series. As shown below, a bid for MM 2  does already exist: 
     
       
         
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                 LMM: Bid 40 @ 1.95 (10:03:09) 
                 LMM: Offer 70 @ 2.05 (10:00:27) 
               
               
                 → MM2: Bid 50 @ 1.95 (10:03:15) 
                 MM3: Offer 60 @ 2.05 (10:02:05) 
               
               
                 MM3: Bid 80 @ 1.95 (10:03:50) 
                 MM2: Offer 50 @ 2.10 (10:00:36) 
               
               
                   
               
             
          
         
       
     
     As a bid for MM 2  already exists, the process continues to step  108 , where it replaces the current bid with the incoming bid and updates its timestamp. At step  109 , the process checks if the new MM 2  bid (2.00) locks or crosses the best market maker offer (2.05). As it does not, the process continues to step  110 . 
     The market maker quote book  33   a  now looks like this: 
     
       
         
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                 → MM2: Bid 50 @ 2.00 (10:04:15) 
                 LMM: Offer 70 @ 2.05 (10:00:27) 
               
               
                 LMM: Bid 40 @ 1.95 (10:03:09) 
                 MM3: Offer 60 @ 2.05 (10:02:05) 
               
               
                 MM3: Bid 80 @ 1.95 (10:03:50) 
                 MM2: Offer 50 @ 2.10 (10:00:36) 
               
               
                   
               
             
          
         
       
     
     At step  110 , the process retrieves the order book for this option series. The order book  29   a  looks like this: 
     
       
         
               
               
               
             
           
               
                   
                   
               
               
                   
                 Buy Orders 
                 Sell Orders 
               
               
                   
                   
               
             
             
               
                   
                 Order A: Buy 20 @ 2.00 (10:02:07) 
                 Order E: Sell 30 @ 2.05 
               
               
                   
                   
                 (10:01:20) 
               
               
                   
                 Order G: Buy 10 @ 1.95 (10:02:45) 
                 Order B: Sell 40 @ 2.05 
               
               
                   
                   
                 (10:02:37) 
               
               
                   
                 Order F: Buy 30 @ 1.90 (09:57:10) 
                 Order H: Sell 60 @ 2.10 
               
               
                   
                   
                 (10:03:43) 
               
               
                   
                 Order D: Buy 50 @ 1.90 (10:04:03) 
                 Order C: Sell 40 @ 2.15 
               
               
                   
                   
                 (09:58:04) 
               
               
                   
                   
               
             
          
         
       
     
     In step  112 , the process checks if the new MM 2  bid price (2.00) is greater than or equal to the best sell order (2.05). As the new MM 2  bid price is inferior to the best sell order, the process terminates in step  116  as indicated. 
     →The market center BBO is now 2.00 to 2.05 (70×200) 
     The public order book looks like this: 
                                             Bids   Offers                            → 70 @ 2.00   200 @ 2.05           → 130 @ 1.95   110 @ 2.10              80 @ 1.90    40 @ 2.15                        
Market Maker MM 3  Sends a Marketable Offer
 
     Referring to  FIG. 3B , at step  200  in this example, the market maker quote engine  32   b  receives the following offer from market maker MM 3 :
         Offer  60 @2.00       

     At step  202 , the process retrieves the market maker quote book  33   a  for this series. At step  204 , the process checks if MM 3  already has an offer in this series. As shown below, an offer for MM 3  does already exist: 
     
       
         
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                 MM2: Bid 50 @ 2.00 (10:04:15) 
                 LMM: Offer 70 @ 2.05 (10:00:27) 
               
               
                 LMM: Bid 40 @ 1.95 (10:03:09) 
                 → MM3: Offer 60 @ 2.05 
               
               
                   
                 (10:02:05) 
               
               
                 MM3: Bid 80 @ 1.95 (10:03:50) 
                 MM2: Offer 50 @ 2.10 (10:00:36) 
               
               
                   
               
             
          
         
       
     
     As an offer for MM 3  already exists, the process continues to step  208 , where it replaces the current offer with the incoming offer and updates its timestamp. It should be noted that although the MM 3  offer has now caused the market maker quote book  33   a  to become locked, the market maker quote engine  32   b  does not disseminate the MM 3  offer to the marketplace, as that would result in the market center  20  generating a locked BBO quotation. 
     The market maker quote book  33   a  momentarily looks like this: 
     
       
         
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                 MM2: Bid 50 @ 2.00 (10:04:15) 
                 → MM3: Offer 60 @ 2.00 
               
               
                   
                 (10:05:05) 
               
               
                 LMM: Bid 40 @ 1.95 (10:03:09) 
                 LMM: Offer 70 @ 2.05 (10:00:27) 
               
               
                 MM3: Bid 80 @ 1.95 (10:03:50) 
                 MM2: Offer 50 @ 2.10 (10:00:36) 
               
               
                   
               
             
          
         
       
     
     At step  209 , the process checks if the new market maker offer locks or crosses the best market maker bid. As the MM 3  offer (2.00) is the same price as the MM 2  bid (2.00), the process continues to step  214 , where it sends a “wake up” message to the order matching engine  21 , alerting it that this series must be evaluated for an execution. The process then terminates in step  216  as indicated. 
     Order Matching Engine Retrieves the Order Book and Quote Books and Combines them into Ranked Lists 
     Referring to  FIG. 4A , at step  300 , the process receives the “wake up” message from the market maker quote engine  32   b , alerting it to the execution opportunity in this series. At step  304 , the process retrieves the order book  29   a  for the series. 
     The order book  29   a  remains the same and still looks like this: 
     
       
         
               
               
               
             
           
               
                   
                   
               
               
                   
                 Buy Orders 
                 Sell Orders 
               
               
                   
                   
               
             
             
               
                   
                 Order A: Buy 20 @ 2.00 (10:02:07) 
                 Order E: Sell 30 @ 2.05 
               
               
                   
                   
                 (10:01:20) 
               
               
                   
                 Order G: Buy 10 @ 1.95 (10:02:45) 
                 Order B: Sell 40 @ 2.05 
               
               
                   
                   
                 (10:02:37) 
               
               
                   
                 Order F: Buy 30 @ 1.90 (09:57:10) 
                 Order H: Sell 60 @ 2.10 
               
               
                   
                   
                 (10:03:43) 
               
               
                   
                 Order D: Buy 50 @ 1.90 (10:04:03) 
                 Order C: Sell 40 @ 2.15 
               
               
                   
                   
                 (09:58:04) 
               
               
                   
                   
               
             
          
         
       
     
     At step  306 , the process takes a snapshot of the market maker quote book  33   a  for this series and a snapshot of the away market BBO book  25   a  for this series and retrieves the snapshots. By way of explanation, as the quote books are too volatile to freeze for the duration of the evaluation and execution, a snapshot is taken and read into a local buffer for processing by the order matching engine  21 . 
     The away market BBO book  25   a  remains unchanged and still looks like this: 
     
       
         
               
               
             
           
               
                   
               
               
                 Away Market Bids 
                 Away Market Offers 
               
               
                   
               
             
             
               
                 Away Market A: Bid 30 @ 2.00 (10:00:03) 
                 Away Market B: 
               
               
                   
                 Offer 40 @ 2.05 (10:01:02) 
               
               
                 Away Market B: Bid 60 @ 1.95 (09:59:57) 
                 Away Market A: 
               
               
                   
                 Offer 50 @ 2.10 (10:00:30) 
               
               
                   
               
             
          
         
       
     
     The market maker quote book  33   a  is momentarily locked and looks like this: 
     
       
         
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                 MM2: Bid 50 @ 2.00 (10:04:15) 
                 → MM3: Offer 60 @ 2.00 
               
               
                   
                 (10:05:05) 
               
               
                 LMM: Bid 40 @ 1.95 (10:03:09) 
                 LMM: Offer 70 @ 2.05 (10:00:27) 
               
               
                 MM3: Bid 80 @ 1.95 (10:03:50) 
                 MM2: Offer 50 @ 2.10 (10:00:36) 
               
               
                   
               
             
          
         
       
     
     At step  307 , the process generates a virtual consolidated order and quote list  42 . It does this by combining the order book  29   a , the snapshot of the market quote book  33   a , and the snapshot of the away market BBO book  25   a  together into a single ranked list of bids and a single ranked list of offers. As the order book does not presently contain any “working” orders, the market maker quotes and the orders are ranked according to strict price/time priority. As resident trading interest always has priority over nonresident trading interest at the same price level, the market maker quotes and the orders are ranked ahead of the away market quotes at the same price level. 
     Accordingly, the ranked list of bids looks like this: 
     
       
         
               
             
               
               
             
           
               
                   
               
               
                 Ranked Bids 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Order A: Buy 20 @ 2.00 (10:02:07) 
               
               
                   
                 MM2: Bid 50 @ 2.00 (10:04:15) 
               
               
                   
                 Away Market A: Bid 30 @ 2.00 (10:00:03) 
               
               
                   
                 Order G: Buy 10 @ 1.95 (10:02:45) 
               
               
                   
                 LMM: Bid 40 @ 1.95 (10:03:09) 
               
               
                   
                 MM3: Bid 80 @ 1.95 (10:03:50) 
               
               
                   
                 Away Market B: Bid 60 @ 1.95 (10:02:57) 
               
               
                   
                 Order F: Buy 30 @ 1.90 (09:57:10) 
               
               
                   
                 Order D: Buy 50 @ 1.90 (10:04:03) 
               
               
                   
                   
               
             
          
         
       
     
     The ranked list of offers looks like this: 
     
       
         
               
             
               
               
             
           
               
                   
               
               
                 Sell Orders 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 MM3: Offer 60 @ 2.00 (10:05:05) 
               
               
                   
                 LMM: Offer 70 @ 2.05 (10:00:27) 
               
               
                   
                 Order E: Sell 30 @ 2.05 (10:01:20) 
               
               
                   
                 Order B: Sell 40 @ 2.05 (10:02:37) 
               
               
                   
                 Away Market B: Offer 40 @ 2.05 (10:01:02) 
               
               
                   
                 MM2: Offer 50 @ 2.10 (10:00:36) 
               
               
                   
                 Order H: Sell 60 @ 2.10 (10:03:43) 
               
               
                   
                 Away Market A: Offer 50 @ 2.10 (10:00:30) 
               
               
                   
                 Order C: Sell 40 @ 2.15 (09:58:04) 
               
               
                   
                   
               
             
          
         
       
     
     The ranked list of bids and the ranked list of offers form the virtual consolidated order and quote list  42 , which momentarily looks like this: 
                                                   Buy Orders   Sell Orders                                Order A:   Buy 20 @ 2.00 (10:02:07)   MM3:   Offer 60 @ 2.00 (10:05:05)       MM2:   Bid 50 @ 2.00 (10:04:15)   LMM:   Offer 70 @ 2.05 (10:00:27)       Away Market A:   Bid 30 @ 2.00 (10:00:03)   Order E:   Sell 30 @ 2.05 (10:01:20)       Order G:   Buy 10 @ 1.95 (10:02:45)   Order B:   Sell 40 @ 2.05 (10:02:37)       LMM:   Bid 40 @ 1.95 (10:03:09)   Away Market B:   Offer 40 @ 2.05 (10:01:02)       MM3:   Bid 80 @ 1.95 (10:03:50)   MM2:   Offer 50 @ 2.10 (10:00:36)       Away Market B:   Bid 60 @ 1.95 (10:02:57)   Order H:   Sell 60 @ 2.10 (10:03:43)       Order F:   Buy 30 @ 1.90 (09:57:10)   Away Market A:   Offer 50 @ 2.10 (10:00:30)       Order D:   Buy 50 @ 1.90 (10:04:03)   Order C:   Sell 40 @ 2.15 (09:58:04)                    
Order Matching Engine Creates a Pseudo-Order on Behalf of the MM 3  Offer, and Matches a Posted Buy Order
 
     At step  308 , the process “walks” the virtual consolidated order and quote list  42  to evaluate the execution opportunities, and determines that the MM 3  offer is marketable against Buy Order A and the MM 2  bid. At step  310 , the process retrieves the MM 3  offer again from the market maker quote book  33   a  to ensure that its price has not changed during the brief interval in which it was evaluating the virtual consolidated order and quote list  42 . As the MM 3  offer has not changed in this example, in step  312 , the process determines that the MM 3  offer is still marketable. 
     At step  318 , the process creates a pseudo-order on behalf of the MM 3  offer:
         Order PSO 1 : Sell  60 @2.00, IOC       

     In step  320 , the process retrieves the best bid, Buy Order A, and matches  20  contracts of Buy Order A at the price of 2.00, completely depleting Buy Order A and removing it from the books. Pseudo-order PSO 1  (and the underlying MM 3  offer) still have 40 contracts available to trade. 
     The order book  29   a  looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Buy Orders 
                 Sell Orders 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Order G: 
                 Buy 10 @ 1.95 
                 Order E: 
                 Sell 30 @ 2.05 (10:01:20) 
               
               
                   
                 (10:02:45) 
                   
                   
               
               
                 Order F: 
                 Buy 30 @ 1.90 
                 Order B: 
                 Sell 40 @ 2.05 (10:02:37) 
               
               
                   
                 (09:57:10) 
                   
                   
               
               
                 Order D: 
                 Buy 50 @ 1.90 
                 Order H: 
                 Sell 60 @ 2.10 (10:03:43) 
               
               
                   
                 (10:04:03) 
                   
                   
               
               
                   
                   
                 Order C: 
                 Sell 40 @ 2.15 (09:58:04) 
               
               
                   
               
             
          
         
       
     
     The virtual consolidated order and quote list  42  momentarily looks like this: 
                                                   Buy Orders   Sell Orders                                MM2:   Bid 50 @ 2.00 (10:04:15)   → MM3:   Offer 40 @ 2.00 (10:05:05)       Away Market A:   Bid 30 @ 2.00 (10:00:03)   LMM:   Offer 70 @ 2.05 (10:00:27)       Order G:   Buy 10 @ 1.95 (10:02:45)   Order E:   Sell 30 @ 2.05 (10:01:20)       LMM:   Bid 40 @ 1.95 (10:03:09)   Order B:   Sell 40 @ 2.05 (10:02:37)       MM3:   Bid 80 @ 1.95 (10:03:50)   Away Market B:   Offer 40 @ 2.05 (10:01:02)       Away Market B:   Bid 60 @ 1.95 (10:02:57)   MM2:   Offer 50 @ 2.10 (10:00:36)       Order F:   Buy 30 @ 1.90 (09:57:10)   Order H:   Sell 60 @ 2.10 (10:03:43)       Order D:   Buy 50 @ 1.90 (10:04:03)   Away Market A:   Offer 50 @ 2.10 (10:00:30)               Order C:   Sell 40 @ 2.15 (09:58:04)                    
Order Matching Engine Creates a Pseudo-Order on Behalf of the MM 2  Bid, and Matches the MM 3  Sell Pseudo-Order Against the MM 2  Buy Pseudo-Order
 
     Still at step  320 , the process determines that pseudo-order PSO 1  is also marketable against the MM 2  bid. Accordingly, the process also checks the MM 2  bid again in the market maker quote book  33   a  to ensure that its price has not changed during the interval while the virtual consolidated order and quote list  42  is being evaluated. The MM 2  bid has not changed in this example. 
     The process creates a pseudo-order on behalf of the MM 2  bid:
         Order PSO 2 : Buy  50 @ 2.00, IOC       

     The process matches the remaining 40 contracts of pseudo-order PSO 1  against 40 contracts of pseudo-order PSO 2  at the price of 2.00, completely depleting pseudo-order PSO 1 . The remaining 10 contracts of pseudo-order PSO 2  are immediately canceled. In step  322 , the process decrements the MM 3  offer by the quantity traded, completely depleting the MM 3  offer and removing it from the virtual consolidated order and quote list  42 . The MM 2  bid still has 10 contracts remaining. 
     The virtual consolidated order and quote list  42  looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Buy Orders 
                 Sell Orders 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 → MM2: 
                 Bid 10 @ 2.00 (10:04:15) 
                 LMM: 
                 Offer 70 @ 2.05 (10:00:27) 
               
               
                 Away Market A: 
                 Bid 30 @ 2.00 (10:00:03) 
                 Order E: 
                 Sell 30 @ 2.05 (10:01:20) 
               
               
                 Order G: 
                 Buy 10 @ 1.95 (10:02:45) 
                 Order B: 
                 Sell 40 @ 2.05 (10:02:37) 
               
               
                 LMM: 
                 Bid 40 @ 1.95 (10:03:09) 
                 Away Market B: 
                 Offer 40 @ 2.05 (10:01:02) 
               
               
                 MM3: 
                 Bid 80 @ 1.95 (10:03:50) 
                 MM2: 
                 Offer 50 @ 2.10 (10:00:36) 
               
               
                 Away Market B: 
                 Bid 60 @ 1.95 (10:02:57) 
                 Order H: 
                 Sell 60 @ 2.10 (10:03:43) 
               
               
                 Order F: 
                 Buy 30 @ 1.90 (09:57:10) 
                 Away Market A: 
                 Offer 50 @ 2.10 (10:00:30) 
               
               
                 Order D: 
                 Buy 50 @ 1.90 (10:04:03) 
                 Order C: 
                 Sell 40 @ 2.15 (09:58:04) 
               
               
                   
               
             
          
         
       
     
     As no further additional orders or quotes can execute at the present time, the virtual consolidated order and quote list  42  is deleted from local memory. 
     Order Matching Engine Notifies the Market Maker Quote Engine of the executed MM 3  Offer Quantity and the Executed MM 2  Bid Quantity 
     At step  324 , the process generates an executed quote message on behalf of the MM 3  offer: 
     →MM 3  Offer ( 60 @2.00) executed  60 , Leaves quantity=0 
     The process also generates an executed quote message on behalf of the MM 2  bid: 
     →MM 2  Bid ( 50 @2.00) executed  40 , Leaves quantity=10 
     The process sends the two executed quote messages to the market maker quote engine  32   b . At step  325 , the process sends the execution reports to the order and execution interface  28 . The trade for Order A is reported to the appropriate order sending firm  26 , the trade for the MM 3  offer is reported to market maker MM 3 , and the trade for the MM 2  bid is reported to market maker MM 2 . The process then terminates in step  326  as indicated. 
     Market Maker Quote Engine Receives the Executed Quote Message for the MM 2  Bid 
     Referring to  FIG. 5 , at step  400  in this example, the market maker quote engine  32   b  receives the executed quote message from the order matching engine  21  regarding the MM 2  bid: 
     →MM 2  Bid ( 50 @2.00) executed  40 , Leaves quantity=10 
     In step  404 , it retrieves the market maker quote book  33   a  for the series. The market maker quote book  33   a  is still momentarily locked and looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 MM2: 
                 Bid 50 @ 2.00 
                 MM3: 
                 Offer 60 @ 2.00 (10:05:05) 
               
               
                   
                 (10:04:15) 
                   
                   
               
               
                 LMM: 
                 Bid 40 @ 1.95 
                 LMM: 
                 Offer 70 @ 2.05 (10:00:27) 
               
               
                   
                 (10:03:09) 
                   
                   
               
               
                 MM3: 
                 Bid 80 @ 1.95 
                 MM2: 
                 Offer 50 @ 2.10 (10:00:36) 
               
               
                   
                 (10:03:50) 
               
               
                   
               
             
          
         
       
     
     In step  408 , the process checks if the price of the MM 2  bid on the executed quote message (2.00) is the same as the current published MM 2  bid (2.00). As the prices are equal, the process continues to step  410 , where it checks if the remaining quote size (10) of the MM 2  bid on the executed quote message is less than the current published MM 2  bid size (50). As the remaining quote size on the message is less, the process continues to step  412 , where the market maker quote engine  32   b  decrements the current published quote size to 10 contracts. 
     The updated market maker quote book  33   a  now looks like this: 
                                                   Market Maker Bids   Market Maker Offers                                → MM2:   Bid 10 @ 2.00   MM3:   Offer 60 @ 2.00 (10:05:05)           (10:04:15)               LMM:   Bid 40 @ 1.95   LMM:   Offer 70 @ 2.05 (10:00:27)           (10:03:09)               MM3:   Bid 80 @ 1.95   MM2:   Offer 50 @ 2.10 (10:00:36)           (10:03:50)                    
MM 3  Sends a New Offer Before Receiving the Fill from the Prior Execution
 
     In this example, in the brief interval before the market maker quote engine  32   b  receives the executed quote message for the MM 3  offer, market maker MM 3  sends a new offer:
         Offer  40 @2.05
 
Referring to  FIG. 3B , at step  202 , the market maker quote engine  32   b  retrieves the market maker quote book  33   a  for the series.
       

     The market maker quote book  33   a  currently looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 MM2: 
                 Bid 10 @ 2.00 
                 MM3: 
                 Offer 60 @ 2.00 (10:05:05) 
               
               
                   
                 (10:04:15) 
                   
                   
               
               
                 LMM: 
                 Bid 40 @ 1.95 
                 LMM: 
                 Offer 70 @ 2.05 (10:00:27) 
               
               
                   
                 (10:03:09) 
                   
                   
               
               
                 MM3: 
                 Bid 80 @ 1.95 
                 MM2: 
                 Offer 50 @ 2.10 (10:00:36) 
               
               
                   
                 (10:03:50) 
               
               
                   
               
             
          
         
       
     
     In step  204 , the process checks if market maker MM 3  already has an offer for this series. As it does, the process continues to step  208 , where it replaces the current MM 3  offer with the new MM 3  offer and ranks the new offer in price/time priority. 
     The updated market maker quote book  33   a  now looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 MM2: 
                 Bid 10 @ 2.00 
                 LMM: 
                 Offer 70 @ 2.05 (10:00:27) 
               
               
                   
                 (10:04:15) 
                   
                   
               
               
                 LMM: 
                 Bid 40 @ 1.95 
                 → MM3: 
                 Offer 40 @ 2.05 (10:05:06) 
               
               
                   
                 (10:03:09) 
                   
                   
               
               
                 MM3: 
                 Bid 80 @ 1.95 
                 MM2: 
                 Offer 50 @ 2.10 (10:00:36) 
               
               
                   
                 (10:03:50) 
               
               
                   
               
             
          
         
       
     
     In step  209 , the process checks if the new market maker offer (2.05) locks or crosses the best market maker bid (2.00). As it does not, at step  210 , the process retrieves the order book for the option series. 
     The order book  29   a  looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Buy Orders 
                 Sell Orders 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Order G: 
                 Buy 10 @ 1.95 
                 Order E: 
                 Sell 30 @ 2.05 (10:01:20) 
               
               
                   
                 (10:02:45) 
                   
                   
               
               
                 Order F: 
                 Buy 30 @ 1.90 
                 Order B: 
                 Sell 40 @ 2.05 (10:02:37) 
               
               
                   
                 (09:57:10) 
                   
                   
               
               
                 Order D: 
                 Buy 50 @ 1.90 
                 Order H: 
                 Sell 60 @ 2.10 (10:03:43) 
               
               
                   
                 (10:04:03) 
                   
                   
               
               
                   
                   
                 Order C: 
                 Sell 40 @ 2.15 (09:58:04) 
               
               
                   
               
             
          
         
       
     
     In step  212 , the process checks if the new MM 3  offer (2.05) is less than or equal to the best buy order. As it is not, the MM 3  offer is not marketable, and the process terminates in step  216  as indicated. As the market maker quote book  33   a  is no longer locked, the new MM 3  offer is disseminated to the public order book and the market center BBO is updated. 
     →The market center BBO is now 2.00 to 2.05 (10×180) 
     The public order book looks like this: 
                                         Bids   Offers                       → 10 @ 2.00   → 180 @ 2.05           130 @ 1.95   110 @ 2.10           80 @ 1.90   40 @ 2.15                    
Market Maker Quote Engine Receives the Executed Quote Message for the Prior MM 3  Offer
 
     Referring to  FIG. 5 , at step  400  in this example, the market maker quote engine  32   b  receives the executed quote message from the order matching engine  21  regarding the MM 3  offer: 
     →MM 3  Offer ( 60 @2.00) executed  60 , Leaves quantity=0 
     In step  404 , it retrieves the market maker quote book  33   a  for the series: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 MM2: 
                 Bid 10 @ 2.00 
                 LMM: 
                 Offer 70 @ 2.05 (10:00:27) 
               
               
                   
                 (10:04:15) 
                   
                   
               
               
                 LMM: 
                 Bid 40 @ 1.95 
                 MM3: 
                 Offer 40 @ 2.05 (10:05:06) 
               
               
                   
                 (10:03:09) 
                   
                   
               
               
                 MM3: 
                 Bid 80 @ 1.95 
                 MM2: 
                 Offer 50 @ 2.10 (10:00:36) 
               
               
                   
                 (10:03:50) 
               
               
                   
               
             
          
         
       
     
     In step  408 , the process checks if the price of the MM 3  offer on the executed quote message (2.00) is the same as the current published MM 3  offer (2.05). As the prices are not equal, the process continues to step  414 , where it terminates as indicated. As shown in this example, the market maker quote engine  32   b  does not reduce the quote size of the current MM 3  offer because its price is different from that of the previous MM 3  offer that executed above. 
     The state of the various books at the conclusion of these examples is shown below. 
     →The NBBO is 2.00 to 2.05 (40×220) 
     The away market BBO book  25   a  remains unchanged and still looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Away Market Bids 
                 Away Market Offers 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Away Market A: 
                 Bid 30 @ 2.00 
                 Away Market B: 
                 Offer 40 @ 2.05 
               
               
                   
                 (10:00:03) 
                   
                 (10:01:02) 
               
               
                 Away Market B: 
                 Bid 60 @ 1.95 
                 Away Market A: 
                 Offer 50 @ 2.10 
               
               
                   
                 (09:59:57) 
                   
                 (10:00:30) 
               
               
                   
               
             
          
         
       
     
     The market maker quote book  33   a  looks like this: 
     
       
         
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Market Maker Bids 
                 Market Maker Offers 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 MM2: 
                 Bid 10 @ 2.00 
                 LMM: 
                 Offer 70 @ 2.05 (10:00:27) 
               
               
                   
                 (10:04:15) 
                   
                   
               
               
                 LMM: 
                 Bid 40 @ 1.95 
                 MM3: 
                 Offer 40 @ 2.05 (10:05:06) 
               
               
                   
                 (10:03:09) 
                   
                   
               
               
                 MM3: 
                 Bid 80 @ 1.95 
                 MM2: 
                 Offer 50 @ 2.10 (10:00:36) 
               
               
                   
                 (10:03:50) 
               
               
                   
               
             
          
         
       
     
     The order book  29   a  looks like this: 
                                                   Buy Orders   Sell Orders                                Order G:   Buy 10 @ 1.95 (10:02:45)   Order E:   Sell 30 @ 2.05                   (10:01:20)       Order F:   Buy 30 @ 1.90 (09:57:10)   Order B:   Sell 40 @ 2.05                   (10:02:37)       Order D:   Buy 50 @ 1.90 (10:04:03)   Order H:   Sell 60 @ 2.10                   (10:03:43)               Order C:   Sell 40 @ 2.15                   (09:58:04)                    
→The market center BBO is 2.00 to 2.05 (10×180)
 
     The public order book looks like this: 
     
       
         
               
               
               
             
           
               
                   
               
               
                   
                 Bids 
                 Offers 
               
               
                   
               
             
             
               
                   
                  10 @ 2.00 
                 180 @ 2.05 
               
               
                   
                 130 @ 1.95 
                 110 @ 2.10 
               
               
                   
                  80 @ 1.90 
                  40 @ 2.15 
               
               
                   
               
             
          
         
       
     
     While the invention has been discussed in terms of certain embodiments, it should be appreciated that the invention is not so limited. The embodiments are explained herein by way of example, and there are numerous modifications, variations and other embodiments that may be employed that would still be within the scope of the present invention.