Abstract:
Systems and methods are provided for calculating margin requirements and stress testing exposures of cleared credit portfolios. These margin requirements are calculated using the following components: spread risk, idiosyncratic risk, interest rate, and liquidity risk. The calculation of these risk components is accomplished with a detailed statistical analysis of the risk factors underlying instruments, such as a credit default swap instrument.

Description:
[0001]    This application claims priority to Provisional Application, U.S. Ser. No. 61/994,624, filed May 16, 2014 and to Provisional Application, U.S. Ser. No. 61/994,611, filed May 16, 2014 which are both incorporated herein by reference in their entirety. 
     
    
     FIELD OF THE INVENTION 
       [0002]    Aspects of the invention relate to determining risks and margin requirements. More particularly, aspects of the invention relate to determining costs associated with liquidity risks using a risk model for cleared credit. 
       BACKGROUND 
       [0003]    Exchanges are typically associated with clearing houses that are responsible for settling trading accounts, clearing trades, collecting and maintaining performance bond funds, regulating delivery and reporting trading data. Clearing is the procedure through which the clearing house becomes buyer to each seller of a contract, and seller to each buyer, and assumes responsibility for protecting buyers and sellers from financial loss by assuring performance on each contract. This is effected through the clearing process, whereby transactions are matched. 
         [0004]    Clearing houses establish clearing level performance bonds (margins) for traded financial products and establishes minimum performance bond requirements for customers. A performance bond, also referred to as a margin, is the funds that may be required to deposited by a customer with his or her broker, by a broker with a clearing member or by a clearing member with the clearing house, for the purpose of insuring the broker or clearing house against loss on open contracts. The performance bond is not a part payment on a purchase and helps to ensure the financial integrity of brokers, clearing members and exchanges or other trading entities as a whole. A performance bond to clearing house refers to the minimum dollar deposit which is required by the clearing house from clearing members in accordance with their positions. Maintenance, or maintenance margin, refers to a sum, usually smaller than the initial performance bond, which must remain on deposit in the customer&#39;s account for any position at all times. In order to minimize risk to an exchange or other trading entity while minimizing the burden on members, it is desirable to approximate the requisite performance bond or margin requirement as closely as possible to the actual risk of the account at any given time. 
         [0005]    Risks and margin requirements can be difficult to determine for illiquid and concentrated positions. Illiquid positions do not allow a clearing house to quickly liquidate positions, which makes it difficult to value risks. Concentrated positions can make it difficult for a clearing house or other entity to find a buyer or seller. Accordingly, there is a need in the art for systems and methods for determining risks and margin requirements for illiquid and concentrated positions. 
       SUMMARY OF THE INVENTION 
       [0006]    Aspects of the invention overcomes at least some of the problems and limitations of the prior art by providing systems and methods for valuing risks and margin requirements for portfolios that are illiquid or have concentrated positions. In some cases a model may include four different terms which are added to yield an aggregate liquidity charge for portfolios consisting of NA indices (IG, HY) and single names, such as a cost of SDV01 hedge for IG sub-portfolio, a cost of SDV01 hedge for HY sub-portfolio, a cost of unwinding hedged index positions, and a cost of unwinding hedged single name positions. In some embodiments of the invention the concentration based liquidity charge includes the sum of a concentration charge for market exposure and a concentration charge for the basis of the portfolio. 
         [0007]    In other embodiments, the present invention can be partially or wholly implemented on a computer-readable medium, for example, by storing computer-executable instructions or modules, or by utilizing computer-readable data structures. 
         [0008]    Of course, the methods and systems of the above-referenced embodiments may also include other additional elements, steps, computer-executable instructions, or computer-readable data structures. In this regard, other embodiments are disclosed and claimed herein as well. 
         [0009]    The details of these and other embodiments of the present invention are set forth in the accompanying drawings and the description below. Other features and advantages of the invention will be apparent from the description and drawings, and from the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    The present invention may take physical form in certain parts and steps, embodiments of which will be described in detail in the following description and illustrated in the accompanying drawings that form a part hereof, wherein: 
           [0011]      FIG. 1  shows a computer network system that may be used to implement aspects of the present invention; 
           [0012]      FIG. 2  shows an illustrative liquidity charge computing device that may be used to implement aspects of the present invention; 
           [0013]      FIG. 3  shows an illustrative method for determining a liquidity charge according to aspects of the present invention; 
           [0014]      FIGS. 4 and 5  show illustrative charts for calibrating an aspect of the liquidity charge associated with a credit default swap according to aspects of the present invention; and 
           [0015]      FIGS. 6-10  show illustrative charts showing an impact on margin accounts according to aspects of the present invention. 
       
    
    
     DETAILED DESCRIPTION 
       [0016]    In some cases, a risk model may be used for risk management pertaining to clearing of Credit Default Swap (CDS) and related credit instruments, including but not limited to NA CDX indices, NA single names, iTraxx indices, iTraxx single names, other credit indices, futures on indices, etc. 
         [0017]    Sources of risks arising from clearing credit default swaps may include the cost of liquidating the CDS portfolio of a clearing member firm in case of default. Efficient modeling and estimation of this cost may be as important as quantifying the market risk related costs, if not more, for credit instruments as these instruments do have varying degrees of liquidity characteristics. A clearing house may offer clearing services for different indices, such as NA indices (IG and HY) and is planning to extend its offering to iTraxx indices (Main, Cross Over), and North American and European single names. The calculation of liquidity risk requirements as part of margin and stress exposures may be important to the success of a risk management model that conforms to regulatory requirements and to the risk appetite of the Clearing House. The liquidity risk model may, therefore, be used to provide good coverage across a representative set of portfolios under a comprehensive set of historical and hypothetical scenarios representing distressed liquidity, to take into account liquidity characteristics of credit instruments based on contract tenors, index families and series, and reference entities. In some cases, the liquidity risk model may also be used to consistently and proportionately model the effect of concentration (position size), to have a robust, intuitive and justifiable parameterization that supports a reliable and transparent calibration and replication process, and to be consistent with a default management process. 
         [0018]    In some cases, a liquidity model used by an illustrative clearing house may address liquidity risk of portfolios consisting of only NA indices (IG and HY). In some cases, the current liquidity requirement may include two components which are intended to cover the costs associated with the steps of a typical liquidation process. The first component may be designed to cover the cost of hedging the market exposure of a defaulted portfolio while the second component may address the cost of liquidating the hedged portfolio. A progressive concentration charge may implicitly embed into the liquidity requirement through a super-linear dependence on position size. The Bid/Ask data across different series and tenors of index instruments may be incorporated in the model through a liquidity floor which is intended to address the liquidity risk of smaller size portfolios, which may be transacted at observed Bid/Ask spreads in case of default. 
         [0019]    A previously used risk model may not differentiate between on-the-run and off-the-run indices and/or contracts of different tenors as long as they have similar market risk exposures measured by their SDV01 (spread adjusted DV01). The model therefore may not address the drop in liquidity of index series when they become off-the-run and the relative illiquidity of contracts on non 5-year tenors. This characteristic of the model makes it harder to extend to single names and other index instruments without making significant adjustments. 
         [0020]    Aspects of the present invention are preferably implemented with computer devices and computer networks that allow users to exchange trading information. An exemplary trading network environment for implementing trading systems and methods is shown in  FIG. 1 . An exchange computer system  100  receives orders and transmits market data related to orders and trades to users. Exchange computer system  100  may be implemented with one or more mainframe, desktop or other computers. A user database  102  includes information identifying traders and other users of exchange computer system  100 . Data may include user names and passwords. An account data module  104  may process account information that may be used during trades. A match engine module  106  is included to match bid and offer prices. Match engine module  106  may be implemented with software that executes one or more algorithms for matching bids and offers. A trade database  108  may be included to store information identifying trades and descriptions of trades. In particular, a trade database may store information identifying the time that a trade took place and the contract price. An order book module  110  may be included to compute or otherwise determine current bid and offer prices. A market data module  112  may be included to collect market data and prepare the data for transmission to users. A risk management module  134  may be included to compute and determine a user&#39;s risk utilization in relation to the user&#39;s defined risk thresholds. An order processing module  136  may be included to decompose delta based and bulk order types for processing by order book module  110  and match engine module  106 . 
         [0021]    The trading network environment shown in  FIG. 1  includes computer devices  114 ,  116 ,  118 ,  120  and  122 . Each computer device includes a central processor that controls the overall operation of the computer and a system bus that connects the central processor to one or more conventional components, such as a network card or modem. Each computer device may also include a variety of interface units and drives for reading and writing data or files. Depending on the type of computer device, a user can interact with the computer with a keyboard, pointing device, microphone, pen device or other input device. 
         [0022]    Computer device  114  is shown directly connected to exchange computer system  100 . Exchange computer system  100  and computer device  114  may be connected via a T1 line, a common local area network (LAN) or other mechanism for connecting computer devices. Computer device  114  is shown connected to a radio  132 . The user of radio  132  may be a trader or exchange employee. The radio user may transmit orders or other information to a user of computer device  114 . The user of computer device  114  may then transmit the trade or other information to exchange computer system  100 . 
         [0023]    Computer devices  116  and  118  are coupled to a LAN  124 . LAN  124  may have one or more of the well-known LAN topologies and may use a variety of different protocols, such as Ethernet. Computers  116  and  118  may communicate with each other and other computers and devices connected to LAN  124 . Computers and other devices may be connected to LAN  124  via twisted pair wires, coaxial cable, fiber optics or other media. Alternatively, a wireless personal digital assistant device (PDA)  122  may communicate with LAN  124  or the Internet  126  via radio waves. PDA  122  may also communicate with exchange computer system  100  via a conventional wireless hub  128 . As used herein, a PDA includes mobile telephones and other wireless devices that communicate with a network via radio waves. 
         [0024]      FIG. 1  also shows LAN  124  connected to the Internet  126 . LAN  124  may include a router to connect LAN  124  to the Internet  126 . Computer device  120  is shown connected directly to the Internet  126 . The connection may be via a modem, DSL line, satellite dish or any other device for connecting a computer device to the Internet. 
         [0025]    One or more market makers  130  may maintain a market by providing constant bid and offer prices for a derivative or security to exchange computer system  100 . Exchange computer system  100  may also exchange information with other trade engines, such as trade engine  138 . One skilled in the art will appreciate that numerous additional computers and systems may be coupled to exchange computer system  100 . Such computers and systems may include clearing, regulatory and fee systems. 
         [0026]    The operations of computer devices and systems shown in  FIG. 1  may be controlled by computer-executable instructions stored on computer-readable medium. For example, computer device  116  may include computer-executable instructions for receiving order information from a user and transmitting that order information to exchange computer system  100 . In another example, computer device  118  may include computer-executable instructions for receiving market data from exchange computer system  100  and displaying that information to a user. 
         [0027]    Of course, numerous additional servers, computers, handheld devices, personal digital assistants, telephones and other devices may also be connected to exchange computer system  100 . Moreover, one skilled in the art will appreciate that the topology shown in  FIG. 1  is merely an example and that the components shown in  FIG. 1  may be connected by numerous alternative topologies. 
         [0028]      FIG. 2  shows an illustrative block diagram representation of a liquidity charge computing system  200  for implementing a model for determining a liquidity charge associated with a credit default swap (CDS) portfolio. In some cases, the liquidity charge computing system may include a liquidity charge computing device  200  communicatively coupled via a network  205  (e.g., a wide area network (WAN), the LAN  124 , the Internet  126 , etc.) to a CDS market computing system  210 . The CDS market computing system may include one or more computing devices configured for receiving and disseminating information corresponding to a CDS market, such as pricing information (e.g., bid information, ask information, etc.), CDS quality information (e.g., investment grade information, high yield information, etc.), tenor information, and/or the like. The liquidity charge computing device  210  may be communicatively coupled to a clearinghouse computing system  240  via the network  205 , or otherwise incorporated into the clearinghouse computing system  240 . 
         [0029]    In some cases, the clearinghouse computing system  240  may include a data repository  242 , one or more computing devices  244  and/or a user interface  246 . The data repository may store instructions, that when executed by the one or more computing devices  244 , may cause the one or more computing devices  244  to perform operations associated with determining performance bond contributions associated with holdings in products that are based on various types of credit default swaps. In some cases, the clearinghouse computing system  240  may present performance bond and/or margining information to a financial institution via the network  205 , wherein the financial institution holds one or more portfolios that include a credit default swap. Further, the clearinghouse computing system  240  may further present the performance bond and/or margining information via one or more user interface screens via the user interface  246 . The user interface  246  may be local to the clearinghouse computing system  240  and/or remote from the clearinghouse computing system  240  and accessible via the network  205 . The user interface screens may graphically and/or textually present information corresponding to a margin requirement determined for a CDS portfolio as determined by the liquidity charge computing device  210 . 
         [0030]    The liquidity charge computing device  210  may include a processor  212 , one or more non-transitory memory devices  214  (e.g., RAM, ROM, a disk drive, a flash drive, a redundant array of independent disks (RAID) server, and/or other such device etc.), a user interface  216 , a data repository  218 , a communication interface to facilitate communications via the network  205 , and/or the like. The liquidity charge computing device  210  may be configured to store instructions in the one or more memory devices  214  and/or the data repository  218  that, when executed by the processor  212 , may configure the liquidity charge computing device  210  to execute a model for determining margining requirements associated with a CDS portfolio. In some cases, the liquidity charge computing device  210  may process the instructions stored in the memory device  214  and/or the data repository  218  to calculate the margining requirements using an outright exposure calculator  220  and/or a basis exposure calculator  230 . In some cases, the outright exposure calculator  220  may be used to calculate an outright exposure to liquidity charges for holdings held in a CDS portfolio. For example, the outright exposure calculator  220  may calculate an exposure associated with hedging an investment grade (IG) sub-portfolio held in the CDS portfolio using an IG exposure calculator  222 . Similarly, the outright exposure calculator  220  may calculate an exposure associated with hedging a high yield (HY) sub-portfolio held in the CDS portfolio using a HY exposure calculator  224 . The basis exposure calculator  230  may be used to calculate a cost of unwinding hedged positions held in the CDS portfolio. For example, the basis exposure calculator  230  may process instructions to calculate a cost of unwinding hedged single name positions held in the CDS portfolio using a single name basis exposure calculator  232 . Similarly, the basis exposure calculator  230  may process instructions to calculate a cost of unwinding hedged index positions held in the CDS portfolio using an index basis exposure calculator  234 . 
         [0031]    The liquidity charge computing device  210  may process instructions corresponding to model to determine a liquidity charge and/or margin requirement associated with any particular CDS swap portfolio. This model may be stored as instructions in the one or more non-transitory memory devices  214  and/or the data repository  218  that, when executed by the processor  212  may cause the liquidity charge computing device to calculate the liquidity charge by calculating up to four different terms that may be added to yield an aggregate liquidity charge for portfolios consisting of indices (IG, HY) and single names, such as a cost of SDV01 hedge for IG sub-portfolio, a cost of SDV01 hedge for HY sub-portfolio, a cost of unwinding hedged index positions, and a cost of unwinding hedged single name positions. In some cases, the indexes and/or single name positions may be associated with a North American CDS market and/or a foreign CDS market (e.g., a European CDS market, an Asian CDS market, etc.). In some cases, a single name CDS may be based on a swap associated with a particular single name (e.g., corporation). An index may include a plurality of single name positions. As such, an index based CDS may be similar to a futures contract and may be based on a value of an index at a given time. 
         [0032]    The liquidity charge computing device  210  may calculate a cost associated with liquidating the CDS positions held in a particular CDS portfolio. This liquidity charge may be used when determining margin requirements for the accounts holding one or more CDS portfolios. The liquidity charge may be calculated by the outright exposure calculator  220  and the basis exposure calculator of the liquidity charge computing device  210  using the formula: 
         [0000]      Liquidity Charge=Outright exposure+Index Basis Exposure+Single Name Basis Exposure   (1)
 
         [0000]    where, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       IG 
                        
                       
                           
                       
                        
                       Outright 
                        
                       
                           
                       
                        
                       Exposure 
                     
                     = 
                     
                       
                         α 
                         IG 
                       
                        
                       
                          
                         
                           SDV 
                            
                           
                               
                           
                            
                           
                             01 
                             IG 
                           
                         
                          
                       
                        
                       max 
                        
                       
                         { 
                         
                           
                             
                                
                               
                                 
                                   SDV 
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       01 
                                       IG 
                                     
                                     / 
                                     SDV 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     01 
                                     
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                                       , 
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                                        
                                       
                                           
                                       
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                                    
                                   
                                       
                                   
                                    
                                   
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                                       , 
                                       IG 
                                       , 
                                       
                                         5 
                                          
                                         
                                             
                                         
                                          
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                                
                             
                             0.5 
                           
                           , 
                           1 
                         
                         } 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     
                       where 
                        
                       
                           
                       
                        
                       SDV 
                        
                       
                           
                       
                        
                       
                         01 
                         IG 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           
                             i 
                             ∈ 
                             
                               IG 
                                
                               
                                   
                               
                                
                               IN 
                                
                               
                                   
                               
                                
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                                
                               
                                   
                               
                                
                               SN 
                             
                           
                           
                             τ 
                             ∈ 
                             
                               { 
                               
                                 1 
                                 , 
                                 3 
                                 , 
                                 5 
                                 , 
                                 7 
                                 , 
                                 10 
                               
                               } 
                             
                           
                         
                       
                        
                       
                         SDV 
                          
                         
                             
                         
                          
                         
                           01 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       HY 
                        
                       
                           
                       
                        
                       Outright 
                        
                       
                           
                       
                        
                       Exposure 
                     
                     = 
                     
                       
                         α 
                         HY 
                       
                        
                       
                          
                         
                           SDV 
                            
                           
                               
                           
                            
                           
                             01 
                             HY 
                           
                         
                          
                       
                        
                       max 
                        
                       
                         { 
                         
                           
                             
                                
                               
                                 
                                   SDV 
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       01 
                                       HY 
                                     
                                     / 
                                     SDV 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                     01 
                                     
                                       OTR 
                                       , 
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                                       , 
                                       
                                         5 
                                          
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                                     w 
                                      
                                     
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                                          
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                                       ) 
                                     
                                   
                                    
                                   
                                       
                                   
                                    
                                   γ 
                                    
                                   
                                       
                                   
                                    
                                   
                                     Q 
                                     
                                       0 
                                       , 
                                       OTR 
                                       , 
                                       HY 
                                       , 
                                       
                                         5 
                                          
                                         Y 
                                       
                                     
                                   
                                 
                               
                                
                             
                             0.5 
                           
                           , 
                           1 
                         
                         } 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                    
                   
                     
                       where 
                        
                       
                           
                       
                        
                       SDV 
                        
                       
                           
                       
                        
                       
                         01 
                         HY 
                       
                     
                     = 
                     
                       
                         ∑ 
                         
                           
                             i 
                             ∈ 
                             
                               HY 
                                
                               
                                   
                               
                                
                               IN 
                                
                               
                                   
                               
                                
                               and 
                                
                               
                                   
                               
                                
                               SN 
                             
                           
                           
                             τ 
                              
                             
                                 
                             
                             ∈ 
                             
                               { 
                               
                                 1 
                                 , 
                                 3 
                                 , 
                                 5 
                                 , 
                                 7 
                                 , 
                                 10 
                               
                               } 
                             
                           
                         
                       
                        
                       
                         SDV 
                          
                         
                             
                         
                          
                         
                           01 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     Index 
                      
                     
                         
                     
                      
                     Basis 
                      
                     
                         
                     
                      
                     Exposure 
                   
                   = 
                   
                     
                       β 
                       IN 
                     
                      
                     
                       
                         ∑ 
                         
                           
                             
                               i 
                               ∈ 
                               IN 
                             
                             , 
                             
                               τ 
                               ∈ 
                               
                                 ( 
                                 
                                   1 
                                   , 
                                   3 
                                   , 
                                   5 
                                   , 
                                   7 
                                   , 
                                   10 
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 - 
                                 IG 
                               
                                
                               
                                   
                               
                                
                               OTR 
                                
                               
                                   
                               
                                
                               5 
                                
                               Y 
                             
                             
                               
                                 - 
                                 HY 
                               
                                
                               
                                   
                               
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                        
                       
                         
                           f 
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                          
                         
                            
                           
                             SDV 
                              
                             
                                 
                             
                              
                             
                               01 
                               
                                 i 
                                 , 
                                 τ 
                               
                             
                           
                            
                         
                          
                         max 
                          
                         
                           { 
                           
                             
                               
                                  
                                 
                                   
                                     Q 
                                     i 
                                   
                                   
                                     
                                       w 
                                        
                                       
                                         ( 
                                         τ 
                                         ) 
                                       
                                     
                                      
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                                      
                                     
                                         
                                     
                                      
                                     
                                       Q 
                                       
                                         0 
                                         , 
                                         i 
                                       
                                     
                                   
                                 
                                  
                               
                               0.5 
                             
                             , 
                             1 
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     Single 
                      
                     
                         
                     
                      
                     Name 
                      
                     
                         
                     
                      
                     Basis 
                      
                     
                         
                     
                      
                     Exposure 
                   
                   = 
                   
                     
                       β 
                       SN 
                     
                      
                     
                       
                         ∑ 
                         
                           
                             i 
                             ∈ 
                             SN 
                           
                           
                             τ 
                              
                             
                                 
                             
                             ∈ 
                             
                               ( 
                               
                                 1 
                                 , 
                                 3 
                                 , 
                                 5 
                                 , 
                                 7 
                                 , 
                                 10 
                               
                               ) 
                             
                           
                         
                       
                        
                       
                         
                           f 
                            
                           
                             ( 
                             τ 
                             ) 
                           
                         
                          
                         
                            
                           
                             SDV 
                              
                             
                                 
                             
                              
                             
                               01 
                               
                                 i 
                                 , 
                                 τ 
                               
                             
                           
                            
                         
                          
                         max 
                          
                         
                           { 
                           
                             
                               
                                  
                                 
                                   
                                     Q 
                                     i 
                                   
                                   
                                     
                                       w 
                                        
                                       
                                         ( 
                                         τ 
                                         ) 
                                       
                                     
                                      
                                     γ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       Q 
                                       
                                         0 
                                         , 
                                         i 
                                       
                                     
                                   
                                 
                                  
                               
                               0.5 
                             
                             , 
                             1 
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0033]    Here, Q 0i  is a median weekly trading volume and may be calibrated to most recent 13 weeks for the entity (e.g., single name) and aggregated across different tenors. Q 0i  is a median weekly trading volume and may be calibrated to most recent 13 weeks for the entity (e.g., single name) and aggregated across different tenors. The function f(τ) is a tenor scalar for calculating the liquidity charge and may be based on a ratio of Bid-Ask/Mid prices across different tenors. The function W(τ) is a tenor adjustor for weekly trading volume and may be a function of f(γ). The constant γ is associated with a proportion of weekly trading volume that can be liquidated per day. This constant may be set to any value and may be set to a same value for the different sub portfolios (e.g., HY, IG) and/or for index basis exposure and/or single name basis exposure. For example, γ may be set to a particular constant value for each equation (2), (4), (6), and (7) (e.g., about 10%, about 15%, about 5%, etc.). In some cases, y may be set to different values when determining the IG or HY outright exposure, the Index basis exposure, and/or the single name basis exposure. 
         [0034]    In an illustrative example, the cost of an SDV01 hedge for an IG sub-portfolio may represent the cost of hedging the aggregate SDV01 exposure of IG indices and IG single names. This cost may be measured as a function of the IG on-the-run notional required for hedging the total SDV01 exposure of the IG sub-portfolio. The charge scales super linearly when the hedge notional may become relatively large compared to a proportion (e.g., about 10%) of the median weekly trading volume of on-the-run IG 5-year contract. The trading volume on the 5-year contract may be estimated by applying a tenor adjustor on the total trading volume of the on-the-run IG contracts. The tenor adjustor may be calibrated to Bid/Ask and Mid spread data on indices. 
         [0035]    The cost of an SDV01 hedge for an HY sub-portfolio may represent the cost of hedging the aggregate SDV01 exposure of HY indices and HY single names. This cost may be measured as a function of the HY on-the-run notional required for hedging the total SDV01 exposure of the HY sub-portfolio. The charge may scale super linearly when the hedge notional becomes relatively large compared to a proportion (e.g., about 10%) of the median weekly trading volume of on-the-run HY 5-year contract. The trading volume on the 5-year contract may be estimated by applying a tenor adjustor on the total trading volume of the on-the-run HY contracts. The tenor adjustor may be calibrated to Bid/Ask and Mid spread data on indices. 
         [0036]    A cost of unwinding hedged index positions may represent the cost of liquidating hedged index positions. This cost may be measured as a function of the SDV01 of each off-the-run or non-5 year index series position. The charge may scale super linearly when the position notional becomes relatively large compared to a proportion (e.g., about 10%) of the median weekly trading volume of the index series and tenor combination. The trading volume of the index series and tenor may be estimated by applying a tenor adjustor on the total trading volume of the index series. The tenor adjustor may be calibrated to Bid/Ask and Mid spread data on indices. 
         [0037]    A cost of unwinding hedged single name positions may represent the cost of liquidating single name positions of the CDS portfolio hedged by corresponding index positions. This cost may be measured as a function of the SDV01 of each single name position. The charge may scale super linearly when the position notional becomes relatively large compared to a proportion (e.g., about 10%) of the median weekly trading volume of the reference entity and tenor combination. The trading volume of the reference entity and tenor may be estimated by applying a tenor adjustor on the total trading volume of the reference entity. The tenor adjustor may be calibrated to Bid/Ask and Mid spread data on single names. 
         [0038]    The liquidity model may include a number of risk aversion parameters, (e.g., four risk aversion parameters as illustrated) which may be associated with different terms in the liquidity formula. These risk aversion parameters may be calibrated and/or back-tested to dealer polls on liquidity. For example, the risk aversion parameters may be calibrated to account for pure index CDS portfolios and/or for single name CDS portfolios. The single name CDS portfolios may include index positions to cover index-single name arbitrage portfolios, and/or the like. 
         [0039]    While the model illustrated in equations (1)-(7) may be configured to cover liquidity exposure (e.g., risk) associated with North American (e.g., NA) CDS markets, the model can easily be extended to cover a liquidity risk of portfolios that may contain other indices (e.g., a European CDS index, an Asian CDS index, etc.) such as iTraxx. The extension of the model to cover other product families may be achieved simply by adding terms for hedging and unwinding such positions (after hedging). Calibration of the risk aversion parameters for these terms may be done using dealer polls on portfolios containing such instruments. 
         [0040]    The model for liquidity charge for CDS portfolios, as executed by the outright exposure calculator  220  and the basis exposure calculator  230  of the liquidity charge computing device, may distinguish between on-the-run/off-the-run indices and single names based on trading volume data, where the different credit default swaps have different levels of liquidity. The model may also differentiate between outright and market (e.g., risk) neutral portfolios, account for an effect of tenors associated with different CDS swaps held in the portfolio on liquidity, and may scale super-linearly (e.g., a 1.5 exponential equation) as a function of notional to account for a concentration of risk. In some cases, the model may incorporate weekly trading volume data from the Depository Trust &amp; Clearing Corporation (DTCC), to differentiate between corporate obligors, on-the-run indexes, and/or off-the-run indexes. In some cases, the model may account for an effect of tenor on liquidity. 
         [0041]      FIG. 3  shows an illustrative method  300  for determining a liquidity charge according to aspects of this disclosure. As discussed above, the liquidity charge computing device  210  may process instructions to calculate a liquidity charge, such as by using equation (1) discussed above. For example, at  310 , the outright exposure calculator  220  may calculate a cost associated with a SDV01 hedge corresponding to an IG sub-portfolio of a CDS portfolio. Similarly, at  320 , the outright exposure calculator  220  may calculate a cost associated with a SDV01 hedge corresponding to a HY sub-portfolio o the CDS portfolio. For example, a scalar value (e.g., α, β, etc.) may be calibrated to one or more dealer polls associated with the representative CDS portfolios. In some cases, the SDV01 hedge value may be calculated at the CDS portfolio level, such as by determining an SDV01 for each position of the portfolio. The SDV01 may be a measure of sensitivity of each CDS to a 1% change in a power spread curve corresponding to the contract. The IG outright exposure calculator  222  may calculate the exposure for the IG sub-portfolio based on a SDV01 determined based on an on-the-run CDS swap having a 5-year tenor. This SDV01 (SDV01 IG ) may be used to determine an amount of notional corresponding to the on-the-run, 5-year CDS required to hedge the SDV01 exposure of the overall IG sub-portfolio. In some cases, a CDS may roll periodically (e.g., March, September), and in such cases, the calculations will roll (e.g., be based on) the new series. In some cases, an adjustment value, w(τ) may be used to calibrate the calculation based on a particular tenor (e.g., a 5-year tenor). This adjustment value may be calibrated based on dealer surveys on a periodic (e.g., semi-annual) basis. In some cases, such as for large CDS portfolios, the IG outright exposure may scale super-linearly, such as by a factor of 1.5. In other cases, such as for small CDS portfolios, the IG outright exposure may scale linearly, such as by using a maximum value. Additionally, the outright exposure calculator may further scale the outright exposure using a median trading volume parameter, such as a trading volume as reported by the DTCC. 
         [0042]    At  330 , the liquidity charge computing device  210  may calculate a cost associated with unwinding one or more hedged index positions associated with the CDS portfolio, such as by using the basis exposure calculator  230 . At  340 , the liquidity charge computing device  210  may calculate a cost associated with unwinding one or more hedged single name positions associated with the CDS portfolio, such as by using the basis exposure calculator  230 . At  350 , the liquidity charge computing device  210  may calculate a liquidity charge associated with the CDS portfolio based on the cost of the SDV01 hedge of the IG sub-portfolio and the cost of the SDV01 hedge of the HY sub-portfolio, the cost of unwinding the hedged index positions and the cost of unwinding the hedged single name positions. In some cases, the liquidity charge computing device  210  may communicate the calculated liquidity charge via the network  205  to the clearinghouse computing system  240 . The clearinghouse computing system  240  may use the liquidity charge in one or more calculations to determine margining requirements corresponding the CDS portfolio. The clearinghouse computing system  240  may further communicate the margining requirements to an account owner of the account containing the CDS portfolio and/or a financial institution associated with the CDS portfolio. 
         [0043]      FIGS. 4 and 5  show illustrative charts  400 ,  500  for calibrating an aspect of the liquidity charge associated with a credit default swap portfolio. In chart  400 , a ratio of (Bid-Ask/Mid) values associated with a particular tenor (e.g., 1-year, 3-year, 5-year, 7 year, 10-year, etc.) are compared to a value of a (Bid-Ask/Mid) ratio associated with a 5-year tenor over one or more different run-rank series. The surface  410  represents the ratio (e.g., f(τ)  415 ) across the different tenors  420  and different run ranks  425 . The run ranks correspond to an on-the-run series (e.g., 0) and different off-the-run series (e.g., −1 year, −2 year, etc.). The chart  500  shows an illustrative (Bid-Ask/Mid) ratio f(τ)  415  associated with a different tenors  420  over a particular run-rank series, such as the on-the-run series. 
         [0044]    In some cases, these ratios for indexes may be calibrated to recent (e.g., weekly, monthly, semiannual, etc.) poll results and ratios for single names may be calibrated to historical data. For example, ratios for single name credit default swaps may be calibrated to historical poll data during a specified time frame, such as by using a preceding year&#39;s poll results. In some cases, additional calibration may be done by calculating a run-rank specific tenor scalar function for indexes and/or by polling on single name bid/ask spreads across tenors for calibration of single name tenor dependence, and/or the like. 
         [0045]      FIGS. 6-10  show illustrative charts showing an impact on margin accounts based on use of a model according to aspects of the invention. For example,  FIG. 6  shows an illustrative chart  600  representing a margin impact on a house account of a plurality of clearing member firms  605 . An illustrative chart  650  represents a margin impact on aggregate customer accounts for a plurality of clearing member firms  605 . For each firm, margin and liquidity  610  are shown based on calculations using a previous model and new margin and new liquidity  620  are shown based on the model discussed above, as implemented using the liquidity charge computing device  210 . Additionally, for each of the clearing member firms  605 , a change in total margin  630  is shown between the margin and liquidity  610  calculated using the previous model and the new margin and new liquidity  620  calculated using the new model. As can be seen in chart  600 , for house accounts, margin requirements including liquidity charges, have been reduced using the new model by at least 10%, with an average of about a 30% reduction in margin costs. For customer accounts, margin requirements including liquidity charges have mostly been reduced from about 2% to about 10%. 
         [0046]    Chart  700  of  FIG. 7  shows an impact of liquidity margin across margin accounts as a ratio of the newly calculated liquidity margin to the liquidity margin calculated using a previous model. As can be seen, in many cases, liquidity margin has increased using the new model. As can be seen in chart  750 , the largest increases  760  in total margin have been seen in credit default swaps having the most associated liquidity risks, such as in off-the-run HY or outright  10 Y positions. 
         [0047]      FIGS. 8 and 9  show illustrative charts  800 ,  900  illustrating changes seen in the margin accounts for firm  6  and firm  12  using the liquidity charges calculated by the liquidity charge computing device  210 . For example, for both firm  6  and firm  12 , margins without liquidity have decreased significantly due to decommissioning of the gross notional based curve charge. Also, for both firms, liquidity margins have increased significantly due to off-the-run positions held in their respective portfolios. Because firm  12  has more relative exposure to off-the-run indexes, the liquidity margin increases more than the liquidity margin increase seen by firm  6 . 
         [0048]      FIG. 10  shows an illustrative chart  1000  showing a rolling effect seen in margin and liquidity requirements. For example, Firm  7  has a relatively hedged portfolio with concentrated positions in IG  18  and IG  20  CDS positions. The liquidity charge, as calculated using equation 1 by the liquidity charge computing device  210 , drops significantly when the concentrated positions are rolled to IG  20  and IG  21  CDS positions. Previously, using other methods, the liquidity charge is unaffected by the roll. 
         [0049]    The present invention has been described in terms of preferred and exemplary embodiments thereof. Numerous other embodiments, modifications and variations within the scope and spirit of the invention will occur to persons of ordinary skill in the art from a review of this disclosure. For example, aspects of the invention may be used to process and communicate data other than market data.