Abstract:
A system and method for creating a volatility arbitrage bench mark index is disclosed. The method includes obtaining closing prices of an underlying instrument, such as a derivative investment instrument, and calculating a value representing a volatility arbitrage benchmark. The value may be displayed at a trading facility and volatility arbitrage benchmark quotes may be transmitted by the trading facility to a market participant.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of U.S. Provisional Application No. 60/858,619, filed Nov. 13, 2006, the entirety of which is incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates generally to financial trading systems and more particularly to the generation, identification, processing, trading, quotation, and valuation of volatility arbitrage benchmark indices and related derivative investment instruments. 
     BACKGROUND 
     An index is a statistical composite that is used to indicate the performance of a market or a market sector over various time periods. Examples of indices that are used to gauge the performance of stocks and other securities in the United States include the Dow Jones Industrial Average, the National Association of Securities Dealers Automated Quotations (NASDAQ) Composite Index, the New York Stock Exchange Composite Index, etc. In general, the Dow Jones Industrial Average contains thirty (30) stocks that trade on the New York Stock Exchange as well as NASDAQ, and is a general indicator of how shares of the largest United States companies are trading. The NASDAQ Composite Index is a composite index of more than three thousand (3,000) companies listed on the NASDAQ (also referred to as over-the-counter or OTC stocks). It is designed to indicate the stock performance of small-cap and technology stocks. Finally, the New York Stock Exchange Composite Index is a composite index of shares listed on the New York Stock Exchange. 
     In equal-dollar weighted indices, the weights of each component are reset to equal values at regular intervals, such as for example, every quarter. Between re-adjustments, the weights of the various index components will deviate from the equal-dollar weighting values as the values of the components fluctuate. Periodically, indices must be adjusted in order to reflect changes in the component companies comprising the index, or to maintain the original intent of the index in view of changing conditions in the market. For example, if a component stock&#39;s weight drops below an arbitrary threshold, or if a component company significantly alters its line of business or is taken over by another company so that it no longer represents the type of company which the index is intended to track, the index may no longer be influenced by, or reflect the aspects of the market for which it was originally designed. In such cases it may be necessary to replace a component stock with a suitable replacement stock. If a suitable replacement that preserves the basic character of the index cannot be found, the stock may simply be dropped without adding a replacement. Conversely, activity in the market for which an index is created may dictate that a new stock (which was not originally included in the index) having a strong impact in the market be added to the index to adequately reflect the market without eliminating other components. In each case, the divisor may be adjusted so that the index remains at the same level immediately after the new stock is added or the old stock is eliminated. 
     Derivatives are financial securities whose values are derived in part from a value or characteristic of some other underlying asset or variable (the underlying asset). The underlying asset may include securities such as stocks, market indicators and indices, interest rate, and corporate debt, such as bonds, to name but a few. Two common forms of derivatives are options contracts and futures contracts, discussed herein below. 
     An option is a contract giving the holder of the option the right, but not the obligation, to buy or sell an underlying asset at a specific price on or before a certain date. Generally, a party who purchases an option is said to have taken a long position with respect to the option. The party who sells the option is said to have taken a short position. There are generally two types of options: calls and puts. An investor who has taken a long position in a call option has bought the right to purchase the underlying asset at a specific price, known as the “strike price.” If the long investor chooses to exercise the call option, the long investor pays the strike price to the short investor, and the short investor is obligated to deliver the underlying asset. 
     Alternatively, an investor who has taken a long position in a put option receives the right, but not the obligation to sell the underlying asset at a specified price, again referred to as the strike price on or before a specified date. If the long investor chooses to exercise the put option, the short investor is obligated to purchase the underlying asset from the long investor at the agreed upon strike price. The long investor must then deliver the underlying asset to the short investor. Thus, the traditional settlement process for option contracts involves the transfer of funds from the purchaser of the underlying asset to the seller, and the transfer of the underlying asset from the seller of the underlying asset to the purchaser. Cash settlement, however, is more common. Cash settlement allows options contracts to be settled without actually transferring the underlying asset. 
     A call option is “in-the-money” when the price or value of the underlying asset rises above the strike price of the option. A put option is “in-the-money” when the price or value of the underlying asset falls below the strike price of the option. An at-the-money option wherein the price or value of the underlying asset is equal to the strike price of the option. A call option is out-of-the-money when the price or value of the underlying asset is below the strike price. A put option is out-of-the-money when the price or value of the underlying asset is above the strike price. If an option expires at-the-money or out-of-the-money, it has no value. The short investor retains the amount paid by the long investor (the option price) and pays nothing to the long investor. Cash settlement of an in-the-money option, be it a call or a put, however, requires the short investor to pay to the long investor the difference between the strike price and the current market value of the underlying asset. 
     Cash settlement allows options to be based on more abstract underlying “assets” such as market indicators, stock indices, interest rates, futures contracts and other derivatives. For example, an investor may take a long position in a market index call option. In this case, the long investor receives the right to “purchase” not the index itself, but rather a cash amount equal to the value of the index (typically multiplied by a multiplier) at a specified strike value. An index call option is in-the-money when the value of the index rises above the strike value. When the holder of an in-the-money index call option exercises the option, the short investor on the opposite side of the contract is obligated to pay the long investor the difference between the current value of the index and the strike price, usually multiplied by the multiplier. If the current value of the index is less than or equal to the strike value, the option has no value. An index put option works in the same way but in reverse, having value, or being in-the-money when the value of the index falls below the strike value. 
     Futures contracts are another common derivative security. In a futures contract a buyer purchases the right to receive delivery of an underlying commodity or asset on a specified date in the future. Conversely, a seller agrees to deliver the commodity or asset to an agreed location on the specified date. Futures contracts originally developed in the trade of agricultural commodities, but quickly spread to other commodities as well. Because futures contracts establish a price for the underlying commodity in advance of the date on which the commodity must be delivered, subsequent changes in the price of the underlying asset will inure to the benefit of one party and to the detriment of the other. If the price rises above the futures price, the seller is obligated to deliver the commodity at the lower agreed upon price. The buyer may then resell the received product at the higher market price to realize a profit. The seller in effect loses the difference between the futures contract price and the market price on the date the goods are delivered. Conversely if the price of the underlying commodity falls below the futures price, the seller can obtain the commodity at the lower market price for delivery to the buyer while retaining the higher futures price. In this case the seller realizes a profit in the amount of the difference between the current market price on the delivery date and the futures contract price. The buyer sees an equivalent loss. 
     Like options contracts, futures contracts may be settled in cash. Rather than actually delivering the underlying asset, cash settlement merely requires payment of the difference between the market price of the underlying commodity or asset on the delivery date and the futures contract price. The difference between the market price and the futures price is to be paid by the short investor to the long investor, or by the long investor to the short investor, depending on which direction the market price has moved. If the prevailing market price is higher than the contract price, the short investor must pay the difference to the long investor. If the market price has fallen, the long investor must pay the difference to the short investor. 
     Again, like options, cash settlement allows futures contracts to be written against more abstract underlying “assets” or “commodities,” such as market indicators, stock indices, interest rates, futures contracts and other derivatives. For example, an investor may take a long position in a market index futures contract. In this case, the long investor “buys” the index at a specified futures price (i.e. a future value of the index on the “delivery” date). The index based futures contract is cash settled. One party to the contract pays the difference between the futures price and the actual value of the index (often multiplied by a specified multiplier) to the other investor depending on which direction the market has moved. If the value of the index has moved above the futures price, or futures value, the short investor pays the difference the long investor. If the value of the index has moved below the futures price, or futures value the long investor pays the difference to the short investor. 
     Cash settlement provides great flexibility regarding the types of underlying assets that derivative investment instruments may be built around. Essentially any variable whose value is subject to change over time, may serve as the underlying asset for a derivative investment instrument. While standard derivatives may be based on many different underlying assets, no index or derivative investment instruments based thereon exist that capture changes in the performance of total return volatility index. 
     BRIEF SUMMARY 
     In order to address the need for improvements on derivative investment instruments, total return volatility index derivative investment instruments and methods for creating a total return volatility index are disclosed herein based on changes in the performance of periodically selling a realized volatility derivatives contract. 
     According to a first aspect of the disclosure, a computer-readable medium containing processor executable program instructions for creating a volatility arbitrage benchmark index is disclosed including obtaining the daily closing prices of a derivative investment instrument since an inception date, calculating a value reflecting a volatility arbitrage benchmark for the derivative investment instrument, and wherein a value reflecting a volatility arbitrage benchmark is calculated according to the formula: 
               Index   t     =       Index     t   -   1       ⨯     [     1   +     (           p   t       -       p     t   -   1               p     t   -   1           )       ]             
where Index t  is a first time period closing index value; Index t-1  is a second time period closing index value; p t  is a first time period closing price for a front-month derivative investment instrument; and p t-1  is a second time period closing price for the front-month derivative investment instrument.
 
     In a second aspect, the invention relates to a computer-readable medium containing processor executable program instructions for creating a volatility arbitrage benchmark index is disclosed including obtaining the daily closing prices of a derivative investment instrument since an inception date, calculating a value reflecting a volatility arbitrage benchmark for the derivative investment instrument, and wherein a value reflecting a volatility arbitrage benchmark is calculated according to the formula: 
               Index   t     =       Index   i     ⨯     [     1   +     (           p   t       -       p   i             p   i         )       ]             
where Index i  is an initial time period closing index value; Index t  is a post-initial time period closing index value; p i  is an initial time period closing price for the front-month derivative investment instrument; and p t  is a post-initial time period closing price for a front-month derivative investment instrument.
 
     In a third aspect, the invention relates to a method for calculating a volatility arbitrage benchmark index value, the method including calculating a value reflecting a volatility arbitrage benchmark of an underlying asset on a processor, the value for the total volatility having a dynamic value which reflects a performance of the underlying asset over a predefined time period, displaying at least one value reflecting the total volatility of the underlying asset on a trading facility display device coupled to a trading platform, and transmitting at least one volatility arbitrage benchmark derivative quote of a liquidity provider from the trading facility to at least one market participant. 
     In a fourth aspect, the invention relates to a system for creating and trading derivatives based on a volatility arbitrage benchmark index module coupled with a communications network for receiving current values of an underlying asset of a derivative investment instrument and calculating a volatility arbitrage benchmark of the underlying asset, a dissemination module coupled with the volatility arbitrage benchmark index module and the communications network for receiving the volatility arbitrage benchmark of the underlying asset from the volatility arbitrage benchmark index module, and disseminating the value of the volatility arbitrage benchmark of the underlying asset to at least one market participant, and a trading module coupled with the dissemination module and the communications network for receiving at least one buy or sell order for the derivative investment instrument, and executing the at least one buy or sell order. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For the purpose of facilitating an understanding of the subject matter sought to be protected, there is illustrated in the accompanying drawings an embodiment thereof, from an inspection of which, when considered in connection with the following description, the subject matter sought to be protected, its construction and operation, and many of its advantages should be readily understood and appreciated. 
         FIG. 1  is a graph illustrating one embodiment of an example volatility arbitrage benchmark index that calculates a value of performance of periodically selling a volatility derivative investment instrument. 
         FIG. 2  is a block diagram of a system for creating and trading derivative investment instruments based on a volatility arbitrage benchmark index. 
         FIG. 3  is a block diagram of a general computing device and network connectivity. 
     
    
    
     DETAILED DESCRIPTION 
     Referring now to  FIG. 1 , a volatility arbitrage benchmark index  100  is illustrated that is designed to reflect and replicate the performance of periodically selling a realized volatility derivative investment instrument, such as a three-month Standard &amp; Poor&#39;s® (“S&amp;P”) 500 index (ticker symbol “SPX”) realized volatility swap/futures contract. The volatility arbitrage benchmark index would be periodically disseminated, for example, every 15 seconds and would serve as the underlying for a derivative investment instrument (such as an option or futures contract). The use of a derivative investment instrument that tracks a volatility arbitrage benchmark index disseminated by an exchange, such as the Chicago Board Options Exchange®, 400 South LaSalle Street, Chicago, Ill. 60605 (“CBOE”), is beneficial to the creation/redemption process. 
     The creation of a volatility arbitrage benchmark index would facilitate development of volatility-based exchange-traded products, such as an exchange-traded fund (ETF). An ETF is typically an index fund that is not actively managed that may hold securities, currencies, commodities and other financial assets. Shares of an ETF are traded on a securities exchange. The traded price of these shares tracks their net asset value through the use of a creation/redemption process, which permits arbitrage. This creation/redemption process and the need for a more active management process are two of the impediments for a volatility-based ETF. 
     In order to overcome the aforementioned limitations, the construction of the volatility arbitrage benchmark index utilizes the daily closing prices of a standardized derivative investment instrument, such as, by way of example below, the CBOE S&amp;P 500 Three-month Realized Variance futures contract. The total return volatility index includes an index base date and the base value (for example, 100). Other standardized derivative investment instruments, such as realized volatility futures and options are contemplated for use in connection with the volatility arbitrage benchmark. 
     Example Index Calculation 1 
     The daily index value for the volatility arbitrage benchmark index in this example is calculated according to the following formula: 
               Index   t     =       Index     t   -   1       ⨯     [     1   +     (           p   t       -       p     t   -   1               p     t   -   1           )       ]             
where,
     Index t-1 =Today&#39;s closing index value.   Index t-1 =Yesterday&#39;s closing index value.   p t =Today&#39;s closing price for the front-month CBOE S&amp;P 500 Three-month Realized Variance future.   p t-1 =Yesterday&#39;s closing price for the front-month CBOE S&amp;P 500 Three-month Realized Variance future.   

     Example Index Calculation 2 
     The daily index value for the volatility arbitrage benchmark index in this example is calculated according to the following formula: 
               Index   t     =       Index   i     ⨯     [     1   +     (           p   t       -       p   i             p   i         )       ]             
where,
     Index i =Initial closing index value.   Index t =Today&#39;s closing index value.   p i =Initial closing price for the front-month CBOE S&amp;P 500 Three-month Realized Variance future.   p t =Today&#39;s closing price for the front-month CBOE S&amp;P 500 Three-month Realized Variance future.   

     In a further alternative embodiment in accordance with the principles of the present invention, the volatility arbitrage benchmark index could be employed as a gauge against which a particular portfolio manager&#39;s performance can be measured. In another embodiment, an exchange-traded fund could be designed to reflect a portfolio that invests in Dow Jones Industrials Average index stocks. In still yet another embodiment, p i  and p t  may be representative of any derivative investment instrument, including but not limited to futures and options. Additionally, it is contemplated that the volatility arbitrage benchmark index is capable for utilization in both settlement and roll processes for standardized derivative investment instruments. 
       FIG. 2  is a block diagram of a system  200  for creating and trading derivative investment instruments based on a volatility arbitrage benchmark index. Generally, the system comprises a volatility arbitrage benchmark index module  202 , a dissemination module  204  coupled with the volatility arbitrage benchmark index module  202 , and a trading module  206  coupled with the dissemination module  204 . Typically, each module  202 ,  204 ,  206  is also coupled to a communication network  208  coupled to various trading facilities  222  and liquidity providers  224 . 
     The volatility arbitrage benchmark index module  202  comprises a communications interface  210 , a processor  212  coupled with the communications interface  210 , and a memory  214  coupled with the processor  212 . Logic stored in the memory  214  is executed by the processor  212  such that that the volatility arbitrage benchmark index module  202  may receive a first set of trade information for each underlying asset representative of a desired group of underlying assets through the communications interface  210 ; aggregate that first set of trade information over a first time period, calculate a volatility arbitrage benchmark index for the desired group of underlying assets with the aggregated first set of trade information, and a standardized measure of the index; and pass the calculated values to the dissemination module  204 . 
     The dissemination module  204  comprises a communications interface  216 , a processor  218  coupled with the communications interface  216 , and a memory  220  coupled with the processor  218 . Logic stored in the memory  220  is executed by the processor  218  such that the dissemination module  204  may receive the calculated values from the volatility arbitrage benchmark index module  202  through the communications interface  216 , and disseminate the calculated values over the communications network  208  to various market participants  222 . 
     The trading module  206  comprises a communications interface  226 , a processor  228  coupled with the communications interface  226 , and a memory  230  coupled with the processor  228 . Logic stored in the memory  230  is executed by the processor  228  such that the trading module  206  may receive buy or sell orders over the communications network  208 , as described above, and pass the results of the buy or sell order to the dissemination module  204  to be disseminated over the communications network  208  to the market participants  222 . 
     Referring to  FIG. 3 , an illustrative embodiment of a general computer system that may be used for one or more of the components shown in  FIG. 2 , or in any other trading system configured to carry out the methods discussed above, is shown and is designated  300 . The computer system  300  can include a set of instructions that can be executed to cause the computer system  300  to perform any one or more of the methods or computer based functions disclosed herein. The computer system  300  may operate as a standalone device or may be connected, e.g., using a network, to other computer systems or peripheral devices. 
     In a networked deployment, the computer system may operate in the capacity of a server or as a client user computer in a server-client user network environment, or as a peer computer system in a peer-to-peer (or distributed) network environment. The computer system  300  can also be implemented as or incorporated into various devices, such as a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a mobile device, a palmtop computer, a laptop computer, a desktop computer, a network router, switch or bridge, or any other machine capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that machine. In a particular embodiment, the computer system  300  can be implemented using electronic devices that provide voice, video or data communication. Further, while a single computer system  300  is illustrated, the term “system” shall also be taken to include any collection of systems or sub-systems that individually or jointly execute a set, or multiple sets, of instructions to perform one or more computer functions. 
     As illustrated in  FIG. 3 , the computer system  300  may include a processor  302 , e.g., a central processing unit (CPU), a graphics processing unit (GPU), or both. Moreover, the computer system  300  can include a main memory  304  and a static memory  306  that can communicate with each other via a bus  308 . As shown, the computer system  300  may further include a video display unit  310 , such as a liquid crystal display (LCD), an organic light emitting diode (OLED), a flat panel display, a solid state display, or a cathode ray tube (CRT). Additionally, the computer system  300  may include an input device  312 , such as a keyboard, and a cursor control device  314 , such as a mouse. The computer system  300  can also include a disk drive unit  316 , a signal generation device  318 , such as a speaker or remote control, and a network interface device  320 . 
     In a particular embodiment, as depicted in  FIG. 3 , the disk drive unit  316  may include a computer-readable medium  322  in which one or more sets of instructions  324 , e.g. software, can be embedded. Further, the instructions  324  may embody one or more of the methods or logic as described herein. In a particular embodiment, the instructions  324  may reside completely, or at least partially, within the main memory  304 , the static memory  306 , and/or within the processor  302  during execution by the computer system  300 . The main memory  304  and the processor  302  also may include computer-readable media. 
     In an alternative embodiment, dedicated hardware implementations, such as application specific integrated circuits, programmable logic arrays and other hardware devices, can be constructed to implement one or more of the methods described herein. Applications that may include the apparatus and systems of various embodiments can broadly include a variety of electronic and computer systems. One or more embodiments described herein may implement functions using two or more specific interconnected hardware modules or devices with related control and data signals that can be communicated between and through the modules, or as portions of an application-specific integrated circuit. Accordingly, the present system encompasses software, firmware, and hardware implementations. 
     In accordance with various embodiments of the present disclosure, the methods described herein may be implemented by software programs executable by a computer system. Further, in an exemplary, non-limited embodiment, implementations can include distributed processing, component/object distributed processing, and parallel processing. Alternatively, virtual computer system processing can be constructed to implement one or more of the methods or functionality as described herein. 
     The present disclosure contemplates a computer-readable medium that includes instructions  324  or receives and executes instructions  324  responsive to a propagated signal, so that a device connected to a network  326  can communicate voice, video or data over the network  326 . Further, the instructions  324  may be transmitted or received over the network  326  via the network interface device  320 . 
     While the computer-readable medium is shown to be a single medium, the term “computer-readable medium” includes a single medium or multiple media, such as a centralized or distributed database, and/or associated caches and servers that store one or more sets of instructions. The term “computer-readable medium” shall also include any medium that is capable of storing, encoding or carrying a set of instructions for execution by a processor or that cause a computer system to perform any one or more of the methods or operations disclosed herein. 
     In a particular non-limiting, exemplary embodiment, the computer-readable medium can include a solid-state memory such as a memory card or other package that houses one or more non-volatile read-only memories. Further, the computer-readable medium can be a random access memory or other volatile re-writable memory. Additionally, the computer-readable medium can include a magneto-optical or optical medium, such as a disk or tapes or other storage device to capture carrier wave signals such as a signal communicated over a transmission medium. A digital file attachment to an e-mail or other self-contained information archive or set of archives may be considered a distribution medium that is equivalent to a tangible storage medium. Accordingly, the disclosure is considered to include any one or more of a computer-readable medium or a distribution medium and other equivalents and successor media, in which data or instructions may be stored. 
     Although the present specification describes components and functions that may be implemented in particular embodiments with reference to particular standards and protocols commonly used on financial exchanges, the invention is not limited to such standards and protocols. For example, standards for Internet and other packet switched network transmission (e.g., TCP/IP, UDP/IP, HTML, HTTP) represent examples of the state of the art. Such standards are periodically superseded by faster or more efficient equivalents having essentially the same functions. Accordingly, replacement standards and protocols having the same or similar functions as those disclosed herein are considered equivalents thereof. 
     One or more embodiments of the disclosure may be referred to herein, individually and/or collectively, by the term “invention” merely for convenience and without intending to voluntarily limit the scope of this application to any particular invention or inventive concept. Moreover, although specific embodiments have been illustrated and described herein, it should be appreciated that any subsequent arrangement designed to achieve the same or similar purpose may be substituted for the specific embodiments shown. This disclosure is intended to cover any and all subsequent adaptations or variations of various embodiments. Combinations of the above embodiments, and other embodiments not specifically described herein, will be apparent to those of skill in the art upon reviewing the description. 
     As will be appreciated by those of ordinary skill in the art, mechanisms for creating a volatility arbitrage benchmark index, derivative investment instruments based thereon and other features described above may all be modified for application to other derivative investment instruments, such as futures, within the purview and scope of the present invention. An advantage of the disclosed methods and derivative investment instruments is that more traders at the exchange may have more opportunity to trade new products and obtain new and valuable market information, thus increasing visibility of orders and the desirability of maintaining a presence at the exchange. 
     The matter set forth in the foregoing description, accompanying drawings and claims is offered by way of illustration only and not as a limitation. While particular embodiments have been shown and described, it will be apparent to those skilled in the art that changes and modifications may be made without departing from the broader aspects of applicants&#39; contribution. It is therefore intended that the foregoing detailed description be regarded as illustrative rather than limiting, and that it be understood that it is the following claims, including all equivalents, that are intended to define the scope of this invention.