Patent Application
20160048921
Aspects of the invention relate to determining risks and liquidation costs. More particularly, aspects of the invention relate to determining liquidations costs associated with portfolios of financial instruments.
Interest rate swaps are agreements between two parties to exchange one stream of future interest payments for another based on a specified principal amount. One stream typical includes fixed payments and another stream typically includes floating payments that are often linked to an interest rate, such as LIBOR. A swaption is an option to enter into an interest rate swap. A buyer pays an option premium to obtain the right but not the obligation to enter into a specified swap agreement with the issuer on a specified future date.
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. Trades may include trades for interest rate swaps and swaptions. 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.
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 be 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'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.
Some existing liquidation models use margin requirements as proxies to determine required add-on amounts to account for liquidation costs. However, margin requirements can be pro-cyclical and often do not reflect the cost of hedging large hedged books. Margin requirements are also not good proxies for determining the cost of liquidating a large option portfolio in a market crises condition.
Accordingly, there is a need in the art for systems and methods for determining liquidation costs associated with portfolios of financial instruments.
Aspects of the invention overcomes at least some of the problems and limitations of the prior art by providing robust systems and methods for determining liquidation costs. Survey data for liquidation costs at different risk profiles are received. The survey data may include stressed market liquidation costs for risk profiles that are available during stressed market conditions and normal market liquidation costs for risk profiles that are not available during a stressed market condition. Cost functions are created from the survey data for the different risk profiles. Next, a hedge cost for hedging a portion of the portfolio at a first time to create a partially hedged portfolio is determined. A warehousing cost for warehousing an unhedged portion of the portfolio of financial instruments until a second time after the first time is also determined. A re-hedge cost is then determined for hedging the partially hedged portfolio at the second time. The liquidation cost is finally determined by combining the hedge cost, the warehousing cost and the re-hedge cost. Weighting for Greek ladder may be created by mapping liquidation costs to Greek ladders. Lookup tables may be created from liquidity cost. The lookup tables may be used to look up for liquidity cost using aggregated Greek generated by weighted sum of Greek ladder and provide a simplified mechanism for determining liquidation costs.
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.
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.
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.
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:
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
The trading network environment shown in
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.
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.
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.
The operations of computer devices and systems shown in
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
The risk profiles may be for various sizes (notional amount or risk amount may be used to measure the size of each risk profile). The survey data may include stressed market liquidation costs for risk profiles that are available during stressed market conditions and normal market liquidation costs for risk profiles that are not available during a stressed market condition. The survey data may be received from FCMs and may represent traders' perceptions of risks. The survey data may include liquidation cost for several representative currencies with significant open interest for liquid tenor points for different risk profiles and for different levels of Risk. Exemplary delta hedging financial instruments include outrights, spreads, butterflies for over the counter transactions and listed futures contacts, such as Eurdollars and treasury contracts. Exemplary delta hedging financial instruments may also include basis swaps (e.g. 1 m vs 3 m, 3 m vs 6 m), OIS swaps and swap spreads (invoice swaps). Exemplary gamma hedging financial instruments include listed options and short-dated straddles. Exemplary vega/skew financial instruments include longer dated straddles, longer dated delta-hedged payers/receivers and risk reversals/butterflies.
The survey data received in step 202 may include discrete data points. In step 204, cost functions may be created from the survey data for the different risk profiles. An exemplary continuous parsimonious cost function that may be used with embodiments of the invention is:
Cost function=a*(Risk̂) Equation 1
Wherein parameters “a” and “b” may be determined by fitting to the mean bid-ask spreads across the survey data quotes per reference instrument.
In an alternative embodiment, Notional values may be used in place of Risk in equation 1.
After costs functions are created, in step 206 a hedge cost may be determined. The hedge cost is for hedging a portion of the portfolio at a first time to create a partially hedged portfolio. Step 206 may include identifying optimal hedges using risk profiles that are available during a market crises by minimizing tail risks. The hedges may include delta and gamma hedges. The minimization process may utilize a conditional value at risk (CVaR) measure. In one embodiment of the invention, the function used to minimize tail risks is:
minimi(CVaR+λ*Hedging Cost Function for Reference Instruments) Equation 2
The parameter “λ” may be used to minimize over fitting. Weighting the hedging cost for the reference instruments, as shown in Equation 2, minimizes over-fitting due to overlapping hedging instruments.
Embodiments of the invention may impose constraints when minimizing tailing risks to ensure that the process will mirror the hedging process likely to be adopted in a default (also practiced in the drills). Hedging cost may include the cost of overall risk transfer into the cost of incremental hedging and may include the impact of overall risk transfer on the cost function of subsequent hedges. For example, as shown in
The process of selecting hedges may account for different risk types (outrights, spreads, butterfly, basis, OIS, gamma, vega, etc.) and the process should not add additional risk to the defaulted portfolio. The process may also require that hedges do not add risk in the same direction as that of the defaulted portfolio.
The cost of hedging may be determined based on the quantities of reference instrument identified and using the equivalent cost functions that take into account of the impact of overall risk transfer. The received survey data may include higher order risk profiles, such as spreads and butterflies, in addition to the outrights. Two embodiments of the invention account for lower liquidity cost instruments. In a first embodiment, all of the instruments included in the survey data, such as outrights, spreads and butterflies are included in an optimizer process that minimizes tail risks. This embodiment may result in some incoherent hedges where outrights only portfolios are hedged with combinations of butterfly and spreads or vice-versa.
In the second embodiment, the optimization process may be configured to solve for the quantities for the pillars tenors and then decompose the pillars tenor quantities into outrights, spreads and butterflies as below:
Returning to
Warehousing costs may also be represented by the following equation:
Cost of WareHousing=Marginday−Marginday Equation 3
The volatility of volatility (e.g. Nu parameter of SABR model) may be used as an indicator in identifying the sufficient level of margin period of risk MPOR. Stabilization of volatility of volatility just after major crises can be a proxy for determining when a supply hedges will return to the market.
In step 210, a re-hedge cost is determined for hedging the partially hedged portfolio at a later time. Step 210 may be performed around the same time as step 206 may assume that the re-hedging will occur after stabilization of the market. Re-hedging may use some or all of the hedging and optimization processes described above.
In step 212 the liquidation cost may be determined by combining the hedge cost, the warehousing cost and the re-hedge cost. In some embodiments the hedge cost, the warehousing cost and the re-hedge cost may be summed. Other embodiments may include weighted sums or other combinations.
In step 214, the liquation costs determined in step 212 may be mapped to Greek coefficients to create tables that are transparent and easy to use. Weights for Greek coefficients may be determined by regressing liquidation costs determined in step 212 to the Greek coefficients.
The weights used in generating aggregated risk number 904 from risk ladder 902 are produced by regressing the risk ladder against the liquidation cost. The weights may be different for positive and negative Greeks due to asymmetric liquidity costs for long and short positions; the weights may be different for different risk profiles of the same Greek type due to the liquidity cost differential (e.g. 1M DV01 of 10yr in general is cheaper to liquidate than 1M DV01 of 30yrs, hence, the weight for 30Y DV01 should be larger than 10Y DV01), which may be considered a key essence of the liquidity cost; in addition, to ensure the aggregated risk number 804 captures not only the liquidity risk for directional portfolios but also captures the liquidity risk for hedged yet very large portfolios, a measurement of gross risk is introduced to the Greek ladder 902.
The cost of liquidating large hedged books may be better regressed on a gross measure of Greek than a net measure (one sided Greek, gross Greek, etc.). One sided Greek and gross Greek examples are shown in
Some embodiments of the invention may utilize minimum thresholds. For small or mid-size portfolios, initial margin requirements may contain enough liquidation premium and liquidation add on costs are not necessary. Liquidation add-on may only be applied to large portfolios that bring in significant liquidation risk. A minimum threshold may be used to differentiate large portfolios vs. small or mid-size portfolios for each of the Greeks. Base initial margin requirements are built on 5-days of un-hedged exposure and portfolios of small to med-size can be hedged and liquidated well within that timeframe. For Delta/Gamma, some portion of the risk may be hedged with access to listed market. For swaptions portfolios decaying the portfolio for 5-days in initial margin calculation captures significant amount of time-decay in the process, more than that required for small portfolios. Portfolios of small to med-size are unlikely to significantly move the market against us upon liquidation; also a DM process includes best practices towards minimizing the cost of liquidation (e.g. splitting the book). From a risk management standpoint, a minimum threshold provides the incentive to spread a large book across different clearing firms.
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.
