Patent Application
20110213692
The present disclosure relates generally to computer-implemented systems and methods for converting of future values and more specifically to the determination of future conversion curves.
Conversions between differing metrics are often facilitated through the use of a conversion factor which identifies how many of a second metric is equal to a first metric. An amount measured in the first metric can then be converted so that it can be measured in the second metric by performing a calculation on the amount in the first metric by the conversion factor.
In accordance with the teachings provided herein, systems and methods for converting future conversion curves are provided. For example, a system and method can be configured to determine a future conversion curve between a first metric and a second metric. One or more paths between the first metric and the second metric may be calculated using two or more conversion curves. A shortest path between the first metric and the second metric may be determined based on the path having the least weight associated with that path. A future conversion curve may be generated by collapsing the two or more conversion curves of the shortest path.
As another example, a system and method can include receiving a selection of a first metric and a second metric. A plurality of conversion curves may be received, where each conversion curve has a corresponding weight, and where each conversion curve identifies a plurality of future conversions between a source metric and a target metric. One or more paths between the first metric and the second metric may be calculated using two or more conversion curves, where each path begins with the first metric and ends with the second metric, and where each path is associated with a path weight based upon the sum of the weights used to calculate the path. A shortest path between the first metric and the second metric may be determined, where the shortest path is the path having the least weight, and a future conversion curve may be generated by collapsing the two or more conversion curves of the shortest path.
As additional examples, each conversion curve in the plurality of conversion curves may be associated with a plurality of future times, where the two or more conversion curves of the shortest path are normalized with respect to one another. The normalizing may include linear interpolation. One of the one or more paths between the first metric and the second metric may include a backward link from a target metric to a source metric, and the backward link may have the same weight as a corresponding forward link. Each conversion curve in the plurality of conversion curves may be associated with a plurality of future times. Collapsing two or more conversion curves may include calculating a product for each conversion curve at a predetermined future time and generating a future conversion curve based upon the calculated product.
As further examples, each conversion curve in the plurality of conversion curves may be associated with a plurality of future times, where an inverse future conversion is used when a backward link is present in the shortest path. Collapsing two or more conversion curves may include calculating a product for each inverse future conversion curve at a predetermined time and generating an inverse future conversion curve based upon the calculated product. Each weight may be equal, where the shortest path between the first metric and the second metric includes the fewest number of conversion curves. One or more paths between the first metric and the second metric may be calculated using a Dijkstra's algorithm or a Bellman-Ford algorithm. The path having the least weight may be chosen from a path having the highest sum of weights or a path having the lowest sum of weights. Calculating one or more paths may include not calculating all possible paths between the first metric and the second metric.
Particular embodiments of the subject matter described in this specification can be implemented to realize one or more of the following advantages including determining a forward conversion curve between a first metric and a second metric where no direct conversion between the first metric and the second metric is known, a high computational efficiency through leveraging shortest path algorithms, the ability to affect a choice of paths away from undesirable conversions through assignments of weights, generating additional known conversion curves for future use, as well as others.
The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the invention will become apparent from the description, the drawings, and the claims.
The future conversion curve calculator 104 can be an integrated web-based analysis tool that provides users 102 flexibility and functionality for performing a determination of a future conversion curve between a first metric and a second metric. The future conversion calculator 104 can also be a wholly automated system. The future conversion calculator 104 can interact with a human user or with one or more computer programs. One or more data stores 110 can store the data to be analyzed by the future conversion curve calculator 104 as well as any intermediate or final data generated by the future conversion curve calculator 104. For example, the data store(s) 110 can store known conversion curves 112 for use in determining the future conversion curve as well as weights 114 for use in selecting conversion curves utilized in the determination. Examples of data store(s) 110 can include relational database management systems (RDBMS), a memory, a flat-file, or a multi-dimensional database (MDDB), such as an Online Analytical Processing (OLAP) database, etc.
A conversion from a first metric to a second metric becomes more complicated when a direct conversion curve from the first metric to the second metric is unknown (e.g., if a user wishes to make a conversion from a first metric to a second metric, and the only known conversion curves are from the first metric to a third metric; from the third metric to a fourth metric; or from the fourth metric to the second metric), then a series of conversions (e.g., using multiple conversion curves), can be executed to perform the conversion from the first metric to the second metric.
Each conversion curve can also be associated with a weight. A weight can correspond to the desirability of using the associated conversion curve to perform a conversion. In some implementations, a small value may be associated with particular conversion curves (e.g., to connote a low cost of using that conversion curve). Alternatively, a high value may be associated with particular conversion curves (e.g., to connote the higher desirability of using that conversion curve). Thus, depending on the weighting protocol, a most desirable path of conversion curves can have a highest sum of weights of all calculated paths or a lowest sum of weights of all calculated paths.
The same or different weights can be associated with a conversion curve for forward or backward traversals of that conversion curve. For example, a weight of 2 may be associated with the forward traversal of a conversion curve from metric A to metric B, while a weight of 4 may be associated with the backward traversal of that conversion curve from metric B to metric A. Each conversion curve can have a differing weight with respect to other conversion curves, or each conversion curve can be associated with a common weight, thereby yielding a “shortest-path” in the literal sense of the phrase.
The future conversion curve calculator 302 can receive a plurality of conversion curves between a source metric and a target metric and can generate a directed graph at 306. A directed graph can identify a network of possible conversions enabled by the received plurality of conversion curves 304. At 308, the future conversion curve calculator 302 can receive an identification of a first metric and a second metric 310. The future conversion curve calculator 302 can perform a conversion between the received first metric and the received second metric. The future conversion curve calculator can calculate one or more paths between the received first metric and the received second metric using the directed graph generated at 306. A path can begin with a conversion curve that includes the received first metric and ends with a conversion curve that includes the received second metric. A path can further include one or more intermediate conversion curves between the received first metric and the received second metric.
The path calculation at 308 can perform an exhaustive search for all possible paths through the directed graph, or the path calculation at 308 may identify a subset of all possible paths. For example, the path calculation 308 can avoid identifying paths that form cycles (e.g., by traversing nodes multiple times). The calculated paths can be analyzed (e.g., to calculate a path weight). In some implementations, a path weight can be determined by calculating a sum of the weights of all conversion curves used in that path. A path having the least weight (e.g., the shortest path that can be used to generate a future conversion curve) can be determined to be the most desirable path. Example algorithms for computing a shortest path include a Dijkstra's algorithm, which can be used for example, if all weights are non-negative, and the Bellman-Ford algorithm, which can be used for example, when negative weights are expected.
At 312, the determined shortest path can be collapsed to generate a single future conversion curve 314 between the received first metric and the received second metric. Collapsing the plurality of conversion curves on a determined shortest path can be performed by calculating a product for all of the conversion factors associated with the conversion curves at a particular time. For example, if the shortest path includes Conversion Curve A, Conversion Curve B, and Conversion Curve C, with conversion factors at 0.5 years, 1.0 years, and 2.0 years, then future conversion curves can be generated according to:
FutureConversionCurve(0.5)=Conversion Curve A(0.5)*Conversion Curve B(0.5)*Conversion Curve C(0.5);
FutureConversionCurve(1.0)=Conversion Curve A(1.0)*Conversion Curve B(1.0)*Conversion Curve C(1.0); and
FutureConversionCurve(2.0)=Conversion Curve A(2.0)*Conversion Curve B(2.0)*Conversion Curve C(2.0).
The future conversion curve calculator 302 can output a future conversion curve 314. Additionally, the future conversion curve calculator 302 can retain future conversion curve 314 (e.g., for use as an additional curve in the plurality of conversion curves 304 used in conversion calculations).
In some implementations, the plurality of conversion curves 304 can be normalized with one another prior to collapsing the shortest path at 312. For example, if the desired output future conversion curve includes conversion factors at times: 0.5 years, 1.0 years, and 2.0 years, and Conversion Curve B on a shortest path does not include a conversion factor at 1.0 years, then Conversion Curve B can be normalized. In this example, Conversion Curve B can be normalized (e.g., to the other conversion curves on the shortest path and the future conversion curve to be output), by using linear interpolation to estimate the conversion factor for Conversion Curve B at 1.0 years. The linear interpolation can be based upon conversion factors for times in close proximity to Conversion Curve B (e.g., conversion factors for times 0.8 years and 1.3 years included in the known Conversion Curve B). Other methods of normalization may also be used including spline interpolation.
The directed graph 400 representing the plurality of conversion curves shows multiple possible paths for converting from a first metric to a second metric. For example, to convert from Metric A 402 to Metric D 410, a path can run from Metric A 402 to Metric B 404 to Metric D 410, from Metric A 402 to Metric C 412 to metric D 410, or from Metric A 402 to Metric B 404 to Metric C 412 to Metric D 410. The weights for each of these paths can be calculated as follows:
Metric A->Metric B->Metric D=W1+W2;
Metric A->Metric C->Metric D=W3+W5; and
Metric A->Metric B->Metric C->Metric D=W1+W4+W5.
A future conversion curve calculator can be useful in a variety of applications. For example, a future conversion curve calculator can be used for calculating forward currency exchange curves. An organization oftentimes deals with more than one currency. A financial system for the organization should be able to handle multiple currency conversions quickly and efficiently. Currency risk management can be an important element of a financial risk management system (e.g., doing business in a fluctuating foreign currency exchange market).
A forward currency exchange curve includes a sequence of forward currency exchange rates and an associated delivery time for each rate. The forward currency exchange curve can be created by joining each delivery date and rate as an ordered pair and placing the pairs on a grid, such as the grid shown in
As an example, a future conversion curve calculator can be provided with a first forward currency exchange curve from currency U.S. Dollar (USD) to currency Euro (EUR), and a second forward exchange curve from currency British Pound (GBP) to currency Euro (EUR). Using these two rate curves, it is possible to construct a new rate curve from currency GBP to currency USD. As noted above, the future conversion curve calculator can configure triangulation of rate curves between currencies using any number of currency curves (e.g., “n” currency curves). Thus, the future conversion curve calculator can include a minimal set of curves with available data, because the future currency curve calculator can deduce other curves as needed (e.g., other curves that don't have available data). The future conversion curve calculator can determine whether defined intermediate curves can be used to construct a new curve between two particular currencies. Additionally, the future conversion curve calculator can choose a desirable set of intermediate curves (e.g., when more than one set of intermediate curves exist).
In some implementations, to determine a set of intermediate curves for triangulation, the future conversion curve calculator can treat available conversion curves as a single, weighted, directed, disconnected graph. Each currency can be mapped to a vertex in the graph. An edge can connect any two vertices that define a rate curve corresponding to two currencies.
Weights can be assigned to the edges of a directed graph such that the weights can encourage or discourage the choice of a particular path (e.g., through certain vertices). For example, strong inflationary pressures in a national economy can create a desire to avoid using the currency association with that national economy in a triangulation. This can be accomplished by assigning large weights to the edges of the directed graph. Impinging on the vertex corresponding to the unstable currency can represent a high cost of using that conversion. Other factors in assigning a weight to a conversion curve can include unfavorable contract terms for performing the conversions, or lack of liquidity of a currency.
In some implementations, a weighting scheme can assign equal weights to each edge. Because the cost of a path is the sum of the weights of all edges along the path, if all edges are of equal weight, then a shortest path algorithm would find a shortest path through the graph that utilizes the fewest number of intermediate vertices.
Following the determination of the shortest path of curves, numerical calculations for the rates of a new forward curve can be generated. The results of the shortest path determination can identify which known curves to use, and in which order the known curves should be used. Additionally, conversion curve inversions, as described herein above, can be necessitated by reverse conversion directions specified in the shortest path.
In some implementations, when the delivery dates and the number of deliveries within each intermediate curve are identical, then the conversion rates for the future conversion curve can be calculated for each corresponding delivery date. However, if the number of delivery dates or a specific delivery dates differs from one curve to another, then the curves can be normalized (e.g., using linear interpolation), to create a set of common delivery dates.
At 912, the system can make a determination as to whether the delivery dates of the known exchange curves on the determined optimum path are compatible. If the delivery dates are not compatible, then the system can estimate rates at common times throughout the curves along the determined optimum path (e.g., using linear interpolation), at 914. When the exchange rate curves along the determined optimum path have a plurality of compatible delivery dates, the system can collapse the exchange rate curves along the optimum path (e.g., by multiplying the exchange rates of all of the known exchange rate curves on the optimum path at each compatible date), at 916. The system can add the newly generated exchange rate curve to the database of known exchange rate curves at 918, and the system can return the exchange rate curve from the first currency to the second currency at 920.
Example scenarios, algorithms, and code segments are provided herein to further illustrate a future conversion curve calculator determining a future conversion curve between a first currency and a second currency where a direct conversion between the first currency and the second currency is unknown.
The following code may be utilized to define 15 risk factor variables representing exchange rates between three pairs of currencies at different future times:
For example:
The variables which convert between the same currencies can be sequenced into arrays as follows:
array usdeurc fx tocur=USD fromcur=EUR
array eurjpyc fx tocur=EUR fromcur=JPY
array usdjpyc fx tocur=USD fromcur=JPY
An example set of values for the first array, usdeurc, could define:
usdeur1m=1.43; usdeur3m=1.41; usdeur6m=1.41; usdeur1y=1.39; usdeur2y=1.39.
A typical application of these rates can include a cash flow analysis with desired reporting currency in U.S. Dollars where, during analysis, a bond position denominated in Euros is encountered. Using the relationships in the usdeurc array, the date of the coupon can be matched against an appropriate maturity on the forward exchange curve stored in the usdeurc array to determine the conversion rate. For example, when evaluating a Euro-valued coupon one year later, the value in euros can be multiplied by 1.39 to give equivalent U.S. Dollars. Similarly, a Euro-valued coupon redeemed in three months can be multiplied by 1.41 to obtain that amount in U.S. Dollars. If a maturity is required that is not explicitly given in the curve, linear interpolation can be used to find an exchange rate.
In a further cash flow analysis, a bond denominated in Japanese Yen can be processed. A curve defining conversions from JPY to USD is therefore needed. In this example, an array for containing such a curve can be named usdjpyc. If usdjpyc is not defined in the system, conversion from JPY to USD cannot be completed.
array usdeurc fx tocur=USD fromcur=EUR
array eurjpyc fx tocur=EUR fromcur=JPY
Once the components for generating a forward conversion curve from JPY to USD have been identified, the corresponding curve delivery dates can to be considered. For example, when each of the curves in the shortest path contains maturities of 1 month, 3 month, 6 month, 1 year and 2 years, no interpolation is necessary.
The known conversion curves along the identified shortest path can be collapsed to generate a future conversion curve between JPY and USD. Variables for holding the component rates and an array for holding those variables can be defined as:
usdjpy1m num fx tocur=USD fromcur=JPY maturity=1 month,
usdjpy3m num fx tocur=USD fromcur=JPY maturity=3 month,
usdjpy6m num fx tocur=USD fromcur=JPY maturity=6 month,
usdjpy1y num fx tocur=USD fromcur=JPY maturity=1 year,
usdjpy2y num fx tocur=USD fromcur=JPY maturity=2 year.
and
array usdjpyc fx tocur=USD fromcur=JPY
array usdeurc fx tocur=USD fromcur=EUR
array jpyeurc fx tocur=JPY fromcur=EUR
In this example, when a future conversion curve from JPY to USD is requested, a shortest path algorithm returns JPY->EUR->USD. Translating this short path to the known conversion curves identifies {jpyeurc(R), usdeurc(F)}, where a reverse link from JPY to EUR is included and denoted by an (R) identifier. The use of the reverse link indicates multiplication by inverse rates during the numerical calculation.
The known conversion curves of the shortest path can be tested for consistent maturities. In this case, inconsistent maturities are found, where the EUR->USD curve contains maturities at {1m, 3m, 6m, 1y, 2y} while the EUR->JPY curve contains maturities at {1m, 3m, 9m, 1y, 2y}. To normalize the two curves along the identified shortest path, maturities at the union of these two sets (i.e., {1m, 3m, 6m, 9m, 1y, 2y}) can be determined, with missing values in the known conversion curves being estimated using linear interpolation. To accomplish this normalization, new variables are declared representing the EUR->JPY curve at 6 months and the EUR->USD curve at 9 months, as follows:
usdjpy1m num fx tocur=USD fromcur=JPY maturity=1 month,
usdjpy3m num fx tocur=USD fromcur=JPY maturity=3 month,
usdjpy6m num fx tocur=USD fromcur=JPY maturity=6 month,
usdjpy9m num fx tocur=USD fromcur=JPY maturity=9 month,
usdjpy1y num fx tocur=USD fromcur=JPY maturity=1 year,
usdjpy2y num fx tocur=USD fromcur=JPY maturity=2 year.
and
array usdjpyc fx tocur=USD fromcur=JPY
In the previous two examples, only one possible path was present in the directed graph of known conversion curves. A graph constructed from a larger database of forward conversion curves can provide multiple paths between desired nodes. The following arrays describe five known curves and weights associated with those types of forward conversion curves:
array usdgbpc fx tocur=GBP fromcur=USD
array gbpjpyc fx tocur=JPY fromcur=GBP
array usdeurc fx tocur=EUR fromcur=USD
array gbpjpyc fx tocur=JPY fromcur=GBP
array eurjpyc fx tocur=JPY fromcur=EUR
Referring again to
Costj=Σwi,
for each of the j identified paths, where wi is a weight for an i-th conversion on the j-th path. As noted in the above defined arrays, the GBP->JPY curve has a weight of 2. The identified paths are calculated to have the following costs/weights:
USD->GBP->JPY=3;
USD->GBP->EUR->JPY=3;
USD->EUR->JPY=2.
Thus, the USD->EUR->JPY path is selected as the least cost path, and it is used to generate the future conversion curve from USD->JPY. Additionally, the USD->EUR and EUR->JPY curves can be collapsed to form the USD->JPY conversion curve.
Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a computer-readable medium for execution by, or to control the operation of, data processing apparatus.
The computer-readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter generating a machine-readable propagated signal, or a combination of one or more of them. The term “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them, A propagated signal is an artificially generated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus.
A computer program (also known as a program, software, software application, script, or code), can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., on or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub-programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.
The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit).
Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio player, a Global Positioning System (GPS) receiver, to name just a few. Computer-readable media suitable for storing computer program instructions and data include all forms of nonvolatile memory, media, and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) to LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any from, including acoustic, speech, or tactile input.
Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), e.g., the Internet.
The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
While this specification contains many specifics, these should not be construed as limitations on the scope of the invention or of what may be claimed, but rather as descriptions of features specific to particular embodiments of the invention. Certain features that are described in this specification in the context or separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed o a subcombination or variation of a subcombination.
Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.
Thus, particular embodiments of the invention have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results.
