CN111966959A - Option pricing data determining method and device based on multi-thread parallel processing mode - Google Patents
Option pricing data determining method and device based on multi-thread parallel processing mode Download PDFInfo
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Abstract
The invention discloses an option pricing data determining method and device based on a multithreading parallel processing mode, wherein the method comprises the following steps: determining option pricing data using partial differential equations; determining a solution area of a partial differential equation; dividing a solving area into a plurality of grids, and distributing the grids to a plurality of threads; finite difference calculations within each grid are performed by multiple threads in a parallel fashion. The invention uses a plurality of threads to process in parallel by a core algorithm which can carry out parallel computation in the finite difference method, thereby greatly reducing the program running time and improving the computation efficiency.
Description
Technical Field
The invention relates to the technical field of software, in particular to an option pricing data determining method and device based on a multithreading parallel processing mode.
Background
This section is intended to provide a background or context to the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.
As is well known, the financial field involves a large number of calculations, such as by computationally efficiently pricing financial products, or by computationally more accurately assessing potential risks, or by computationally enhancing quick response capabilities, improving program trading efficiency, and the like. At present, the calculation in the existing financial field adopts a serial processing mode, and the technical problems of long calculation time and low calculation efficiency exist.
Disclosure of Invention
The embodiment of the invention provides an option pricing data determining method based on a multithreading parallel processing mode, which is used for solving the technical problems of long calculation time and low calculation efficiency due to the fact that a serial processing mode is adopted in calculation in the prior financial field, and comprises the following steps: determining option pricing data using partial differential equations; determining a solution area of a partial differential equation; dividing a solving area into a plurality of grids, and distributing the grids to a plurality of threads; finite difference calculations within each grid are performed by multiple threads in a parallel fashion.
The embodiment of the invention also provides an option pricing data determining device based on a multithreading parallel processing mode, which is used for solving the technical problems of long computing time and low computing efficiency caused by the adoption of a serial processing mode in the computing in the prior financial field, and comprises the following steps: a pricing model determining module for determining option pricing data using partial differential equations; the pricing model solving module is used for determining a solving area of a partial differential equation; the thread distribution module is used for dividing the solving area into a plurality of grids and distributing the grids to a plurality of threads; and the parallel computing module is used for executing the finite difference computation in each grid by a plurality of threads in a parallel mode.
The embodiment of the invention also provides computer equipment for solving the technical problems of long computing time and low computing efficiency of the existing serial processing mode adopted by computing in the financial field.
The embodiment of the invention also provides a computer readable storage medium, which is used for solving the technical problems of long calculation time and low calculation efficiency caused by the adoption of a serial processing mode in the calculation in the prior financial field.
In the embodiment of the invention, the option pricing data is determined by utilizing the partial differential equation, after the solving area of the partial differential equation is determined, the solving area is divided into a plurality of grids and distributed to a plurality of threads, and the finite difference calculation in each grid is executed by the plurality of threads in a parallel mode.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts. In the drawings:
fig. 1 is a flowchart of an option pricing data determining method based on a multi-thread parallel processing manner according to an embodiment of the present invention;
fig. 2 is a schematic diagram of solution area division provided in the embodiment of the present invention;
fig. 3 is a flowchart of an option pricing data determining method based on a multi-thread parallel processing manner according to an embodiment of the present invention;
fig. 4 is a schematic diagram of an option pricing data determining apparatus based on a multi-thread parallel processing manner according to an embodiment of the present invention;
fig. 5 is a schematic diagram of an option pricing data determining apparatus based on a multi-thread parallel processing manner according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention are further described in detail below with reference to the accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
An option pricing data determining method based on a multi-thread parallel processing mode is provided in an embodiment of the present invention, fig. 1 is a flowchart of an option pricing data determining method based on a multi-thread parallel processing mode provided in an embodiment of the present invention, and as shown in fig. 1, the method may include the following steps:
and S101, determining option pricing data by using a partial differential equation.
It should be noted that, the determination of option pricing data is mainly solved in a data manner at present, and from the viewpoint of numerical solution, the options pricing data is mainly divided into three categories: a grid prediction method, a finite difference method, and a monte carlo simulation method. The embodiments of the present invention are described by taking a finite difference method as an example. Then the option pricing data determination can be summarized as a second order partial differential equation. Finite difference methods are efficient tools for computing partial differential equations. The finite difference method is a common data simulation method, a solution domain is divided into difference grids, and a finite number of grid nodes are used for replacing a continuous solution domain, so that an algebraic equation system with values on the grid nodes as unknowns is established. The core idea of the finite difference method is to discretize the derivative, convert the partial differential equation into a differential equation, and then solve the differential equation set, and the solution process may adopt various iteration methods, such as Successive Relaxation (SOR), Line Successive Relaxation (LSOR), Alternating inversion iteration (IADI), strong inversion iteration (SIP), and so on.
In the embodiment of the invention, the core algorithm of the finite difference is analyzed by utilizing the boundary problem of the classical partial differential equation, and the core algorithm is optimized, so that the high-performance computing method of the finite difference is obtained, and the computing efficiency of the financial option pricing is improved.
S102, determining a solution area of the partial differential equation.
For a given partial differential equation boundary problem, a given region needs to be divided, and as shown in fig. 2, the region is divided in a five-point difference manner. D shown in fig. 2 denotes a solution area, and L denotes a boundary. In specific implementation, the embodiment of the invention adopts a subdivision mode of square grids, and divides the solving area by adopting the regular division mode, so that the differential equation with the same form can be obtained on each discrete point, the problem can be simplified, and the calculation speed can be effectively improved.
And S103, dividing the solving area into a plurality of grids and distributing the grids to a plurality of threads.
In the embodiment of the invention, the grids in the solution area are assigned to a plurality of processor threads according to the area division method, the finite difference calculation in the grids can be simultaneously carried out, the parallelization processing is realized, and the calculation efficiency is improved.
And S104, executing finite difference calculation in each grid by a plurality of threads in a parallel mode.
In a specific implementation, the step S104 may be implemented as follows; determining a differential equation set which approximately replaces a partial differential equation; and solving the difference equation set by adopting an iteration method.
As shown in fig. 2, the value of the center point U (i, j) can be approximated using the average value of the points 1, 2, 3, 4 around the center point 0, resulting in a difference equation that approximately replaces the partial differential equation, that is:
U(i,j)＝(U(i-1,j)+U(i+1,j)+U(i,j-1)+U(i,j+1))×0.25。
and solving a difference equation set by using an iterative method aiming at the core algorithm of the finite difference. In specific implementation, an approximate substitution equation is used to obtain a new value of U (i, j), after all elements are updated, a second iteration is performed until the difference between the values of the two iterations satisfies a preset threshold (i.e., is very small), and the obtained matrix is a solution of the difference equation set.
In one embodiment, as shown in fig. 3, the option pricing data determining method based on the multi-thread parallel processing mode provided in the embodiment of the present invention may further include the following steps:
s105, acquiring the preset thread number N. In specific implementation, a reasonable thread number is preset so as to distribute a solution area according to the set thread number, discretize the solution area and calculate solution equations in parallel. The core algorithm which can carry out parallel computation in the finite difference method is processed in parallel, so that the program running time is greatly reduced, and the computation efficiency is improved.
Based on the above embodiment, the above S103 may be implemented by the following steps: dividing the solution area into an n multiplied by n matrix; dividing a solving area into a plurality of grids according to the thread number N and the row number N of the matrix; each grid is assigned to a thread.
In specific implementation, the option pricing data determining method based on the multi-thread parallel processing mode provided in the embodiment of the present invention includes three steps of solving area discretization, approximate substitution, and solving a difference equation set:
first, a solution area is discretized, the solution area is divided into an n × n matrix, the element values of the first row, the first column, the last row and the last column of the matrix are known, and the element values of other positions of the matrix need to be obtained. In the embodiment of the invention, the parallel computation is realized by using multiple threads, firstly, the solving area is distributed according to the set thread number, and the solving area is discretized.
Secondly, the value of each element in the matrix is expressed by utilizing a five-point difference format approximation. The values of the elements (i, j) in the surrogate matrix are approximated using the following equation:
U(i,j)＝(U(i-1,j)+U(i+1,j)+U(i,j-1)+U(i,j+1))×0.25。
finally, the system of difference equations is solved. Solving the differential equation set is an iterative process, the values of each element in the matrix are expressed by using an approximate substitution equation, then the values are used as a new value to update the matrix, the new matrix is used for iteration again, and when the iteration times are enough, the obtained matrix is the solution of the differential equation set.
The code for solving the area discretization is realized as follows:
"totalsize- (totalsize/NUM _ THREADS) # NUM _ THREADS row matrix multiplication.
num＝totalsize/NUM_THREADS；
if(totalsize＝＝num*NUM_THREADS)
remain＝num；
else
{
num＝num+1；
remain＝totalsize-num*(NUM_THREADS-1)；
}”
The approximate alternative code implementation is as follows:
“for(i＝1；i<totalsize-1；i++)
for(j＝1；j<totalsize-1；j++)
b[i][j]＝(a[i][j+1]+a[i][j-1]+a[i+1][j]+a[i-1][j])*0.25；”
the code for solving the system of difference equations is implemented as follows:
solving the system of difference equations is an iterative process in which we first represent the value of each element in the matrix using an approximate substitution equation, i.e.
“for(i＝1；i<totalsize-1；i++)
for(j＝1；j<totalsize-1；j++)
b[i][j]＝(a[i][j+1]+a[i][j-1]+a[i+1][j]+a[i-1][j])*0.25；”
These values will then be updated as a new value to the matrix, and the iteration will be performed again with the new matrix, i.e.
“for(i＝0；i<totalsize；i++)
for(j＝0；j<totalsize-；j++)
a[i][j]＝b[i][j]；”
When the number of iterations is sufficient, the resulting matrix is the solution to the system of difference equations.
In the embodiment of the invention, multithreading is adopted, the solving area is distributed according to the set thread number, the solving area is discretized, and the process of solving the equation set is calculated in parallel, so the program operation time is greatly reduced, and the calculation efficiency is improved.
Based on the same inventive concept, an option pricing data determining apparatus based on a multi-thread parallel processing mode is further provided in the embodiments of the present invention, as described in the following embodiments. Because the principle of solving the problem of the device is similar to the option pricing data determining method based on the multithreading parallel processing mode, the implementation of the device can refer to the implementation of the option pricing data determining method based on the multithreading parallel processing mode, and repeated parts are not repeated.
Fig. 4 is a schematic diagram of an option pricing data determining apparatus based on a multi-thread parallel processing manner according to an embodiment of the present invention, as shown in fig. 4, the apparatus may include:
wherein, the pricing model determining module 41 is configured to determine option pricing data by using partial differential equations; a pricing model solving module 42 for determining a solution region of partial differential equations; a thread allocation module 43, configured to divide the solution area into multiple grids and allocate the grids to multiple threads; and the parallel computing module 44 is used for executing the finite difference computation in each grid by a plurality of threads in a parallel mode.
Optionally, the parallel computing module 44 is further configured to determine a differential equation set that approximately replaces the partial differential equation, and solve the differential equation set using an iterative method.
In one embodiment, as shown in fig. 5, the option pricing data determining apparatus based on a multi-thread parallel processing manner provided in the embodiment of the present invention may further include: and the thread configuration module 45 is configured to obtain the number N of threads configured in advance.
Based on the above embodiment, the thread allocating module 43 may further be configured to: dividing the solution area into an n multiplied by n matrix; dividing a solving area into a plurality of grids according to the thread number N and the row number N of the matrix; each grid is assigned to a thread.
Based on the same inventive concept, the embodiment of the invention also provides a computer device, which is used for solving the technical problems of long calculation time and low calculation efficiency caused by the adoption of a serial processing mode in the existing financial field.
Based on the same inventive concept, the embodiment of the invention also provides a computer readable storage medium, which is used for solving the technical problems of long calculation time and low calculation efficiency caused by the adoption of a serial processing mode in the calculation in the prior financial field.
In summary, embodiments of the present invention provide an option pricing data determining method, apparatus, computer device, and computer readable storage medium based on a multi-thread parallel processing manner, where option pricing data is determined by using a partial differential equation, after a solution area of the partial differential equation is determined, the solution area is divided into multiple grids and allocated to multiple threads, and the multiple threads execute finite difference computations in each grid in a parallel manner.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. An option pricing data determining method based on a multi-thread parallel processing mode is characterized by comprising the following steps:
determining option pricing data using partial differential equations;
determining a solution area of a partial differential equation;
dividing the solving area into a plurality of grids, and distributing the grids to a plurality of threads;
and executing finite difference calculation in each grid by the plurality of threads in a parallel mode.
2. The method of claim 1, wherein the method further comprises:
and acquiring the pre-configured thread number N.
3. The method of claim 2, wherein partitioning the solution area into a plurality of grids, allocated to a plurality of threads, comprises:
dividing the solution area into an n multiplied by n matrix;
dividing the solving area into a plurality of grids according to the thread number N and the row number N of the matrix;
each grid is assigned to a thread.
4. The method of claim 1, wherein performing finite difference computations within each grid in parallel by the plurality of threads comprises:
determining a set of differential equations that approximately replace the partial differential equations;
and solving the difference equation set by adopting an iteration method.
5. An option pricing data determining apparatus based on a multi-thread parallel processing method, comprising:
a pricing model determining module for determining option pricing data using partial differential equations;
the pricing model solving module is used for determining a solving area of a partial differential equation;
the thread distribution module is used for dividing the solving area into a plurality of grids and distributing the grids to a plurality of threads;
and the parallel computing module is used for executing the finite difference computation in each grid by the multiple threads in a parallel mode.
6. The apparatus of claim 5, wherein the apparatus further comprises:
and the thread configuration module is used for acquiring the number N of the threads configured in advance.
7. The apparatus of claim 6, wherein the thread allocation module is further to: dividing the solution area into an n multiplied by n matrix; dividing the solving area into a plurality of grids according to the thread number N and the row number N of the matrix; each grid is assigned to a thread.
8. The apparatus of claim 5, wherein the parallel computation module is further configured to determine a set of differential equations that approximately replace the partial differential equations, and to solve the set of differential equations using an iterative method.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the option pricing data determining method according to any one of claims 1 to 4 based on a multi-thread parallel processing manner.
10. A computer-readable storage medium storing a computer program for executing the option pricing data determining method based on the multi-thread parallel processing method according to any one of claims 1 to 4.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102930473A (en) * | 2012-10-19 | 2013-02-13 | 浪潮电子信息产业股份有限公司 | Option pricing method based on backward stochastic differential equation (BSDE) |
| CN110162804A (en) * | 2018-01-10 | 2019-08-23 | 成都信息工程大学 | The wavefield forward modeling optimization method accelerated based on CPU |
| CN111507837A (en) * | 2020-04-10 | 2020-08-07 | 浙江万里学院 | Option value calculation system based on time fractional order option pricing model |
-
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- 2020-08-17 CN CN202010825152.0A patent/CN111966959A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102930473A (en) * | 2012-10-19 | 2013-02-13 | 浪潮电子信息产业股份有限公司 | Option pricing method based on backward stochastic differential equation (BSDE) |
| CN110162804A (en) * | 2018-01-10 | 2019-08-23 | 成都信息工程大学 | The wavefield forward modeling optimization method accelerated based on CPU |
| CN111507837A (en) * | 2020-04-10 | 2020-08-07 | 浙江万里学院 | Option value calculation system based on time fractional order option pricing model |
Non-Patent Citations (2)
| Title |
|---|
| 晏益慧: "基于多核平台多流体网格法的MPI-OMP嵌套并行实现", 计算机工程与科学, no. 1, pages 214 - 215 * |
| 李慧: "航空客运单航段动态定价问题研究", 今日科苑, no. 14, pages 132 - 133 * |
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