JP2003099411A - Monte carlo simulation parallel processing system, method, program and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To accelerate parallel processing using Monte Carlo simulation. SOLUTION: When dividing Monte Carlo simulation by the number of the times of simulation, parallel processing is performed including the generation of a random number. Namely, the random number is generated in the first and second processes 11a and 12a of respective server No.1 device 11 and server No.2 device. In addition, in consideration of a processing time for generating extra random numbers in the second process 12a in this case, the number of the times of simulation to be shared by the first and second processes 11a and 12a is adjusted. For example, the first process 11a takes the charge of 10 to 600 thousands of times of simulation and the second process 12a takes the charge of 600 thousands to one million of times of simulation.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for parallelizing a Monte Carlo simulation, and more particularly to a Monte Carlo simulation parallel processing technique suitable for speeding up financial risk metric or the like by Monte Carlo simulation.

[0002]

2. Description of the Related Art Currently, for example, in a financial institution, Monte Carlo simulation is used as a technique for quantifying financial risk using a computer. This Monte Carlo simulation is a simulation that uses random numbers.

The use of this Monte Carlo simulation for financial risk quantification is described below.

First, a random number is generated, and then the computer uses the random number to predict and calculate future credit rating fluctuations, interest rate fluctuations, foreign currency fluctuations, and stock price fluctuations to calculate the loss amount. Furthermore, this processing is performed many times (thousands to tens of thousands of times).
repeat. Then, the calculated loss amounts are sorted in descending order of amount, and the maximum loss amount is calculated.

This maximum loss amount means a loss amount that can occur in the worst situation. Considering the calculated maximum loss amount,
You can review the contents of owned assets and the contents of transactions. This maximum loss is usually calculated by "99% point to 95%
Use "point".

The "99% point" refers to the 100th (10,000 times × 1%) loss amount from the largest amount, assuming that the number of simulations is 10,000. This is 99%
With the probability of, it means that the actual loss amount should fall within the predicted 99% point amount. The same applies to the "95% point".

By the way, in recent years, there is a tendency to use the "99.9% point" in order to predict the loss amount under worse conditions. However, when the number of simulations is about tens of thousands, only a few times out of the tens of thousands of "99.9% points"
Does not occur in the vicinity. In this case, depending on the random number used,
The loss of "99.9% point" is greatly shaken.

In order to cope with this and to precisely predict the loss amount of "99.9% point", it is necessary to increase the number of simulations on the computer to several millions.

Further, the conventional financial risk quantification by a computer quantifies credit risk, interest rate risk and foreign exchange risk individually, and does not deal with compound risk such as credit risk and interest rate risk. There are many.

However, in reality, there is a possibility that "the yen depreciation", "the domestic corporate credit rating decline" and "the domestic interest rate rise" may occur at the same time, so it is essential to deal with the compound risk.

As described above, in computerized financial risk quantification using Monte Carlo simulation, it is indispensable to increase the number of simulations and deal with complex risks.

However, increasing the number of simulations and dealing with complex risks requires increasing the amount of calculation on the computer,
This results in increased processing time.

As a conventional technique for dealing with such a problem and shortening the processing time, (A) a technique for dividing transaction details and held debts into parallel processing, and (B) dividing by the number of simulations. There is a technology for parallelizing future credit rating fluctuations, interest rate fluctuations, foreign currency fluctuations, stock price fluctuations, and loss calculation (in this technology, random number generation processing is performed by one computer).

However, each of these techniques has the following problems.

In the prior art (A), it is necessary to finally transfer the loss amount calculated for each parallel process to one process and total it. In this case, the amount of data to be transferred increases as the degree of parallelism increases, so that data transfer becomes a bottleneck in processing performance. In particular, in a system in which data transfer between processes is not performed directly between processes but via a database, it becomes a fatal bottleneck.

On the other hand, in the prior art (B), since each parallel process processes all transaction details and all held credits, the loss amount calculated for each parallel process is finally converted into one process. No need to transfer. However, in this technique, when the number of random numbers used increases, random number generation and transfer become a bottleneck.

This is because, in this technique (B), only one computer is assigned to generate random numbers, and the random numbers generated by this computer must be transferred to each computer.

[0018]

The problem to be solved by the present invention is to avoid data transfer, which is a bottleneck for speeding up, in the conventional technique when, for example, parallelizing financial risk quantification using Monte Carlo simulation. This is a point that cannot be done.

The object of the present invention is to solve these problems of the prior art and to speed up parallel processing using Monte Carlo simulation, and to increase the number of simulations of financial risk quantification and cope with complex risks, for example. Then, it is to improve the prediction accuracy in financial risk quantification using a computer.

[0020]

In order to achieve the above object, in the present invention, when the Monte Carlo simulation is divided by the number of simulations, random number generation is performed and parallel processing is performed. That is, a random number is generated in each parallel processing process. Further, in this case, if the division is simple, for example, the number of simulations 1 to
The second process will share 500,000 times, and the second process will share 500,000 to 1,000,000 simulations. In this case, the second process will also generate random numbers for 1 to 500,000 times. In the present invention, in consideration of the processing time for generating an extra random number in such a second process, for example, the number of simulations is 1 in the first process.
.About.600,000 times, and the second process shares 600,000 to 1,000,000 simulation times. In this way, by considering the processing time for generating extra random numbers in each process and adjusting the number of simulations shared by each parallel processing process, the processing time between each parallel processing process is made uniform, and the overall processing is performed. The time can be further shortened.

[0021]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described in detail below with reference to the drawings. 1 is a block diagram showing a configuration example of a Monte Carlo simulation parallel processing system according to the present invention, FIG. 2 is a flow chart showing an example of a processing procedure according to the present invention of the Monte Carlo simulation parallel processing system in FIG. 1, and FIG. 2 is a block diagram showing a hardware configuration example of each server machine in FIG. 1. FIG.

In FIG. 3, 31 is a CRT (Cathode Ra
y Tube) or LCD (Liquid Crystal Display) or the like, 32 is an input device such as a keyboard or mouse, 33 is an external storage device such as HDD (Hard Disk Drive), and 34 is a CPU (Central Processing Uni
t) An information processing device for performing computer processing, which is provided with 34a, a main memory 34b, an input / output interface 34c and the like, and 35 is a CD-ROM (Compact Disc-Read Only Memor) in which programs and data according to the present invention are recorded
y) or DVD (Digital Video Disc / Digital Vers
An optical disc made of a tile disc) or the like, a drive device 36 for reading programs and data recorded on the optical disc 35, and a communication device 37 made of a LAN (Local Area Network) card or the like.

After the program and data stored in the optical disk 35 are installed in the external storage device 33 by the information processing device 34 via the drive device 36, the program and data are read from the external storage device 33 into the main memory 34b and the CPU 34a is read.
1 is configured in the information processing device 34 by processing.

In FIG. 1, 1 is a client machine and 11
Is a server No. 1 and 12 is a server No. 2. The operator of the system of the present example performs a simulation instruction operation via the client unit 1, and the server No. 1 unit 11 and the server No. 2 unit 12 have the client unit 1 Parallel processing of the simulation instructed by.

In this example, the client machine 1 has
Parallel processing control unit 1a, sort processing unit 1b, database (described as "transaction details, database of held debt" in the figure)
1c, a database (described as "a loss amount database" in the figure) 1d, an input device 1e, and a display device 1f are provided, and the first server 11 and the second server 12 have a first server.
Process 11a and second process 12a (“Monte Carlo simulation parallel processing first and second process” in the figure)
Will be implemented).

In the system of this example having such a configuration, the Monte Carlo simulation is divided by the number of simulations, but unlike the technique described in the prior art (B), parallel processing is performed including random number generation.

That is, in the prior art (B), one process (for example, the client machine 1) generates a random number, and the generated random number is used for each parallel processing process (for example, the server 1).
No. 11 and server No. 2) were transferred to each parallel processing process, that is, server No. 1 1
A random number is generated in the server 1 and the server 2-12.

In this case, for example, the first process 11a of the first server shares the simulation count of 1 to 500,000 times, and the second process 12a of the second server shares the simulation count of 501 to 1,000,000. , Second
The process 11a will also generate a random number for 100,000 to 500,000 times.

This is related to the fact that in the current Monte Carlo simulation in financial institutions and the like, arithmetic random numbers (pseudo random numbers) are often used instead of using physical random numbers.

In other words, arithmetic random numbers are different from physical random numbers generated by utilizing a random physical phenomenon (for example, dice) in that the previous random numbers are substituted into the arithmetic expression to generate new random numbers. is there. Therefore, with the arithmetic random number, the random number of 500,000 times or more cannot be calculated unless the random number of 1 to 500,000 times is generated in the second process 12a.

However, it is preferable to generate an extra random number for 500,000 times as in the prior art (B).
The processing time as a whole is shorter than that of transferring the random number for ten thousand times.

Further, in this example, not only is the random number generation process parallelized in this way, but the second process 12a is also used.
Considering the processing time to generate an extra random number in
By adjusting the number of simulations shared by the first process 11a and the second process 12a,
The processing time between the processes 11a and 12a is made uniform to reduce the processing time of the entire system. The description will be given below.

As described above, if the number of simulations is evenly allocated to the respective parallel processing processes (the first and second processes 11a and 12a of the server No. 11 and the server No. 12), the second process in the server No. 12 is distributed. 12
Since a random number is additionally generated in a, a processing time difference with the first process 11a in the server No. 1 machine 11 occurs.

Considering the processing time of the simulation in the entire system, the longest processing time among the processing times of the respective parallel processing processes is the processing time in the entire system. Therefore, if there is a large difference in the processing time between the parallel processing processes, the overall processing time of the simulation cannot be effectively reduced, and as a result, the efficiency of parallel processing cannot be maximized.

As a case where there is a large difference in processing time between parallel processing processes, firstly, it is possible to assume a case where the ratio of the random number generation processing time to the simulation processing time is large because the random numbers of advanced arithmetic expressions are used. .

Secondly, it can be assumed that the number of servers is increased and the parallelism is increased in order to further increase the speed.
That is, if the degree of parallelism is increased in this way, the number of random numbers to be additionally generated in the last parallel processing process increases, and the random number generation processing time increases by that amount. growing.

In order to deal with such a problem, it is effective to make the processing time of each parallel processing process uniform.

Therefore, in this example, the number of simulations shared by each of the first process 11a in the first server 11 and the second process 12a in the second server 12 is taken into consideration in consideration of the processing time for generating an extra random number. Adjust.

For example, in this example, the number of simulations 1 to 6 in the first process 11a in the first server 11
0,000 times, the second process 12a in the second server 12
The number of simulations is from 600,000 to 1,000,000.

As a result, the processing time between the first process 11a in the server No. 1 machine 11 and the second process 12a in the server No. 2 machine 12 is made uniform, and the processing time of the entire system can be further shortened.

Hereinafter, such a processing operation will be described with reference to FIG.

First, in the client machine 1, when an execution request (a Monte Carlo simulation effective request) is output from the input device 1e to the parallel processing control section 1a based on the operation of the operator, for example, the parallel processing control section 1a.
However, each parallel processing process (the first process 11a of the first server 11 and the second process 12a of the second server 12)
The number of simulations to be shared is calculated for each, and an instruction is given to each parallel processing process.

In this way, the respective parallel processing processes (the first process 11a of the first server 11 and the second process 12a of the second server 12) receiving the instruction from the parallel processing control unit 1a of the client machine 1 First, data of all transaction details and all held credits are acquired from the database 1c of the client machine 1.

Next, each parallel processing process, that is, the first process 11a of the first server 11 and the second server 1
The second process 12a of No. 2 is an extra random number generation processing unit 11
In b and 12b, the random numbers immediately before the random numbers used in the shared simulation are generated.

Further, in the random number generation processing units 11c and 12c, random numbers after the random numbers already generated in the extra random number generation processing units 11b and 12b are generated for one simulation, and then, in the prediction units 11d and 12d. Based on the random numbers generated by the generation processing units 11c and 12c,
Predict future rating fluctuations, interest rate fluctuations, currency fluctuations, stock price fluctuations, etc.

Then, in the loss amount calculation units 11e and 12e, the loss amount is calculated based on the future rating fluctuation, interest rate fluctuation, foreign currency fluctuation, stock price fluctuation predicted by the prediction units 11d and 12d, and the calculated loss amount. Is output to the database 1d of the client machine 1.

The first process 11 of the first server 11
a and the second process 12a of the server No. 2 12 process by the random number generation processing units 11c and 12c, the prediction units 11d and 12d, and the loss amount calculation units 11e and 12e, and write to the database 1d of the client device 1. The process is executed from the start simulation count to the end simulation count.

In the client machine 1, the sort processing section 1b
Thus, the database 1d whose output from the server No. 11 and the server No. 12 has been completed is sorted by the loss amount,
The maximum loss amount is calculated and displayed on the display device 1f.

Hereinafter, such an operation will be described with reference to FIG. In addition, in FIG. 2, the plurality of parallel processing processes p (1 ≦ 1) are not limited to the configuration in FIG. 1, that is, the two first and second processes 11a and 12a of the server No. 11 and the server No. 12 are not limited. For p ≦ P), the content indicates the number of simulations to be shared.

First, at step 201, a random number generation processing time Tr for one simulation and a processing time Tm for one simulation (including the random number generation processing time).
To get. In addition, these values are measured in advance.

Next, in step 202, the number of parallel processing processes P and the number of times of simulation Sa are acquired,
In step 203, from the processing time Tm of one simulation (including the random number generation processing time), the random number generation processing time Tr of one simulation, the number of parallel processing processes P, and the number of times of simulation Sa, the parallel processing process p (1 ≦ p ≦ The number of simulations S that P) should share
p is calculated by the following formula.

[0052]

[Equation 1]

In this way, the number of simulations Sp that makes the processing time between the parallel processing processes uniform is obtained, and the parallel processing processes p (1
≦ p ≦ P) calculates the number of start simulations and the number of end simulations for each parallel processing process from the number of simulations Sp to be shared, and issues a processing request to each parallel processing process (steps 204 to 209).

For example, the first process is instructed to execute the start simulation count "1" to the end simulation count "S1" (step 20).
6), for the p-th (1 <p <P) process,
It is instructed to execute the start simulation number consisting of "pre-process end simulation number + 1" to the end simulation number consisting of "pre-process end simulation number + Sp" (step 207), and for the P-th process, It is instructed to execute the start simulation count to the end simulation count "Sa" consisting of "end simulation count of previous process + 1" (step 208).

In this way, the number of simulations shared by each parallel processing process is adjusted in consideration of the processing time required for generating an extra random number.

As described above with reference to FIGS. 1 to 3, in this example, when the Monte Carlo simulation is divided by the number of simulations, parallel processing is performed including random number generation. That is, the parallel processing processes (first and second processes 1) of the server No. 11 and the server No. 2 respectively.
A random number is generated in 1a, 12a). Further, at this time, the first process 11a merely shares the number of simulations of 1 to 500,000 times, and the second process 12a shares the number of simulations of 500,000 to 1 million times. The number of simulations shared by the first and second processes 11a and 12a is adjusted in consideration of the processing time for generating extra random numbers in the process 12a. In this example, the first process 11a shares the simulation count of 1 to 600,000 times, and the second process 12a shares the simulation count of 600,000 to 1,000,000 times.

As described above, the number of simulations shared by each parallel processing process is adjusted in consideration of the processing time for generating an extra random number in the second process 12a, so that each of the first and second processes 11a is adjusted. , 12a
The processing time between them can be made uniform, and the processing time of the entire system can be further shortened.

By applying the technique of this example to parallel processing of financial risk quantification using, for example, Monte Carlo simulation, the parallel processing of financial risk quantification can be more effectively performed. It is possible to increase the number of simulations and deal with complex risks, which are necessary for improving the accuracy of financial risk simulations.

The present invention is not limited to the examples described with reference to FIGS. 1 to 3, and various modifications can be made without departing from the scope of the invention. For example, in this example,
Although the parallel processing control unit 1a is mounted on the client machine 1 side, the parallel processing control unit 1a is installed in the first server 1
It may be mounted on either one of the server 1 and the server 2-12.

In this example, the financial risk quantification system has been mainly described, but the present invention can be applied to the speedup of the system using another Monte Carlo simulation.

Further, in this example, the computer configuration example of FIG. 2 is shown as the configuration of the client machine and the server machine, but a computer configuration without a keyboard or an optical disk drive may be used. Further, in this example, an optical disk is used as a recording medium, but an FD (Flexible Disk) is used.
Etc. may be used as the recording medium. Further, regarding the installation of the program, the program may be downloaded and installed via the network via the communication device.

[0062]

According to the present invention, parallel processing using Monte Carlo simulation can be speeded up,
For example, it is possible to increase the number of simulations of financial risk quantification and deal with complex risks, and it is possible to improve the prediction accuracy in financial risk quantification using a computer.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration example of a Monte Carlo simulation parallel processing system according to the present invention.

FIG. 2 is a flow chart showing an example of a processing procedure according to the present invention of the Monte Carlo simulation parallel processing system in FIG.

3 is a block diagram showing an example of a hardware configuration of each server machine in FIG.

[Explanation of symbols]

1: client machine, 1a: parallel processing control unit, 1b: sort processing unit, 1c: database (“transaction details, database of held debt”), 1d: database (“loss database”), 1e: input device, 1f: display device, 11: server 1st machine, 12: server 2nd machine, 11
a: first process, 12a: second process, 11b, 1
2b: extra random number generation processing unit, 11c, 12c: random number generation processing unit, 11d, 12d: prediction unit, 11e, 12e:
Loss amount calculation unit, 31: display device, 32: input device, 3
3: external storage device, 34: information processing device, 34a: CP
U, 34b: main memory, 34c: input / output interface, 35: optical disk, 36: drive device, 37: communication device.

Claims (6)

[Claims] 1. A system for performing a simulation using a Monte Carlo simulation by a plurality of computers in a distributed manner, wherein the number of simulations of the Monte Carlo simulation is divided and assigned to the plurality of computers, and a random number used for the simulation is calculated. A Monte Carlo simulation parallel processing system comprising: means for generating by a computer; and means for calculating the number of simulations assigned to each of the plurality of computers according to the random number generation processing time at each computer. 2. A parallel processing method for a system in which a simulation using Monte Carlo simulation is performed by distributed processing in a plurality of processes, wherein the number of simulations in the Monte Carlo simulation is divided and assigned to the plurality of processes, and Monte Carlo simulation parallel processing method characterized by having a procedure for generating a random number to be used in each process, and a procedure for calculating the number of simulations to be assigned to each of the plurality of processes in accordance with the random number generation processing time in each process. . 3. The Monte Carlo simulation parallel processing method according to claim 2, wherein the random number generation processing time Tr for one simulation and the random number generation processing time Tr.
Based on the procedure of measuring the processing time Tm for one simulation including the above, the measured random number generation processing time Tr for one simulation and the processing time Tm for one simulation, and the number of processes P and the number of simulations Sa, And a procedure for calculating the number of simulations Sp assigned to the process p (1 ≦ p ≦ P). 4. The Monte Carlo simulation parallel processing method according to claim 3, wherein Sp = Sa × {(Tm−Tr) / Tm} ^p−1 / Σ.
Monte Carlo simulation characterized by having a procedure for calculating the number of simulations Sp assigned to the process p (1 ≦ p ≦ P) by {(Tm−Tr) / Tm} ⁱ (i = 0 to P−1) Parallel processing method. 5. The computer according to any one of claims 2 to 4.
A program for executing each step in the Monte Carlo simulation parallel processing method according to any one of 1. 6. The computer according to any one of claims 2 to 4.
A computer-readable recording medium recording a program for executing each step in the Monte Carlo simulation parallel processing method according to any one of 1.