Monte-Carlo Simulation-Based Financial Computing... 41
FPGA FPGA FPGA FPGA FPGA FPGA FPGA FPGA
FPGA FPGA FPGA FPGA FPGA FPGA FPGA FPGA
CPU0 CPU1 CPU2 CPU32
Standard Network
Switch
Rocket IO
PCI-X
Network Protocol
Node
Application Process
(Sofware on Host)
Parallel Toolkit (PTK)
Accelerator
Function on
FPGA logic
blocks
Function on
FPGA logic
blocks
Memory
Function on
PowerPC
External
communication to
neighbour
...
...
...
Fig. 3 Architecture of the Maxwell FPGA parallel machine
that a European option has a life length of 1 year, which is discretized to 100
time steps, and 10
6
paths are generated in the Monte-Carlo simulation, therefore,
100 ×10
6
=10
8
random variables are needed for the simulation. Several considera-
tions arise when constructing a random number generator [21]:
• Period length: any pseudo-random number generator will eventually repeat itself.
Generally, we want generators with very longer periods.
• Reproducibility: it is often important to be able to re-run a simulation using
exactly the same random samples as the previous simulation.
• Speed: as mentioned above, millions or even billions of samples are needed for a
single simulation. It is very important to keep a very high throughput of random
samples to feed a Monte-Carlo simulation engine.
• Portability: an algorithm for generating random numbers should produce the
same sequence of values on all computing platforms.
• Randomness: this is the most important consideration. Theoretical properties and
statistical tests could be used to evaluate the quality of the random samples.
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