The Pure Mathematics
at the Heart of Quantitative Finance
The use of Maple
to analyze complicated financial data
Robert Gibson* is a quantitative analyst with a leading
UK bank, providing a broad range of financial services
and innovative banking methods. He uses Maple mathematical
problemsolving software to validate the analytics that
underpin his trading tasks. The team of quantitative analysts
at the bank has a pivotal function within the organization
in pricing and assessing financial risk for share dealing
and trading internationally. As part of that team, Gibson
needs to carry out complex numeric and symbolic calculations
on a daily basis. These calculations involve him in the
construction of complex, bespoke mathematical instruments
for analyzing the complicated financial data he grapples
with daily.
The Pure Mathematics at the Heart of Quantitative Finance
Before he joined the company, Gibson began using Maple
mathematical problemsolving software in his teaching and
research years during the 1990s at his local university.
He now finds Maple to be an indispensable tool in his daily
work at the bank.
As Gibson observes, Maple products was originally designed
for use in an academic, educational environment. As such
Maple is a powerful piece of problemsolving software capable
of rigorous mathematical computations.
Developed and tested in context over the past twentyfive
years, Maple technology is now the solution of choice for
scientists, engineers and mathematicians around the world,
in industry, commerce and research as well as education.
Gibson encapsulates the reason why Maple is as well suited
for use in a financial context: “There is a great
deal of pure maths in quantitative finance, where Maple
retains its full applicability”.
Gibson uses the functionalities provided by Maple software
in building and validating analytics for working out pricing
problems. Maple has its own mathematical programming language
which can be used to generate code and live interactive
technical documents.
Gibson uses Maple alongside Excel/VBA and C++. Using Maple
most for validation purposes, Gibson tended to write his
own code, and then checked the constituent parts using
Maple. Maple’s advanced, complete and errorfree
mathematical capabilities enable him to check the output
of the prototypes he has built with his code. “Even
when Maple is not used directly it is still beneficial”,
he adds, “even if there are other available routes
for building analytics, because it can be used for validation.
You have the software that performs the calculation; Maple
allows you to do an independent check and verify that the
two sets of results obtained through the two routes are
identical”.
A Fast and Accurate Calculator that Saves Time and Reduces
Error
According to Gibson some of the tasks he carries out require
heavy numeric or symbolic computations. Using Maple as
a tool for quantitative work enables him to perform these
difficulttomanage computations, some of which would otherwise
have to be carried out manually. He describes how “Maple
is a powerful problemsolving tool capable of rigorous
mathematical computations. It is automatic and therefore
uses up much less time. The computations are rarely simple
linear computations. Maple is a very useful tool as you
can extract an answer straightaway because of its builtin
functions”.
Maple’s intuitive and easytouse software provides
users with advanced capabilities including palettes of
maths functions and symbols, easy maths editing, an equation
editor and automatic labelling of textbook equations, task
templates and an integrated dictionary of over 5000 mathematical
terms. The 2005 Maple 10 version offers enhanced interface
and document generation functions.
Gibson calculates that “as a rule of thumb, using
Maple takes up a third or even a quarter of the time it
would otherwise take for a validation. It's a very
fast calculator and its quick code enables you to enhance
existing capabilities”. Employing Maple’s technology
saves him time and reduces error.
He sums up thus: “Maple is complete with a wide palette
of mathematical capabilities. It is used in lots of fields.
Most problems in quantitative finance can be tackled by
the use of a Maple package because the system is so comprehensive.
I haven’t found a scenario where Maple cannot be
useful in some way”.
Some Specific Mathematical Functions Robert Gibson
uses Maple for:
Discrete Fourier Transform
Areas of quantitative finance such as computing transforms
require analysts to come up with a closed form of multivariate
distribution. The DFT technique is required to achieve
this. “This
would be close to impossible using pen and paper”.
Root Finding
Maple assists in root finder problems which might occur
for example within pricing credit default swaps. “
Maple allows a solution to be found quickly and with some
degree of robustness, and it is user friendly”.
Matrix Algebra
Maple also supports analysts in their generation and employment
of matrix algebra, in the solution of “
problems concerned with simulating or forecasting the behaviour
of many financial variables and to account for the comovements
between them”.
*This case study is based on a genuine case study, but
the name of the person has been changed and the company
name has been removed. This has been done to preserve the confidentiality
and security of our customer.
