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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 problem-solving 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 problem-solving 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 problem-solving software capable of rigorous mathematical computations.

Developed and tested in context over the past twenty-five 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 error-free 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 difficult-to-manage computations, some of which would otherwise have to be carried out manually. He describes how “Maple is a powerful problem-solving 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 built-in functions”.

Maple’s intuitive and easy-to-use 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 co-movements 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.