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Maple™, from Maplesoft™ is an advanced mathematics software extensively used in the research, engineering, and academic fields. With its vast functional libraries for symbolic and numeric computation, combined with an intuitive graphical interface, Maple offers finance professionals an ideal platform to develop, design, and implement solutions for various problems. These include visualization and pricing of an interest rate option with stochastic volatility or finding a particular solution to a jump-diffusion PDE. The tool has been used for many years at Mitsubishi UFJ Securities International, a large investment bank headquartered in London, England.

Igor Hlivka, Co-Head of the Quantitative Analytics Group at Mitsubishi UFJ Securities International plc, has been using the package for the last 10 years at various stages of financial product modelling, design, prototyping, and implementation.

Since modern finance theory draws heavily from theorems, rules and methods of mathematical physics, probability and statistics, Maple is ideally positioned and thoroughly equipped to assist financial modellers, developers, researchers, and structurers in finding the right answer to their needs and tasks. Many problems in finance focus on the notion of fair value, risk, or sensitivity. To get there, one needs to come up with a valuation model, find a set of input parameters, solve equations, and optimize the whole process for speed and accuracy. Equally important is to present, visualize, and document the work so that any user can intuitively understand it. This is where Maple becomes particularly effective.

Hlivka has been working with Maple predominantly in derivative product modelling and development where he relies heavily on Maple’s symbolic engine and refined numerical routines to assist him in complex modelling tasks.

“I have worked with a number of mathematics software packages; however, I found Maple the most comprehensive and best-structured product on the market,” said Hlivka. “My preference for Maple stems from the attributes I have discovered in it over years of active interaction. From my perspective, Maple is powerful, robust, flexible, intuitive, and user-friendly. I particularly appreciate Maple’s ability to prototype models quickly and effectively and use it as a benchmark for implementation work on other programming platforms. One can build a complex model or solution with just a few lines of Maple code and thoroughly document it too. This, for example, is all one needs to visualize and price an interest rate option with stochastic volatility.”

Below is an extract from his work in this area.

Visualization of an interest rate option with stochastic volatility

Maple is particularly useful when one requires frequent interaction with calculus (both functional and vector), linear algebra, probability and statistics routines, optimization, integral transforms, and all types of differential equations (ordinary, stochastic, and partial).

For example, finding a particular solution to a jump-diffusion PDE with Maple is not a difficult task:

Particular solution to a jump-diffusion PDE

“Although deriving a model’s price is an essential task, where Maple becomes truly competitive is at comparative static – differentiation of a model’s price with respect to various input variables,” continued Hlivka. “Obtaining CMT (Constant Maturity Treasury)Cash Management Treasury) first and second derivatives with respect to yield is not particularly easy. However, Maple returns an elegant answer that can be evaluated in arbitrary dimension.”

“What I like in Maple in particular is the intuitive logic. Maple knows how to handle sub-expressions and partial routines even if the process depends on numerical methods to solve it. I can still differentiate an option pricing formula with stochastic / jump-diffusion volatility, even though the final result is derived through numerical integration. That’s the clever and highly efficient implementation that makes Maple a versatile tool for financial engineers,” added Hlivka.

Maple’s appeal to finance professionals has been recently enhanced by two separate developments: (i) the introduction of a completely re-written Statistics package that was first introduced in Maple 10 and (ii) the launch of a new Finance Toolbox earlier this year.

“Maple’s Statistics package is the most comprehensive set of rules and routines in any general purpose math package,” explains Hlivka. “It provides the breadth and depth of probabilistic and statistical routines one needs in financial data analysis. On the other hand, the new Finance Toolbox is a selection of more than 100 new functions and routines designed for modelling, simulation, and pricing of almost every type of financial product currently traded in the market. With this new addition, Maplesoft has clearly positioned itself as a serious contender and the first choice solution provider in this market segment. With dedicated resources and qualified support, one may expect further enhancements.”

About Mitsubishi UFJ Securities International plc (“MUSI”)
MUSI is the English-incorporated European hub of the global securities and investment banking business of Mitsubishi UFJ Securities Co., Ltd. – itself part of the Mitsubishi UFJ Financial Group, the biggest financial institution in the world. MUSI is based in London, England with branches in Zurich, Frankfurt and Milan. It is active in most areas of the international capital markets, with particular specialities in debt, equity, derivatives, and structured products. It provides a wide range of services in the world-wide securities and derivatives business to governments, their monetary authorities and central banks, supra-national and sub-national organisations, private financial institutions (for example, banks and insurance funds), and corporations. The Company has a staff of approximately 600 people, based across its offices in London, Zurich, Frankfurt and Milan. MUSI is authorised and regulated by The Financial Services Authority (FSA) and is a member of the International Capital Markets Association (ICMA) and the Futures and Options Association (FOA). It is also an associate member of The International Swaps and Derivatives Association (ISDA).
Visit http://www.int.sc.mufg.jp to learn more.

Maplesoft offers powerful and easy-to-use tools that save time and reduce errors.
Maple™ is a powerful tool for solving complex mathematical problems and creating rich technical documents
Maple Toolbox for MATLAB® combines the best in symbolic and numeric computation to develop mathematical solutions
BlockBuilder™ for Simulink® is a First Principles physical modelling environment that offers automated export to Simulink
Maple Financial Modelling Toolbox complements Maple’s multi-disciplinary environment with over 100 new commands, designed specifically for quantitative financial modelling and analysis
MapleNet™ allows users to publish live Maple documents on the Web
The Professional Toolbox Series provides domain-specific tools that focus the core Maplesoft products on discipline-specific applications
We believe that if you use math, you need Maple. Click here to learn more.

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