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Technical White Paper

Basle Capital AdequacyAccord with MathematicaThe Mathematica System—everything you need to build your Risk Management Platform!

MATHEMATICA AND MATHEMATICAL FINANCE i

Introduction

“We have no choice but to continue to plan for a successor to the simple risk-weighting approach to capital requirements embodied within the currentregulatory standard. While it is unclear at present exactly what that successormight be, it seems clear that adding more and more layers of arbitrary regulationwould be counter productive. We should, rather, look for ways to harnessmarket tools and market-like incentives wherever possible, by using banks’ ownpolicies, behaviors, and technologies in improving the supervisory process.”

Alan Greenspan, 1998

The Basle Capital Adequacy Accord marks a major milestone of banking regulation. Companies arerequired to cushion the risks of their business activities with appropriate allocations of risk capitalwhile having great methodological freedoms to determine the amount of economic risk capital.Increasing sophistication of markets and products, competitive forces, globalization, and collidinginterests of various stakeholders such as board members, customers, employees, investors, supervi-sory agencies, and creditors necessitate a balancing act between efficient use of capital and prudentcapital allocation to cover these business risks. This requires first and foremost the development ofappropriate risk models to identify and quantify all significant risks accurately.

To meet the requirements of the Capital Accord, companies need to perform a detailed evaluation oftheir existing risk management principles, regulatory systems, and processes. They have to recog-nize and implement the changes necessary to fulfill the risk management and reporting obligationsin a timely and accurate way. They also have to provide capital to support the regulatory framework.

The new regulation provides a spectrum of approaches, from simple to advanced methodologies, forthe measurement of credit, operational, and market risks and the determination of capital allocations.Compliance with the new regulation will present companies with significant issues and challenges,particularly as there is no standard approach prescribed, and no particular framework mandated forits effective management.

Functionalities of a comprehensive risk management system.

The Basle Accord has established Value-at-Risk (VaR) and Stress Testing as the basis for the esti-mation of economic capital to cover market risk. Most companies opt to utilize the VaR approachinstead of following the Capital Accord’s “bucket approach” to quantify the economic risks inherentin their business transactions. These, however, present enormous data and computation challenges.

User Functionality Business Specific Technical

• Front End Interface • Counterparty Credit • Data Supplier Interface

• Limits • FASB 133 • Interface to Data Systems

• Model API • Fund of Fund Structure • OLE/DB Wrap

• Portfolio Hierarchy • Pension Liabilities • Software Package/ASP

• Report Writer • Real Estate • Systems Security

• Screening Filtering • Risk Arbitrage • User-Defined Fields

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Challenges, Approaches, and Technology

Several numerical schemes have been developed to manage the risks addressed by the Capital Accordat various levels and aggregations and across divers risk groupings, product types, and counterpartytypes. Large institutions, having thousands of customers, accounts, and institutional counter-parties,and transacting thousands of derivatives trades every day, face a set of huge computational tasks thatrequire the latest in computation technology. Especially very flexible methodologies, such as Monte-Carlo sampling that allow for the inclusion of nonlinearities and correlations, pose new challenges interms of data management and computing power.

A solid risk management system also includes stress testing to account for extreme unexpected marketmoves. To model stress scenarios realistically, nonparallel rate curve moves, correlations, volatilites,illiquidities, and skewness ought to be included in the stress testing. Further, a professional risk manage-ment system includes periodic backtesting to unearth the gaps between model results and actual resultsto improve the parameters of the model or reassess the risk management methodology.

Unexpected financial shocks.

1987 Stock Market Crash

1990 Nikkei Crash High Yield Tumbles

1992 European Currency Crisis

1994 U.S. Interest Rate Hike(1994-1995) Mexican Peso Crisis

1995 Latin American Crisis

1997 Asian Crisis

1998 Russian Crisis LTCM

1999 Brazil Crisis

2000 Tech Meltdown

2001 Tech Meltdown 9/11 Terrorist Attacks

MATHEMATICA AND MATHEMATICAL FINANCE 1

Differential Advantages of UsingMathematica as Your RiskManagement System

Market RiskCalculate your portfolios’ VaRs and Conditional Value-at-Risk (CVaRs):

Variance-Covariance:Use an analytic approach to build a vector of average daily changes in each parameter and a historicalvariance-covariance matrix with ultrafast numerics. Calculate a linear delta-approximation of yourportfolio with lightning speed, and include parameter correlations in the model for superior modelaccuracy. Measure the lowest q-quantile of the resulting P/L to any degree of precision.

Sample VaR calculation in Mathematica.

Historical Simulation:Value current holdings distribution free based on specified market conditions with Mathematica’sextremely fast data sampling methods. Handle “fat tails” (kurtosis, i.e. extreme event risk), asymmetricdistributions (skewness), and include nonlinearities in the model with ease.

Monte-Carlo Simulation:Include Mathematica standard features for an analytic approach to include nonlinearities by utilizing ajoint distribution of market changes. Draw thousands of scenarios randomly from the joint distributionand reprice the portfolio. Determine the lowest q-quantile to get the VaR.

MATHEMATICA AND MATHEMATICAL FINANCE 3

Technical White Paper

Credit RiskMathematica makes it easy to use the most advanced statistical packages for the identification of theexpected distribution frequency (EDF), probability of default (POD), as well as your expected andunexpected losses. You can use a comprehensive KMV™ model, access representative online creditdefault databases for unbiased market data, and include CreditMetrics™ transition matrices to modelthe defaults of your bond issuers. Mathematica lets you control credit allocations. You can conductfinancial analysis using state-of-the art graphical representations and develop credit scorecards usingdata mining techniques or fuzzy logic. With our tools you can track the credit exposure and creditmigrations you have to report to rating agencies and internal audit. Mathematica points out your riskconcentrations and performs collateral analysis to let you understand the aging of your receivables.

Mathematica classification plot of log-normally distributed samples.

Operational RiskYou have complete flexibility to model event risk, business risk, and other company-specific risks,either by utilizing your own business models or by including models supplied by vendors of yourchoice. Use operational risk methodologies such as AMA and Bayesian Networks to control theserisks. Mathematica’s extremely fast numerics functions allow you to model your losses due to oper-ational risk with tail-adjusted nonsymmetric distributions, truncations, closed-form solutions, andMonte-Carlo simulations. Multiple severity distributions can be used, and event scenarios can beset up. You can view results by cause, business unit, industry sector, or loss type, as identified inthe Basle working papers. The resulting loss distributions will provide operational Capital-at-Riskestimates at every confidence interval.

Mathematica plot of a family of parametrized log-normal distributions.

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4 MATHEMATICA AND MATHEMATICAL FINANCE

Additional Benefits of theMathematica Computation Platform• Single, unified platform simple enough for novices, powerful enough to keep pace with the high

demands of practitioners, and comprehensive enough to transcend asset classes, risk types, andcustomer segments across all departments.

• Customizable front end, supporting Mathematica, Excel, Java, and C user interfaces.

• Supports all standard data formats. Easy data access with CSV, XML, Java, real-time data feeds,or user-defined data formats. Virtually all data supplier interfaces are supported.

• Automatic report generation including graphics output and limit compliance.

• Full cross-platform compatibility.

• Extensive collection of add-on packages.

• Easy web publication through HTML, XML, and authoring tools.

Driver selection User Interface with Mathematica Data source selection User Interface with MathematicaDatabase Access Kit. Database Access Kit.

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Technical White Paper

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Option trading and risk management screen in Mathematica.

Various examples of Time Series and Technical Analysis Graphs in Mathematica. Various calculation outputs in Mathematica.

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