emerging architecture of tools and components for quantitative modeling and decision support

EMERGING ARCHITECTURE OF TOOLS AND EMERGING ARCHITECTURE OF TOOLS AND COMPONENTS FOR QUANTITATIVE MODELING COMPONENTS FOR QUANTITATIVE MODELING

AND DECISION SUPPORTAND DECISION SUPPORT

Presented To:Presented To:““Landelijk Netwerk Mathematische Besliskunde” Landelijk Netwerk Mathematische Besliskunde”

(LNMB) and the (LNMB) and the “Nederlands Genootschap voor Besliskunde” “Nederlands Genootschap voor Besliskunde”

(NGB)(NGB)16 January 2003 16 January 2003

Gautam MitraGautam MitraCARISMACARISMA

Department of Mathematical Sciences, Brunel Department of Mathematical Sciences, Brunel UniversityUniversity

andandOptiRisK SystemsOptiRisK Systems

EMERGING ARCHITECTURE OF TOOLS AND EMERGING ARCHITECTURE OF TOOLS AND COMPONENTS FOR QUANTITATIVE MODELING COMPONENTS FOR QUANTITATIVE MODELING

AND DECISION SUPPORTAND DECISION SUPPORT

Supported by researchers and colleagues including:Supported by researchers and colleagues including:

E F D Ellison, C A Lucas, N Jobst, P Valente, E F D Ellison, C A Lucas, N Jobst, P Valente, N S Koutsoukis, C Poojari, B Dominguez-Ballesteros, N S Koutsoukis, C Poojari, B Dominguez-Ballesteros,

T Kyriakis, A Mirhassani, G BirbilisT Kyriakis, A Mirhassani, G Birbilis

AcknowledgementAcknowledgementUK Research Council: EPSRC and UK GovtUK Research Council: EPSRC and UK Govt

Industrial sponsors include:Industrial sponsors include:Fidelity Investments, APT Inc., UBS Warburg, Unilever Fidelity Investments, APT Inc., UBS Warburg, Unilever

Research, EU sponsored: OSP CRAFT , SCHUMANN project Research, EU sponsored: OSP CRAFT , SCHUMANN project (Daimler Chrysler, Ford Spain, Yamanouchi BV, Iberinco, LCP)(Daimler Chrysler, Ford Spain, Yamanouchi BV, Iberinco, LCP)

OutlineOutline1. Introduction and Background1. Introduction and Background2. A historical /skills perspective2. A historical /skills perspective3. An information systems perspective3. An information systems perspective4. Mix and Match Models 4. Mix and Match Models 5. Illustrative Applications5. Illustrative Applications6. DSS and IS Connections6. DSS and IS Connections7. A Web perspective7. A Web perspective8. Discussions8. Discussions

InformationSystems

ComputationalOptimisation

LinearProgramming

InteriorPoint

Method

IntegerProgramming Constraint

Satisfaction

LP Modelling

Modelling

SparseSimplex

Branch & BoundPolyhedral CP

IP Models

Preprocessing Algebraic LPLanguage

Solution Systems Knowledge Systems

Parallel platforms

1. Introduction and Background1. Introduction and Background

Risk Decisions

StochasticProgramming

MPG to CARISMAMPG to CARISMA

Convergent activities/developmentsConvergent activities/developments

• CARISMA CARISMA The Centre for the Analysis of Risk and Optimisation Modelling Applications

• SPInE: Stochastic Programing Integrated Environment

• BOOK: Interaction of information systems and decision technologies.by Nikitas S Koutsoukis and Gautam Mitra, Kluwer.

• OSP-CRAFT and WEBOPT: Optimisation Services provision over the net


The mission of CARISMA is to be a The mission of CARISMA is to be a centrecentre of excellence of excellence recognised for its research and scholarship in the following:recognised for its research and scholarship in the following:

Mission of CARISMAMission of CARISMA

the analysis of risk,the analysis of risk, optimisation modelling,optimisation modelling, the combined paradigm of risk and return the combined paradigm of risk and return

quantification.quantification.

Industry FocusIndustry FocusFinance Industry - Bank, Insurance, Pension FundsFinance Industry - Bank, Insurance, Pension FundsLarge Corporates - FTSE 100, Multinationals, EUROTOPLarge Corporates - FTSE 100, Multinationals, EUROTOPPublic Sector/Utilities, Environment, Food, Agriculture, Public Sector/Utilities, Environment, Food, Agriculture, HealthHealth


Director: Professor Gautam Mitra

Deputy Director: Professor Christos Ioannidis

Faculty members: 7 professors and 5 lecturers

Research Associates : 4

Ph.D. Students: 16

Research Lecturers: Paresh Date, Fabio Spagnolo, Chandra Poojari

Newly approved open positions :Research professor in Risk Modelling and Research Lecturer in Financial Risk

The Faculty1. Introduction and Background1. Introduction and Background

Nineties to theCurrent Century

Seventies &Eighties

Fifties & Sixties

Computer-based DecisionSupport System

(Application Generation)

Computer-basedModelling of Optimisation

Problem

Computation and Solutionof Optimisation Problem

2. A historical /skills perspective2. A historical /skills perspective

Decision-Maker

ModelSpecialist -Analyst,Database expert

Solving Expert

Analytic Database, SolutionAnalysis, Reporting:

high interaction with users

Algebraic Form Modelling,Data Modelling:

medium interaction with users

Solution:low Interaction with users

Domain Expert

Constituents and their interactionConstituents and their interaction


Skills RequirementSkills Requirement– Algorithm design and tuning Algorithm design and tuning – Software engineering and testingSoftware engineering and testing– Information engineeringInformation engineering– Domain expertiseDomain expertise

Financial engineeringFinancial engineering Logistics and supply chainLogistics and supply chain Transportation planning and schedulingTransportation planning and scheduling

– Project development (solutions/applications)Project development (solutions/applications) Proof of concept Proof of concept quick win quick win deployment deployment (System integrators)(System integrators)


OutlineOutline1. Introduction and Background1. Introduction and Background2. A historical /skills perspective2. A historical /skills perspective3. An information systems 3. An information systems

perspectiveperspective4. Mix and Match Models 4. Mix and Match Models 5. Illustrative Applications5. Illustrative Applications6. DSS and IS Connections6. DSS and IS Connections7. A Web perspective7. A Web perspective8. Discussions8. Discussions

Information and Decision TechnologiesInformation and Decision Technologies

Business Intelligence: Competitive Advantage

Middleware

Middleware

Decision Modelling

Analytic Database

Data Mining, KDD

Production Database

3. An information systems perspective3. An information systems perspective

14

Information &Information & Knowledge: The Value Chain Knowledge: The Value Chain

EIS, OLAP

Production Database

Data Analysis & Synthesis

Analytic Database

Information Application of Models

Knowledge

DeploymentDeployment

INFORMATION CONSUMERSINFORMATION CONSUMERS

Desktopsoftware

Browser

Browser

Browser

WebWebServerServer

Paper Reports

Extract

Cleanse

Impute

Transform

Calculate

Enrich

Manage

Load

DataDatapreparationpreparation

Legacy Legacy databasesdatabases

Data collection software

External data

ERP systems

Other transaction

systems

Functional department

systems

DataDatasourcessources

KNOWLEDGEKNOWLEDGEWORKERSWORKERSDescription

SummarizationPattern

recognitionException detection

SegmentationClassification

ProfilingScoring

ForecastingSimulation

Optimization

MODEL MODEL BUILDERSBUILDERS

Data analysis Data analysis & data mining& data mining

DataDatastoragestorage

DataDatamartmart

DataDatamartmart

DataDatawarehousewarehouse

OLAP and MultidimensionalOLAP and MultidimensionalViewing: Main featuresViewing: Main features

Multidimensionality = DataMultidimensionality = Data

OutlineOutline1. Introduction and Background1. Introduction and Background2. A historical /skills perspective2. A historical /skills perspective3. An information systems perspective3. An information systems perspective4. Mix and Match Models4. Mix and Match Models 5. Illustrative Applications5. Illustrative Applications6. DSS and IS Connections6. DSS and IS Connections7. A Web perspective7. A Web perspective8. Discussions8. Discussions

Modelling SPModelling SP

STOCHASTIC PROGRAMMING

MODELLING

Modelling distribution of random variables

Optimum AllocationModelling

- Scenario Analysis- Expected Value- Two Stage RP- Multistage RP- Chance Constrained Problems- Others

Event treeEvent tree Historical data 1978 – 1996Historical data 1978 – 1996 1 year horizon divided in 4 quarters1 year horizon divided in 4 quarters

t=1 t=2 t=3 t=4

Scenario GenerationScenario Generation

Dividend yields

Liabilities Cash Bonds Stock prices

Historical data

Long run interest rates

Short run interest rates

Consumer price index

Extended Syntax for AMLsExtended Syntax for AMLs

Consider SP models as refinement of Consider SP models as refinement of deterministic problems by introduction of deterministic problems by introduction of uncertaintyuncertainty

SP models identify:SP models identify:– An underlying deterministic model (core)An underlying deterministic model (core)– Information related to the randomness of the model Information related to the randomness of the model

(stochastic framework)(stochastic framework)

Time index

Stages aggregations

Scenario tree structure

Scenario index

Random parameters

Scenario probabilities

Probabilistic constraints

SP Modelling ConstructsSP Modelling Constructs

Indices

Objectives

Constraints

Variables

Parameters

Scenario Generation and SP Scenario Generation and SP ModellingModelling

Model of randomness

Scenarioset

SP recourse model

(requires tree structure):

’

H

’ H

: Scenario tree structure : SP model tree structure : Model of randomness : Other parameters of : Historical data : Set of scenarios

Consistency condition:

’

ALM model in SPInE: solutionALM model in SPInE: solution

EV WS HN VSS EVPI 151072.86 341025.08 195006.06 Infinite 146019.02

Value at RiskValue at Risk Finance industry has introduced Value at Risk

(VAR) also known as the β-var.

}),(:min{),( :function quantile

),(),( :functiony probabilit),(

xx

dyyxpxyxr

-fractile

return r(x,y)

VaR ComputationVaR Computation

Optimisation scenarios

Simulation scenarios

HN solut ion EV solut ion

HN VaR EV VaR

ALM optimisation

model

VaR simulat ion

model

Fix 1st stage Solve WS

SPInE

Excel

VaR ResultsVaR Results

0

10

20

30

40

50

60

70

80

90

6655

0.50

1017

92.4

0

1370

34.3

0

1722

76.2

0

2075

18.1

0

2427

60.0

0

2780

01.9

0

3132

43.8

0

3484

85.7

0

3837

27.6

0

4189

69.5

0

4542

11.4

0

4894

53.3

0

5246

95.2

0

5599

37.1

0

5951

79.0

0

Expected Wealth

Freq

uenc

yHNEV

Implemented Solution VaRHN 131638EV 82565

Supply Chain ApplicationSupply Chain Application

Stochastic ProgrammingStochastic ProgrammingSupply Chain Model 1Supply Chain Model 1

ProductionProduction(PR)(PR)

Customer Customer Zones (CZ)Zones (CZ)

DistributionDistributionCentres (DC)Centres (DC)

Packing (PC)Packing (PC)

Outsourced suppliers

Subassembly dealers

Distributor

Distributor

Customer

Customer

Outsourced suppliers Subassembly

dealers

Assembly Line

Assembly Line

Production Line

Production Line

Raw Materials

Raw Materials

Manufacturing Assembling

Stochastic ProgrammingStochastic Programming

Supply Chain Model 2Supply Chain Model 2

Stochastic Programming with recourse Stochastic Programming with recourse models are models are ideally suited .. two perspectivesideally suited .. two perspectives– (near) optimum resource allocation(near) optimum resource allocation– hedge against uncertain future outcomeshedge against uncertain future outcomes– Decisions not optimum for any one outcome, good for Decisions not optimum for any one outcome, good for

many outcomes !many outcomes ! Two stage modelsTwo stage models

– First Stage: ‘ Here-and-Now’ asset allocation decisions First Stage: ‘ Here-and-Now’ asset allocation decisions … takes into consideration scenarios(outcomes)… takes into consideration scenarios(outcomes)

– Second Stage: Recourse decisions optimal corrective Second Stage: Recourse decisions optimal corrective actions as future unfolds… actions as future unfolds…


Stochastic ProgrammingStochastic ProgrammingModel and data instancesModel and data instances

Network Components Dimensions

The number of Sites, I : 8

The types of packing line technology, YC: 4

The types of production line technology, YR: 2

The number of distribution centres , J : 15

The types of DC line technology , YD: 2

The number of Customer Zones , H : 30

The number of Products , P : 13

The number of time periods, T : 6

Model Statistics

Logical Constraints:

Sites, DCs opening and closing, Limit on

number of Sites, DCs, and Lines

968

Mixed

850Other Constraints: Production,

Packing, Ordering,

Transportation, Balance,

Demand, and also Production

and Packing Capacities.Continuous

4950

6768

Discrete Decision Variables:

Sites, DCs, Production lines, Packing lines,

DC lines.

2096

Continuous Variables:

Production, Packing, Ordering,

Transportation, and Shortage quantities.

54400 56496

Non zeroes 1154034Scenarios: 100Scenarios: 100

Portfolio ApplicationPortfolio Application

Construct decision models which capture return and risk (due to uncertainty)

Combine models of optimum resource allocation and models of randomness

Uncertainty… optimum Uncertainty… optimum decisionsdecisions

Modelling approachModelling approach

HISTORICAL / TRANSACTIONAL

DATA

SUB-MODELS OF RANDOMNESS

DETERMINISTIC MODEL

HEDGED DECISIONS

SCENARIOS / UNCERTAINTY

LINEAR REPRESENTATION

OPTIMISATION / UNCERTAINTY

QP, SP, CP

OPTIMISATION

RISK AVERSION

Information Systems…Data Information Systems…Data martsmarts

Transactional Database

Information Analysis Models

Portfolio Models

Data Mart

Decision Database

Analytical Database

Information Systems…Information Systems…DatamartsDatamarts

Information Analysis Models

Pre-analysis Model Data Parameters

Solution Analysis Post-analysis

Performance Indicators

Style AnalysisFinancial Ratios

CAPMAPT

Simulation ModelsInternal Company

Models

Historical dataWeighted Moving

AverageFactor ModelsTime Series

ModelsARCH, GARCH,…Neural Networks

Genetic AlgorithmsKalman Filters

ChaosInternal Company

Models

What if AnalysisScenario Analysis

SimulationBacktesting

Internal Company Models

Performance Indicators

Risk Statistics and Indices

Financial RatiosCAPMAPT

Simulation ModelsRisk Metrics

Internal Company Models

Information Systems…Data martsInformation Systems…Data marts

Data MartProduction Database

Internal Data:Portfolios, Cashflows...

Market Data:Historical Prices

Analytical Models

Optimisation Engine

Solver

Modelling System

Portfolio Optimisation Model

Continuous or Discrete

User Input:Risk Aversion,

Target Portfolio Return ..

Pre-Analytical Database

Pre Analytics:Styles, Risk Statistics, Financial

Ratios ...

Model Data Parameters:Average Return

Var/Cov Matrix ...

Decision Database

Optimisation Results:Portfolio Returns, Potfolio Risk,

Optimum Asset Mix

Post-Analytical Database

Results Analytics:What if, Different objectives...

Post Analytics:Backtesting, Risk Analysis...

Analytical Models

Model/Results ExplanationModel/Results Explanation

11 22 33 44

Supply ChainSupply ChainCost ($)Cost ($)

Customer Service Customer Service measured in measured in maximal delivery maximal delivery time (days)time (days)

EfficientEfficientFrontierFrontier

CC

BB11

AA

BB22

BB

Financial RisksFinancial Risks

RISK

RET

UR

N Markowitz (Nobel Prize)Markowitz (Nobel Prize)

– Mean variance (M-V Theory)Mean variance (M-V Theory)– Diversification through Diversification through

‘not strongly correlated assets’‘not strongly correlated assets’

Portfolio Holdings dataPortfolio Holdings data

Portfolio Benchmark Difference

x(i) b(i) d(i)

Totals = 100% 100% 0%

Stocks = 50% 60% -10%

Bonds = 40% 40% 0%

Cash = 10% 0% 10%

Aknowledgment to Alpha StrategiesAknowledgment to Alpha Strategies

Absolute Volatilities & Absolute Volatilities & CorrelationsCorrelations

Stocks Bonds Cash

Std. dev. 15.00 8.00 0.00

15.00 1.00 0.40 0.00

8.00 0.40 1.00 0.00

0.00 0.00 0.00 1.00

Absolute Volatility & Correlation Matrix


The Algebra of Risk The Algebra of Risk DecompositionDecomposition

We begin by breaking down the total We begin by breaking down the total variance of a portfolio into contributions variance of a portfolio into contributions from individual holdingsfrom individual holdings

We haveWe have

From which we derive individual From which we derive individual contributions to variance ascontributions to variance as

ijjij

N

i

N

p CxxV

ijjij

N

i CxxACV


Contributions from Groups Contributions from Groups of Holdingsof Holdings

We can generalise these expressions We can generalise these expressions from individual holdings to groups of from individual holdings to groups of holdings as follows :-holdings as follows :-

iEnergyiEnergy ACVACV

%PCV%PCV iEnergyiEnergy


Marginal Contributions to Marginal Contributions to RiskRisk

MCV(i) = 2.634

MCV(i) = 0.992

MCV(i) = 0.000

Marginal Contributions to Portfolio Variance

Stocks

Bonds

Cash

MCR(i) = 0.142

MCR(i) = 0.054

MCR(i) = 0.000

Marginal Contributions to Portfolio Risk

Stocks

Bonds

Cash


Summary of Absolute Summary of Absolute DecompositionDecomposition

Holding x(i) S(i) C(i,P) = ACV(i) = PCV(i) = MCV(i) = MCR(i) = Corr(i,P)

Stocks 50% 15.00 131.70 65.85 77% 2.634 0.142 0.948 1.54 1.54

Bonds 40% 8.00 49.60 19.84 23% 0.992 0.054 0.670 0.58 0.58

Cash 10% 0.00 0.00 0.00 0% 0.000 0.000 0.000 0.00 0.00

Portfolio 100% 85.69 100% 1.00 1.00

V(p) = 85.69 S(p) = 9.26

= Beta(i,P)

(C(i,P)/100) / (S(p)

PCV(i) / x(i)

C(i,P) / (S(i)*S(p))

100*ACV(i) / V(p)x(i) * C(i,P) 2 * C(i,P)

/ 100

Absolute Risk Decomposition by Holdings - Portfolio

C(i,P) / V(p)Formulae =

Portfolio variance = Portfolio risk (s.d.) =


Traditional Optimisation-Traditional Optimisation-based DSSbased DSS

Traditionally, optimisation applications comprise Traditionally, optimisation applications comprise models, the optimiser, and a data mart, connected via models, the optimiser, and a data mart, connected via a model management system.a model management system.

Data Mart

Models

Modelling SystemComputationAlgorithms:Solutions

End-UserApplication

Typical Optimisation

Decision Support System

A typical Optimisation A typical Optimisation SolutionSolution

Data Mart

Models

Modelling SystemComputation:AlgorithmicSolutions

End-UserApplication

End-User Interaction with System

Training

Consultancy

Analyst Interaction

R & D

Specialist Interaction

Access to ToolsAccess to Tools

Internet,WAN,

Other NET

End User

End User

End User Groups

End User Groups

Models

Modelling Systems

ComputationTools

Data MartTechnology

Access to Vertical Access to Vertical Solutions/DSSSolutions/DSS

Data Mart

Models

Modelling System

Computation:AlgorithmicSolutionsEnd-User

Application

Data Mart

Models

Modelling System

Computation:AlgorithmicSolutions

End-UserApplication

DSS 1DSS 1

DSS 2DSS 2

Internet,WAN,

Other NET

End User

End User

End User Groups

End User Groups

Discussion 1Discussion 1 OR software tools and components are OR software tools and components are

developed to developed to – Respond to business needsRespond to business needs– Incorporate current technology platformsIncorporate current technology platforms

Different skill sets are required to bring together Different skill sets are required to bring together technology solutionstechnology solutions

New developments inNew developments inRisk modelling and risk management bring simulationa Risk modelling and risk management bring simulationa

nd optimisation closernd optimisation closerRole of Model explanationRole of Model explanation

Web is ‘the’ preferred / chosen delivery platformWeb is ‘the’ preferred / chosen delivery platform

Discussion 2Discussion 2

Thank YouThank You for your attention …for your attention …any questions ? I would any questions ? I would

appreciate your feedback…appreciate your feedback…comments comments

www.carisma.brunel.ac.uk

www.optirisk-systems.com

http://www.carisma.brunel.ac.uk/

http://www.financewise.com/public/edit/riskm/rmcatindex.htm

emerging architecture of tools and components for quantitative modeling and decision support

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