Presentation is loading. Please wait.

Presentation is loading. Please wait.

Tools and components for optimisation and risk analysis Professor Gautam Mitra Presented to Clarifi, New York.

Similar presentations


Presentation on theme: "Tools and components for optimisation and risk analysis Professor Gautam Mitra Presented to Clarifi, New York."— Presentation transcript:

1 Tools and components for optimisation and risk analysis Professor Gautam Mitra Presented to Clarifi, New York.

2 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Solvers (FortMP / FortSP) –Linear / Mixed Integer (LP / IP) –Quadratic / Mixed (QP / QMIP) –Stochastic optimization (SP) –FortMP-MEX Matlab add-on Portfolio Optimisation model and engine Modelling Systems (AMPL Suite) –AMPL Studio –AMPL COM –AMPL SPInE Liability Determined Investment (LDI) / Asset and Liability Management ALM Outline

3 Solvers AMPL Suite LDI/ALM Porfolio Opt Solvers – FortMP FortMP is a large scale optimiser Rich functionality Robust solution algorithm [Math Programming Article] Solves medium to large models Not suitable for very large hyper sparse model Available in stand-alone and library versions

4 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Solvers - FortMP Barrier and sparse simplex algorithms Solves variable separable programming including special ordered sets of Type 1 and Type 2 (SOS1 and SOS2) problems Extends LP to process MIP problems –Branch and bound –Cutting planes –Pre processing techniques

5 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Solvers – FortMP/QP/QMIP FortMP processes quadratic programs (QP) and quadratic mixed integer programs (QMIP) using –Branch and bound –Branch and relax

6 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Solvers - FortSP Processes stochastic programming problems with recourse using –Benders decomposition (nested) –Stochastic decomposition In contrast to deterministic equivalent, these algorithms scale up

7 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Solvers – FortMP MEX Matlab environment add-in Permits the use of FortMPs rich and robust optimising functionalities directly from Matlab Ideal for rapid application prototyping and for using in research environment

8 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Portfolio Optimisation Model An optimum asset allocation strategy explores a return and risk (pareto) efficient frontier and in this respect is a two objective (linear return and quadratic risk) constrained optimisation problem. The Mean-Variance model is the basic portfolio optimisation model which –linear part is E[R x ] –risk measure is cov(R i,R j )

9 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Mean Variance model It can be expressed as a quadratic program (QP): max Can be refined adding more restriction on the choice of the assets

10 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Other restrictions Factor model subject to Index tracking model –where b j are normalized coefficients of the chosen benchmark portfolio

11 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Other restrictions Rebalancing model Threshold constraints where δ j are binary decision variables

12 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Other restrictions Cardinality constraints –at most C assets are held The last two constraints transforms the QP problem in QMIP Non linear transaction cost Segment 3 Segment 2 Segment 1 Segment 1: Steep initial cost or set up cost. Segment 2: Nearly linear incremental cost over a range. Segment 3: Steep increase in cost of the asset for large volumes of transaction.

13 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Models statistics Model Asset universe Cardinality limit No of Factors No of G.O. constraints Cfu50850815022556 Cfu5255255026579 Cfu10571,05750261,109 Cfu15331,53350261,614 Cfu95839,58350269,665 Elu2501,528250211,569 Msci1505,591150215,635 Msci7585575211,057 MsciE10054310024591 US505005026547 Ussa505005026547 Msci75sc85575211,057

14 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Models statistics Model Rows ColumnsNon-zerosQ-rowsQ-nzros Cfu508 2,117 2,79013,917530606 Cfu525 2,185 3,32016,215551701 Cfu1057 4,311 6,50231,4381,0831,233 Cfu1533 6,244 9,40746,1361,5591,709 Cfu9583 38,445 48,127242,9419,6099,759 Elu250 6,179 77,92236,4701,5491,623 Msci150 22,434 28,236135,1825,6125,702 Msci75 3,491 4,47320,255876950 MsciE100 2,249 3,40215,749567650 US50 2,078 2,62013,588526620 Ussa50 2,078 2,69213,732526620 Msci75sc 3,501 4,48321,083950

15 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Benchmarks Model CPLEXFortMP TimeFinal objectiveTimeFinal objective Cfu50821.06 -.21349129640e-2 3.58-.21357886E-02 Cfu525600.03 -.18568727790e-2 21.06-.18559756E-02 Cfu10577.87 -.45888022432e-2 15.39-.45887767E-02 Cfu1533152.64 -.26654366558e-2 121.72-.26657032E-02 Cfu95831102.10 0.29656464844e-1 180.11-.31311094E-02 Elu2501.40 0.97411801870e-1 7.590.97411804E-01 Msci150751.71 0.59109482779e-2 92.19-.11110079E-02 Msci75600.23 -.96858354537e-2 22.11-.96916174E-02 MsciE100600.01 -.20717965889e-2 21.63-.20881854E-02 US500.06 0.29570565523 0.270.29570565 Ussa50600.02 -.18411673090e-2 23.16-.18477797E-02 Msci75sc600.04 -.30444937767e-2 30.140.29694054 Results obtained using FortMPs accelerated heuristic functionality

16 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt AMPL Overview AMPL: comprehensive and powerful algebraic modelling language for linear and non-linear optimisation problems Optimal for rapid prototyping and model development Extended to express stochastic optimisation models (SAMPL)

17 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt AMPL Products Offer Data AMPL Models AMPL Interactive AMPL Studio AMPL COM Object C# / C++ / VB / VBA Application SAMPL/SPInE

18 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt AMPL Studio Integrated modelling system based on AMPL language. Benefits: –Rich and user-friendly graphical interface –Compact and easy database connection –Workspace management –Model (set / variables) explorer –Seamless integration through memory interaction with various solvers

19 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt AMPL Studio Menu Bar Editing Area Multifunctional Output Console Workspace and Model Explorer

20 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt AMPL-COM Object Object Oriented Component Library, based on Microsoft COM software technologies Rationale: –Utilise the features of a programming language and AMPL individually as well as in combination Benefits: –Enable to build powerful DSS applications –Hide Models from End Users –Accessible the full AMPL features within any major development environments

21 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt AMPL-COM Object AMPL Models Solvers Command Model VariablesConstraintsObjectivesOptions SolTime Solution Variable Constraint Objective

22 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt AMPL Studio-SPInE Seamlessly integrated into AMPL studio environment Extends AMPL language with constructs specific for modelling SP problems and interprets them Time Index Scenario Tree Structure Scenario Probabilities Scenario Index Probabilistic Constraints Stages Aggregations Random Parameters Parameters Indices Variables Constraints Objectives

23 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Liability Determined Investment (LDI) Asset and Liability Management (ALM)

24 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Scope and Purpose of LDI Modelling System Balance cash in-flow streams of asset returns and asset sales with cash out-flow streams of liability obligation as well as asset purchases Objective: maximise surplus wealth or terminal wealth at the end of the planning period: Surpluswealth=assets – PV(liabilities) – PV(goals)

25 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt LDI Tool Description Cash flow matching over a long planning horizon: up to 50 years or more Portfolio mix: mainly fixed income, derivatives (swaps) and if necessary equities

26 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt LDI Tool Description Multi-Objective: –Minimise PV01 Deviations (Deterministic) –Minimise Net PV Deviations (Stochastic) –Maximise Surplus Wealth –Minimise Initial Injected Cash –Minimise Member Contributions

27 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Solving the Decision Model The decision problem can be formulated and processed as: –LP/IP –SP with recourse –Chance Constrained Programming –Robust Optimisation

28 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Scenario tree structure

29 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Stochastic Features Scenario generation (User supplied): –Asset prices –Liabilities Ex-ante asset decisions Ex-post evaluation (Simulation)

30 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt LDI Information Flow RESULTS Simulation and visualization to RISKWATCH Market Data RISKWATCH + Data Builder Information Data Sources RISKWATCH + Customer Data Builder POPULATE DATA Consolidator + Diagnostic DATA MART #.TAB AMPL Modelling Environment [AMPL Com Object + LDI Model File + #.DAT File + #.RUN File] Optimisers - FortMP - CPLEX MODEL DATA

31 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt LDI Project Control

32 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt LDI Information Flow Market Data RISKWATCH + Data Builder Information Data Sources RISKWATCH + Customer Data Builder POPULATE DATA Consolidator + Diagnostic DATA MART #.TAB RESULTS Simulation and visualization to RISKWATCH AMPL Modelling Environment [AMPL Com Object + LDI Model File + #.DAT File + #.RUN File] Optimisers - FortMP - CPLEX MODEL DATA

33 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt LDI Optimising Engine

34 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt LDI Information Flow Market Data RISKWATCH + Data Builder Information Data Sources RISKWATCH + Customer Data Builder POPULATE DATA Consolidator + Diagnostic DATA MART #.TAB AMPL Modelling Environment [AMPL Com Object + LDI Model File + #.DAT File + #.RUN File] Optimisers - FortMP - CPLEX RESULTS Simulation and visualization to RISKWATCH MODEL DATA

35 Outline Solvers AMPL Suite LDI/ALM Porfolio Opt Simulation and analysis


Download ppt "Tools and components for optimisation and risk analysis Professor Gautam Mitra Presented to Clarifi, New York."

Similar presentations


Ads by Google