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1、1,UNIVERSITY OF REGINAFACULTY OF ENGINEERINGMaster of Applied Science In Industrial Engineering“AN INFERENCE SYSTEM APPROACH TO FINANCIAL MODELING”Maria M.Ortiz LermaDr.Rene V.MayorgaFall 2003,2,Contents,Thesis Objective Introduction Technical AnalysisScenario AnalysisPortfolio SelectionConclusion,3
2、,Thesis Objective,The use of Intelligent Systems methodologies for the modeling of some systems behaviours characterized by highly non-linear relationships and having a high degree of uncertainty.In particular,the implementation of Artificial/Computational Intelligence and Soft Computing techniques
3、in some Financial Engineering(closely related to Operations Research)problems.,4,Proposed Methodology,Here,it is proposed a novel Framework to use Adaptive Neuro-Fuzzy Inference System(ANFIS);and Fuzzy Inference Systems(FIS)for market indicators and prices modeling,and Optimization tools based on Me
4、an-Variance method for portfolio(short term estimation)selection.In this framework it is necessary to consider three main components:,Technical AnalysisAdaptive Neuro-Fuzzy Inference System,Scenario AnalysisFuzzy Inference System,Portfolio SelectionOptimization tool,5,Introduction,Non-conventional T
5、echniques:Increasing literature on Fuzzy Inference Systems(FIS)and their use in Financial Engineering;Many of these examples are related to stock market trading,Deboeck(1994),and recently Tseng et al.(2001)integrate Fuzzy and ARIMA models to forecast the Taiwan/US exchange rate.Artificial Neural Net
6、works has been used as a tool for forecasting financial markets Peray(1999)determines an opportunity for equity fund investments using market fundamentals.,Conventional techniques:Optimization and Mean-Variance ModelAsymmetric risk measures for portfolio optimization under uncertainty(King,1993),and
7、 the arithmetic mean and the standard deviation of the different financial assets(Markowitz,1952,1987.Levy,1970),6,Introduction,Financial markets:Reasons of uncertainty Expansive fluctuations in prices over short and long termsEach model in portfolio selection has its own advantages and disadvantage
8、sMarket risk cannot be avoided with diversificationLarge number of deals produced by agents that act independently from each otherThe effective operation of the portfolio selection in practice requires an integrated decision support framework,7,Framework General Structure,ANFIS,FUZZY INFERENCE SYSTE
9、M,OPTIMIZA-TION,Inputs(ti),Outputs(ti+6),OutputsScenario(ti+6),Inputs,TECHNICAL ANALYSISSTAGE I,PRE-ANALYSIS,SCENARIO ANALYSISSTAGE II,PORTFOLIO SELECTIONSTAGE III,ANFIS,ANFIS,ANFIS,Inputs,Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti+6),Price(ti+6),Market indicator(ti),Market in
10、dicator(ti),Market indicator(ti),Price(ti),Very Optimistic,Optimistic,Very Pessimistic,Pessimistic,Weakly Pessimistic,Medium Pessimistic,Hold,Weakly Optimistic,Medium Optimistic,8,Technical Analysis:Stage I,ANFIS,FUZZY INFERENCE SYSTEM,OPTIMIZA-TION,Inputs(ti),Outputs(ti+6),OutputsScenario(ti+6),Inp
11、uts,TECHNICAL ANALYSISSTAGE I,PRE-ANALYSIS,SCENARIO ANALYSISSTAGE II,PORTFOLIO SELECTIONSTAGE III,ANFIS,ANFIS,ANFIS,Inputs,Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti+6),Price(ti+6),Market indicator(ti),Market indicator(ti),Market indicator(ti),Price(ti),Very Optimistic,Optimis
12、tic,Very Pessimistic,Pessimistic,Weakly Pessimistic,Medium Pessimistic,Hold,Weakly Optimistic,Medium Optimistic,Historical data from January 1st,1993 to August 29th,2003,9,Market indicators,a)Monetary,b)Sentiment,c)MomentumPricesRate of ChangeStochastic%KStochastic%D,10,Indexes,.,Dow Jones Average(D
13、OW)DJ 65 Composite Average:DJANew York Stock Exchange(NYSE)NYSE Financial:FNANational Association of Securities Dealers Automated Quotation System(NASDAQ)259 Telecommunications:IXUTU.S.Treasury securities(Yieldx10)30 year bond:TYX,11,ANFIS Process,Time Series:Mackey-Glass Differential Delay Equation
14、,Multidimensional input-output highly non-linear mapping,y=f(x).,The quantity of nodes,linear and non-linear parameters in the hidden layers is the same for each index,12,ANFIS Structure Information,13,ANFIS Process for Prices and Rate of Change in one index,N,N,N,N,x(t-18),R1(1),R1(2),x(t-12),R1(3)
15、,x(t-6),x(t),x(t+6),N,1,2,3,4,5,Price(ti+6)Y1(nT),R1(4),Price(ti)R1(nT),R(nT),Y(nT),N,N,N,N,x(t-18),R2(1),R2(2),x(t-12),R2(3),x(t-6),x(t),x(t+6),N,1,2,3,4,5,Rate of Change(ti+6)Y2(nT),R2(4),Rate of Change(ti)R2(nT),R(nT),Y(nT),x(t-18),x(t-12),x(t-6),and x(t)to predict x(t+6).,Inputs(ti),Outputs(ti+6
16、),Hidden Layers 1 2 3,14,ANFIS Modeling Results:NYSE Financial FNA,15,NYSE Financial FNA:Price and Rate of Change modeling,16,NYSE Financial FNA:Stochastic%K and%D modeling,17,ANFIS modeling results for Market Indicators and Price in ti+6,18,Scenario Analysis:Stage II,ANFIS,FUZZY INFERENCE SYSTEM,OP
17、TIMIZA-TION,Inputs(ti),OutputsScenario(ti+6),Inputs,TECHNICAL ANALYSISSTAGE I,PRE-ANALYSIS,SCENARIO ANALYSISSTAGE II,PORTFOLIO SELECTIONSTAGE III,ANFIS,ANFIS,ANFIS,Inputs,Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti),Market indicator
18、(ti),Market indicator(ti),Market indicator(ti),Very Optimistic,Optimistic,Very Pessimistic,Pessimistic,Weakly Pessimistic,Medium Pessimistic,Hold,Weakly Optimistic,Medium Optimistic,Inputs(ti+6),19,Fuzzy Inference System,18 fuzzy rules in the system Reasoning used to develop these fuzzy rules are st
19、atements such as:ScenarioIf the rate of change is large,(+)Optimisticthen the price is likely to move higherIf the stochastic%K is low,(-)Pessimisticthen the price is likely to move lower,1 0.5 0,20,Fuzzy Inference System,FUZZY INFERENCE SYSTEM,OUTPUTS SCENARIO(ti+6),INPUTS(ti+6),1.Very Pessimistic
20、2.Pessimistic3.Medium Pessimistic4.Weakly Pessimistic5.Hold6.Weakly Optimistic7.Medium Optimistic8.Optimistic9.Very Optimistic,FUZZY INFERENCE SYSTEM,FUZZY INFERENCE SYSTEM,FUZZY INFERENCE SYSTEM,1.Very low2.Low3.Medium low4.Weakly low 5.Stable6.Weakly large7.Medium Large8.Large9.Very large,Classifi
21、cation,21,Investment Scenario,22,Deffuzification for NFA,Defuzzification system for NFA index:inputs rules and output scenario,0 100,23,Investment Scenario for NFA,Weakly Optimistic scenario,NFA weakly optimistic scenario surface,24,Portfolio Selection:Stage III,ANFIS,FUZZY INFERENCE SYSTEM,OPTIMIZA
22、-TION,Inputs(ti),Outputs(ti+6),OutputsScenario(ti+6),Inputs,TECHNICAL ANALYSISSTAGE I,PRE-ANALYSIS,SCENARIO ANALYSISSTAGE II,PORTFOLIO SELECTIONSTAGE III,ANFIS,ANFIS,ANFIS,Input,Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti+6),Market indicator(ti),Market in
23、dicator(ti),Market indicator(ti),Market indicator(ti),Very Optimistic,Optimistic,Very Pessimistic,Pessimistic,Weakly Pessimistic,Medium Pessimistic,Hold,Weakly Optimistic,Medium Optimistic,25,Securities from NYSE Financial,26,Mean-Variance Criterion,General Optimization Problem,Optimal portfolio mus
24、t meet the following constraints:The sum of the portfolio weights must be equal to 1.The weight of each asset must be greater than or equal to zero.,Markowitz(1959)The return estimate is represented by the mean and asset risk is represented by the standard deviation,27,Portfolio Selection,Subject to
25、,Objective function,The monthly return rates and risk are calculated for each one of the 430 assets in accordance with the Mean-Variance modelMonthly data from January 2nd 1997 to September 2nd,2003,28,Returns and Standard Deviations of the Optimal Interval for the Portfolio Selection,29,Optimal Por
26、tfolio Selection,30,Conclusions,This is an innovative methodology,principaly,because of the use of Soft Computer technologies such as,Fuzzy Inference Systems(FIS),and Adaptive Neuro-Fuzzy Inference Systems(ANFIS).In addition,the originality of this work consists in the application of the simulated framework where before solving financial problems based on future security values in the short term,we construct a good representation of this future.,31,Thank you,
