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Introduction to Computational Finance
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Computational financeChaiyakorn [email protected] June 2013 Chulalongkorn University1OutlineWhat is Computational Finance / Why we need it?Techniques in Computational FinanceCase Study: Algorithmic TradingConclusion
In the past decade we seenAn explosive growth in financial market
3In the past decade we seenAn explosive growth in financial marketIncreasing power of computers
4In the past decade we seenAn explosive growth in financial marketIncreasing power of computersRapid exchange of information via the Internet5These give raise to Computation Finance
A cross disciplinary field that utilizes computational methods to solve problem in finance and economics
6Why Computational Finance? Business Reason
More profitFaster Less LabourProcessing powerAvailable amount of financial data Why Computational Finance? Academic ReasonUse traditional statistics and analytical methodsMake several assumptions to simplify the problemTraditional Methods
Computational FinanceUse modern computational methodsMake as less assumptions as possibleModern approximation techniques to solve complex problemModern data analysis techniques to model complex dataLog-ReturnProbabilityHappened once in< -6.00%1.98 x 10-550,364 days < -7.00%8.31 x 10-71,202,951days < -8.00%2.22 x 10-844,983,759 daysLog return of SET index1975 2013 9,360 Samplesmean = 2.93 x 10-4s.d. = 1.47 x 10-28OutlineWhat is Computational Finance / Why we need it?Techniques in Computational FinanceCase Study: Algorithmic TradingConclusion
Common Techniques in CFOptimizationRegressionClassification
Optimization ProblemFind the best variables satisfying a given constraints that maximize (minimize) the objective functionxf(x)solution constraint variablesAnalytical ApproachFirst order condition, Lagrange Multipliers Numerical AnalysisGradient decent, Simplex AlgorithmArtificial IntelligenceGenetic Algorithm, Ant Colony OptimizationReinforcement learning
Regression ProblemLearn to imitate a function y = f(X) from a finite set of noisy example { (X1,y1), (X2, y2), }
Traditional ApproachLinear regression, ARMA ModelComputational StatisticsGaussian processesArtificial IntelligenceNeural Network, Support Vector RegressionGenetic Programming
Traditional Methodlinear regressionlogistic regressionComputational Statisticsbayesian methodsArtificial Intelligence neural networksupport vector machinegenetic programming
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Classification ProblemLearn to imitate a function y = f(X) to classify an object X into k predefined categoriesTraditional ApproachProbit/Logit ModelComputational StatisticsBayesian ClassifierArtificial IntelligenceDecision Tree, k-Nearest Neighbor Neural Network, Support Vector Machine
Decision TreeGenetic ProgrammingFirst-order learningBayesian ClassifierArtificial Neural NetworkSupport Vector Machinek-Nearest Neighbor Classification13OutlineWhat is Computational Finance / Why we need it?Techniques in Computational FinanceCase Study: Algorithmic TradingConclusion
Case Study: Algorithmic TradingStock SelectionTraditional ApproachFundamental AnalysisTechnical AnalysisComputational Finance ApproachRegressionClassificationStock Selection: Traditional ApproachPrice & Volume
ChartsShort-termTradingBuy if the trend is upQuantitative & Qualitative factorFinancial StatementLong-termInvestingBuy if current price is less than fundamental valueTechnical AnalysisFundamental AnalysisFocus
DataTimeGoalCriteriaStock Selection: CF ApproachFundamental & Technical DataFuture returns
Buy if future return > th
Fundamental & Technical DataWhether stock will have more than k% return in the next d days or notBuy if it is more likely to has k% return
RegressionClassificationInput
Output
CriteriaPortfolio Optimization: Mean Variance Optimization FrameworkAssumptionThe return of each asset is a random variableInputExpected return of each asset R The correlation matrix between these asset Risk tolerance parameter OutputThe weight that we should invest in each asset wi
Mathematical model
cardinality constraint19Trade Execution: Trade ScheduleSell the shares immediatelySplitting the order into smaller one and executed it over timeVolumeBidOfferVolume2,00030.0030.504,5005,00029.9030.606,0008,00029.8030.707,5009,50029.7030.808,000How to sell 60,000 shares in 1 hours?20Trade Execution: Trade ScheduleHow to sell 60,000 shares in 1 hours?
21Trade Execution: Trade ScheduleAssumptionAsset price follow arithmetic random walkInputTime frame Volatility of the asset Price impact function g(ni/)Total number of share to trade XOutputNumber of shares to trade in each period ni
22ConclusionComputational Finance is a cross disciplinary field that utilizes computational methods to solve problem in finance and economicsCommon techniques include optimization, regression and classificationExample applications include Algorithmic Trading, Financial Forecasting, Bankruptcy Prediction and Credit Rating