introducing differential evolution-introduction to cuda programming in finance

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1、Chapter14IntroducingDifferentialEvolution14.1IntroductionWhilealmostanyproblemfoundineverydaylifecanbethoughtasanoptimisationproblem,wesawthatinclassicaleconomicstheagentdecisionmakingprocesswasrepresentedasthemaximisationofsomeexpectedutilityfunc-tions.Assumingrandomness,portfolioselectio

2、nandfairpricewereintroduced,suchasCAPMandBSformula,andquantitativeoptimisationtechniquescouldbeused.Further,econometricmodelsweredevisedtoforecastpriceprocessesinviewofeithercomputingtheCAPM/BSformula,or,takingadvantageofmarketinefficiencies.Intheformer,simplicityledtoasingleoptimalsolution

3、,whileinthelatter,complexityledtoarangeoffairvalues.Withthegrowingquantityofdataavailable,machinelearningmethodsthathavebeensuccessfullyappliedinsciencearenowappliedtominingthemarkets.Dataminingandmorerecentmachine-learningmethodologiesprovidearangeofgeneraltechniquesfortheclassification,pr

4、ediction,andoptimisationofstructuredandunstructureddata.Allofthesemethodsrequiretheuseofquantitativeoptimisationtechniquesknownasstochasticoptimisationalgorithms,suchascombinatorialoptimisation,simulatedannealing(SA),geneticalgorithms(GA),orreinforcedlearning.Whilestochasticmethodshavesome

5、degreeofrandomnesswhenoperating,heuristicmethodsincorporateadditionalstrate-giesorknowledgetotheiroperation.Someofthesealgorithmsuseheuristicsinspiredbyreallifeprocesses.Forinstance,geneticalgorithmsareinspiredbytheprocessofevolution,andsimulatedannealingisinspiredbythepro-cessofannealingm

6、etals.WearegoingtoconsideranEvolutionaryAlgorithm(EA)whichwewillillustratewiththeproblemofmodelcalibrationtoafinitesetofoptionprices.14.2Calibrationtoimpliedvolatility14.2.1Introducingcalibration14.2.1.1ThegeneralideaForeveryparametricmodelthatonecandefine,suchasregressionmodelsoroptionprici

7、ngmodels,weneedtoestimatethemodelparametersfromthemarketpricesortheimpliedvolatilitysurface.Itleadstoanill-posedinverseproblembecausetheinversionisnotstableandamplifiesmarketdataerrorsinthesolution.Tobemoreprecise,lettingxbethevectorofmodelparametersandybetheve