heuristic optimization strategies in finance - an overviewcomisef.eu/files/marianna.pdf ·...
TRANSCRIPT
![Page 1: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/1.jpg)
logo
Heuristic Optimization Strategies inFinance - An Overview
Marianna Lyra
COMISEF Fellows’ Workshop: Numerical Methods and Optimization in Finance
Financial support from the EU Commission through COMISEF is gratefullyacknowledged
June 18, 2009
![Page 2: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/2.jpg)
logo
Marianna LyraEarly Stage Researcher - COMISEFResearch Network
1 BA Business Administration -minor Finance, UCY
2 MSc Finance, UCY3 PhD student JLU Giessen, DE4 Research Interests: Apply
Optimization Heuristics inFinance (Credit RiskManagement)
5 Contact Info:http://comisef.wikidot.com/mariannalyra
![Page 3: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/3.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
1 IntroductionFinancial WorldComplexity
2 Heuristic Optimization TechniquesClassical conceptDifferential Evolution
3 Financial ApplicationsOptimization heuristic strategies in finance
4 ConclusionHave in mind
![Page 4: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/4.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
1 IntroductionFinancial WorldComplexity
2 Heuristic Optimization TechniquesClassical conceptDifferential Evolution
3 Financial ApplicationsOptimization heuristic strategies in finance
4 ConclusionHave in mind
![Page 5: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/5.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Financial World
Financial world
Optimization
Financial problems
![Page 6: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/6.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Complexity
Least median of squares residuals as a function of α and β
Multiple local minima (optima)Apply optimization heuristic techniques
![Page 7: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/7.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
1 IntroductionFinancial WorldComplexity
2 Heuristic Optimization TechniquesClassical conceptDifferential Evolution
3 Financial ApplicationsOptimization heuristic strategies in finance
4 ConclusionHave in mind
![Page 8: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/8.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Classical concept
Local search procedure
1: Generate initial solution xc
2: while stopping criteria not met do3: Select xn ∈ N (xc) (neighbor to current solution)4: if f (xn) < f (xc) then5: xc = xn
6: end if7: end while
![Page 9: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/9.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Classical concept
Heuristic Techniques
uulllllllllllll
))RRRRRRRRRRRRRR
_ _ _ _ _ _��
��
_ _ _ _ _ _Construction methods Local search methods
Trajectory methodsmmmmmm
vvmmmmm Population searchOOO
OOO
''OOOO
Thresholdaccepting
���
Differentialevolution
���
Tabusearch
Geneticalgorithms
Hybrid Meta Heuristics
<<dd
![Page 10: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/10.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Classical concept
Heuristic Techniques
uulllllllllllll
))RRRRRRRRRRRRRR
_ _ _ _ _ _��
��_ _ _ _ _ _Construction methods Local search methods
Trajectory methodsnnnnnnn
wwnnnnnn Population search
PPPPPPP
((PPP
Thresholdaccepting
���
Differentialevolution
���
Tabusearch
Geneticalgorithms
Hybrid Meta Heuristics
99dd
![Page 11: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/11.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionPopulation based heuristic with remarkable performance incontinuous numerical problems.
Example
Capital Asset Pricing Model (CAPM): Risk-returnequilibrium.
ri,t − r st = α + β(rm,t − r s
t ) + εi,t (1)
Least Median of Squares Estimators (LMS) (Rousseeuwand Leroy (1987)):
minα,β
(med(ε2i,t)) (2)
![Page 12: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/12.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM usingLMS estimators
1 Generate random set values α and β (initialsolutions)
2 Evaluate initial solutions minimizing LMS3 Generate new candidate solutions from the
initial one4 Evaluate new candidate solutions minimizing
LMS5 Repeat until a very good solution is found
![Page 13: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/13.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM usingLMS estimators
1 Generate random set values α and β (initialsolutions)
2 Evaluate initial solutions minimizing LMS3 Generate new candidate solutions from the
initial one4 Evaluate new candidate solutions minimizing
LMS5 Repeat until a very good solution is found
![Page 14: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/14.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM usingLMS estimators
1 Generate random set values α and β (initialsolutions)
2 Evaluate initial solutions minimizing LMS3 Generate new candidate solutions from the
initial one4 Evaluate new candidate solutions minimizing
LMS5 Repeat until a very good solution is found
![Page 15: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/15.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM usingLMS estimators
1 Generate random set values α and β (initialsolutions)
2 Evaluate initial solutions minimizing LMS3 Generate new candidate solutions from the
initial one4 Evaluate new candidate solutions minimizing
LMS5 Repeat until a very good solution is found
![Page 16: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/16.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM usingLMS estimators
1 Generate random set values α and β (initialsolutions)
2 Evaluate initial solutions minimizing LMS3 Generate new candidate solutions from the
initial one4 Evaluate new candidate solutions minimizing
LMS5 Repeat until a very good solution is found
![Page 17: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/17.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
InitializationStep 1 & 2: Generate and evaluate random set valuesα[−1, 2] and β[0, 1] (initial solutions)
P(0)=
d
12
np
minα,β(med(ε2
i,t))
![Page 18: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/18.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
InitializationStep 1 & 2: Generate and evaluate random set valuesα[−1, 2] and β[0, 1] (initial solutions)
P(0)=
d
12
np
minα,β(med(ε2
i,t))
![Page 19: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/19.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
Generate new candidate solutions from the initial oneStep 3a: Differential mutation
P(0)1,i =
1 2 ... r3 ... r1 ... r2 ... np
P(υ)
1,i = P(0)1,r1
+ F × (P(0)1,r2
- P(0)1,r3
)
F scale factor ∈ [0, 1+] determines speed of shrinkage
![Page 20: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/20.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
......u1 ud
CR CR
uniform crossover
...u1
ud
P(u)1,i
. . . P(u)d ,i
Random crossoverStep 3b: Crossover elements fromP(0)
1,i and P(υ)1,i
1 Generate for each parameter auniform random number,ud ∈ [0, 1]
2 Determine the crossoverprobability, CR ∈ [0, 1]
3 Only if u < CR, P(u)1,i = P(υ)
1,i
4 else P(u)1,i = P(0)
1,i
![Page 21: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/21.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
Generate new candidate solutions from the initial oneStep 3a: Differential mutation
P(0)1,i =
1 2 ... r3 ... r1 ... r2 ... np
P(υ)
2,i = P(0)2,r1
+ F × (P(0)2,r2
- P(0)2,r3
)
F scale factor ∈ [0, 1+] determines speed of shrinkage
![Page 22: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/22.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
......u1 ud
CR CR
uniform crossover
...u1
ud
P(u)1,i
. . . P(u)d ,i
Random crossoverStep 3b: Crossover elements fromP(0)
d ,i and P(υ)d ,i
1 Generate for each parameter auniform random number,ud ∈ [0, 1]
2 Determine the crossoverprobability, CR ∈ [0, 1]
3 Only if u < CR, P(u)d ,i = P(υ)
d ,i
4 else P(u)d ,i = P(0)
d ,i
![Page 23: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/23.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
InitializationStep 4: Evaluate new candidate solutions minimizing LMS
if f (P(u).,i ) < f (P(0)
.,i ) then f (P(0).,i ) = f (P(u)
.,i )
![Page 24: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/24.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
InitializationStep 4: Evaluate new candidate solutions minimizing LMS
if f (P(u).,i ) < f (P(0)
.,i ) then f (P(0).,i ) = f (P(u)
.,i )
![Page 25: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/25.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
InitializationStep 5: Repeat steps 3 & 4 until a good solution is found orfor a predefined number
![Page 26: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/26.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Differential Evolution
Differential EvolutionOptimal parameter estimation of CAPM using LMS estimators
InitializationStep 5: Repeat steps 3 & 4 until a good solution is found orfor a predefined number
![Page 27: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/27.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
1 IntroductionFinancial WorldComplexity
2 Heuristic Optimization TechniquesClassical conceptDifferential Evolution
3 Financial ApplicationsOptimization heuristic strategies in finance
4 ConclusionHave in mind
![Page 28: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/28.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
VAR
Transaction Costs
Cardinality constraints
Index tracking
Model estimation
Model selectionFinancial forecasting
Portfolio improvement
Mutual funds style
Portfolio OptimizationRobust methods
Clustering
![Page 29: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/29.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
VAR
Transaction Costs
Cardinality constraints
Index tracking
Heuristics
Model estimation
Model selectionFinancial forecasting
Portfolio improvement
Mutual funds style
Portfolio OptimizationRobust methods
Clustering
![Page 30: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/30.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Portfolio SelectionDueck and Winker (1992) appliedThreshold Accepting
1 Portfolio optimization usingvarious risk measures
2 Index tracking to mutual fundreplication
3 Currency portfolio optimization
![Page 31: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/31.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Portfolio SelectionDueck and Winker (1992) appliedThreshold Accepting
1 Portfolio optimization usingvarious risk measures
2 Index tracking to mutual fundreplication
3 Currency portfolio optimization
![Page 32: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/32.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Portfolio SelectionDueck and Winker (1992) appliedThreshold Accepting
1 Portfolio optimization usingvarious risk measures
2 Index tracking to mutual fundreplication
3 Currency portfolio optimization
![Page 33: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/33.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Model estimation1 Risk estimation and GARCH models2 Indirect estimation and Agent Based Models3 Yield curve estimation
![Page 34: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/34.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Model estimation1 Risk estimation and GARCH models2 Indirect estimation and Agent Based Models3 Yield curve estimation
![Page 35: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/35.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Model estimation1 Risk estimation and GARCH models2 Indirect estimation and Agent Based Models3 Yield curve estimation
![Page 36: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/36.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Yield curve estimation
Fig. 6. Error in the estimation of the interest rates. Comparison of the traditional non-linear least squares and the GA for the Nelson and Siegel (1987) on
the left and for the Svensson (1994) function on the right for 1 year (top graph) and 10 years (bottom graph) government bonds.
![Page 37: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/37.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Model selection1 Risk factor selection (Asset Pricing Theory model (APT))
ri,t = α +k∑
f=1
βf rf ,t + εi,t (3)
2 Selection of bankruptcy predictors
BMW assets = 0.8German factor + 0.2US factor+0.9automotive factor + 0.1finance factor
+BMW non − systematic risk (4)
![Page 38: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/38.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Model selection1 Risk factor selection (Asset Pricing Theory model (APT))
ri,t = α +k∑
f=1
βf rf ,t + εi,t (3)
2 Selection of bankruptcy predictors
BMW assets = 0.8German factor + 0.2US factor+0.9automotive factor + 0.1finance factor
+BMW non − systematic risk (4)
![Page 39: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/39.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Clustering1 Bankruptcy prediction2 Credit risk rating3 Portfolio performance improvement4 Identify optimal number of clusters
![Page 40: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/40.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Clustering1 Bankruptcy prediction2 Credit risk rating3 Portfolio performance improvement4 Identify optimal number of clusters
![Page 41: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/41.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Clustering1 Bankruptcy prediction2 Credit risk rating3 Portfolio performance improvement4 Identify optimal number of clusters
![Page 42: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/42.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Optimization heuristic strategies in finance
Clustering1 Bankruptcy prediction2 Credit risk rating3 Portfolio performance improvement4 Identify optimal number of clusters
![Page 43: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/43.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
1 IntroductionFinancial WorldComplexity
2 Heuristic Optimization TechniquesClassical conceptDifferential Evolution
3 Financial ApplicationsOptimization heuristic strategies in finance
4 ConclusionHave in mind
![Page 44: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/44.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Have in mind
Heuristic optimization techniquesFlexible to tackle many complex optimization problems
Flexibility costMight be computationally more demanding than traditionalmethods (not a limitation nowadays)Results carefully interpreted
![Page 45: Heuristic Optimization Strategies in Finance - An Overviewcomisef.eu/files/Marianna.pdf · Heuristic Optimization Strategies in Finance - An Overview Marianna Lyra COMISEF Fellows’](https://reader034.vdocument.in/reader034/viewer/2022051512/6039cef7e491d36a8753ebe5/html5/thumbnails/45.jpg)
logo
Introduction Heuristic Optimization Techniques Financial Applications Conclusion
Have in mind
SummaryApply Optimization Heuristics