portfolio optimization ai in financemath.bme.hu › ~gnagy › mmsz › eloadasok ›...
TRANSCRIPT
![Page 1: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/1.jpg)
Portfolio Optimization Artificial Intelligence in Finance
Zsolt Bihary (Morgan Stanley)
2013, Budapest
![Page 2: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/2.jpg)
Structuring (Securitization)
Pool of
Loans
Cash-flow Bank
Bank wants to • Get rid of risk • Realize future cash-flow now
Investors
Investors want to • Invest in the long run • with different risk
![Page 3: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/3.jpg)
Structuring (Securitization)
A
B
D
C
Pool of
Loans
Cash-flow
Wate
r-fall
Investors
Investors
Investors
Bonds
Bank
![Page 4: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/4.jpg)
The Structuring Problem
A
B
D
C
Pool of
Loans
Cash-flow
Wate
r-fall
Bonds
How to choose bond sizes? Bank is interested in great bond sizes and high ratings. Regulators seek to limit bond sizes before giving high ratings.
Bank
![Page 5: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/5.jpg)
The Black Box Simulator
A
B
D
C
Black Box Simulator
• Pricing • Scenario 1 • Scenario 2 • Scenario 3 • Scenario 4
INPUT
Bonds
OUTPUT
Structure (bond sizes)
• Proceeds • Scenario 1 result • Scenario 2 result • Scenario 3 result • Scenario 4 result
![Page 6: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/6.jpg)
The Black Box Simulator
A
B
D
C
Black Box Simulator
• Pricing • Scenario 1 • Scenario 2 • Scenario 3 • Scenario 4
INPUT
Bonds
OUTPUT
Structure (bond sizes)
• Proceeds • Scenario 1 result • Scenario 2 result • Scenario 3 result • Scenario 4 result
We want to maximize proceeds, under the constraint that the structure passes all stress-test scenarios.
![Page 7: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/7.jpg)
Nature of the Optimization Problem
• Objective function and constraints evaluated by Black Box (no gradients available)
• Objective function and constraints evaluated simultaneously (unknown constraints)
• Constraints returned as pass/fail Booleans (no differentiable discriminant functions)
• Black Box is very slow (we can afford only 5 iterations)
• We can run Black Box parallel on 20 servers
![Page 8: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/8.jpg)
Synthetic Example
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
A bond size
B bond size
A (20%)
B (50%)
D (30%)
Example structure
![Page 9: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/9.jpg)
Synthetic Example
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
A bond size
B bond size
A (20%)
B (50%)
D (30%)
Example structure
Global optimum
![Page 10: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/10.jpg)
Synthetic Example
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
A bond size
B bond size
A (20%)
B (50%)
D (30%)
Example structure
Global optimum
Local optimum
![Page 11: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/11.jpg)
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
![Page 12: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/12.jpg)
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Initially, put down random structures
![Page 13: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/13.jpg)
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
![Page 14: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/14.jpg)
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
![Page 15: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/15.jpg)
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
![Page 16: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/16.jpg)
Reinforcement Learning
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
At each iteration, new structures are selected
based on information on previous structures
![Page 17: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/17.jpg)
Surrogate Model Approach
Initial Random Structures
Surrogate Model New Design Structures
Best Structure Found
Black Box Simulator
Results on Structures
![Page 18: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/18.jpg)
Surrogate Model Approach
Initial Random Structures
Surrogate Model New Design Structures
Best Structure Found
Black Box Simulator
Results on Structures
Objective function:
Linear Regression
Constraints:
Support Vector
Machine (SVM)
![Page 19: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/19.jpg)
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Gives a surrogate model for the
pass – fail boundary
![Page 20: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/20.jpg)
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, SVM gives more
and more accurate boundary
![Page 21: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/21.jpg)
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, SVM gives more
and more accurate boundary
![Page 22: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/22.jpg)
Support Vector Machine (SVM)
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, SVM gives more
and more accurate boundary
![Page 23: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/23.jpg)
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
SVM maps out the pass probability
in structure space
![Page 24: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/24.jpg)
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, pass probability
map becomes more and more accurate
![Page 25: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/25.jpg)
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, pass probability
map becomes more and more accurate
![Page 26: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/26.jpg)
Pass Probability
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more points, pass probability
map becomes more and more accurate
![Page 27: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/27.jpg)
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
Surrogate model maps out the most
promising regions of structure space
![Page 28: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/28.jpg)
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more and more points, surrogate
model zeros in to the optimal region
![Page 29: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/29.jpg)
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more and more points, surrogate
model zeros in to the optimal region
![Page 30: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/30.jpg)
Expected Improvement
0 20 40 60 80 1000
10
20
30
40
50
60
70
80
90
100
With more and more points, surrogate
model zeros in to the optimal region
![Page 31: Portfolio Optimization AI in Financemath.bme.hu › ~gnagy › mmsz › eloadasok › BiharyZsolt2013.pdf · 2013-09-26 · Portfolio Optimization Artificial Intelligence in Finance](https://reader034.vdocuments.site/reader034/viewer/2022042402/5f12f2d366b1147e18719e12/html5/thumbnails/31.jpg)
Conclusion
Using Machine Learning techniques
on the Portfolio Structuring Problem,
we could provide a useful tool
for our structuring business
Thank you for your attention