The document outlines a thesis project on developing and evaluating nonlinear models for predicting volatility in financial markets. It introduces the goal of predicting volatility, provides definitions of volatility, and discusses why volatility prediction is important. It then outlines various prediction models that were considered, including GARCH, linear regression, neural networks, and nonlinear set membership models. The results, modeling GUI, and conclusions sections are also briefly outlined.

1. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Nonlinear Models
for Volatility Prediction
in the Financial Markets
Matteo Ainardi
Advisors: Prof. Gianpiero Cabodi, Prof. Derong Liu
University of Illinois at Chicago
Master of Science in Electrical and Computer Engineering
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

2. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Outline
1 Introduction
Volatility
2 Prediction Models
Volatility Models
3 Results
Volatility Prediction
Investment Strategy
4 Modeling GUI
5 Conclusions
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

3. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Thesis goal
Development and evaluation of models for volatility prediction.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

4. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Thesis goal
Development and evaluation of models for volatility prediction.
Qualitative definition
Volatility: degree of price variation over time.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

5. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Thesis goal
Development and evaluation of models for volatility prediction.
Qualitative definition
Volatility: degree of price variation over time.
Why Volatility?
Investors assess expected returns of an asset against its risk.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

6. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Thesis goal
Development and evaluation of models for volatility prediction.
Qualitative definition
Volatility: degree of price variation over time.
Why Volatility?
Investors assess expected returns of an asset against its risk.
Financial institutions want to ensure that the value of their
assets does not fall below some minimum level that would
expose them to insolvency.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

7. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Volatility Features
not directly observable
not constant over time
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

8. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Volatility Features
not directly observable
not constant over time
Quantitative Definition
Time varying volatility measure from the price time series:
σt = (rt − r )2
2
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

9. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Volatility Features
not directly observable
not constant over time
Quantitative Definition
Time varying volatility measure from the price time series:
σt = (rt − r )2
2
pt −pt−1
rt = pt−1 : return on day t,
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

10. Outline
Introduction
Prediction Models
Volatility
Results
Modeling GUI
Conclusions
Volatility
Volatility Features
not directly observable
not constant over time
Quantitative Definition
Time varying volatility measure from the price time series:
σt = (rt − r )2
2
pt −pt−1
rt = pt−1 : return on day t,
r : mean return over the last 200 days period.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

11. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Prediction Models
Let’s assume that the system to forecast can be described by a
regression equation of the form
yt+1 = f0 (ϕt ) + dt
ϕt = [rt , . . . , rt−N+1 , yt , . . . , yt−M+1 ]
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

12. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Prediction Models
Let’s assume that the system to forecast can be described by a
regression equation of the form
yt+1 = f0 (ϕt ) + dt
ϕt = [rt , . . . , rt−N+1 , yt , . . . , yt−M+1 ]
t ∈ N: time [days],
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

13. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Prediction Models
Let’s assume that the system to forecast can be described by a
regression equation of the form
yt+1 = f0 (ϕt ) + dt
ϕt = [rt , . . . , rt−N+1 , yt , . . . , yt−M+1 ]
t ∈ N: time [days],
yt : volatility at day t,
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

14. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Prediction Models
Let’s assume that the system to forecast can be described by a
regression equation of the form
yt+1 = f0 (ϕt ) + dt
ϕt = [rt , . . . , rt−N+1 , yt , . . . , yt−M+1 ]
t ∈ N: time [days],
yt : volatility at day t,
ϕt : regressor,
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

15. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Prediction Models
Let’s assume that the system to forecast can be described by a
regression equation of the form
yt+1 = f0 (ϕt ) + dt
ϕt = [rt , . . . , rt−N+1 , yt , . . . , yt−M+1 ]
t ∈ N: time [days],
yt : volatility at day t,
ϕt : regressor,
dt : noise affecting the system.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

16. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Prediction Models
A prediction model f can be defined as an approximation of f0 ,
providing a prediction yt+1 of yt+1 :
yt+1 = f (ϕt ),
where ϕt represents an estimate of the true regressor ϕt .
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

17. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Prediction Models - Statistical/Parametric Approach
The traditional approach followed to build a model implies a choice
of a specific structure for the functional form f0 and statistical
assumptions on the noise dt affecting the system.
if possible, physical/economical laws are used to obtain a
parametric representation of the system f (ϕ, θ)
as a parametric combination of basis functions (polynomial,
sigmoid, ...)
The parameters θ are then estimated from data by optimizing
Least Squares or Maximum Likelihood functions.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

18. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
GARCH Models
Linear Regression / Moving Average Models
Neural Network Models
Nonlinear Set Membership Models
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

19. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
GARCH Models
Generalized Autoregressive Conditional Heteroskedasticity
This methodology is the most widely adopted and led its creator,
Prof. Robert Engle, to the Nobel Prize in Economy in 2003.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

20. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
GARCH Models
Generalized Autoregressive Conditional Heteroskedasticity
This methodology is the most widely adopted and led its creator,
Prof. Robert Engle, to the Nobel Prize in Economy in 2003.
The volatility prediction is based on
long run constant
volatility
yt+1 = ω + α˜t2 + βyt
r
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

21. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
GARCH Models
Generalized Autoregressive Conditional Heteroskedasticity
This methodology is the most widely adopted and led its creator,
Prof. Robert Engle, to the Nobel Prize in Economy in 2003.
The volatility prediction is based on
long run constant
volatility
most recent return yt+1 = ω + α˜t2 + βyt
r
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

22. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
GARCH Models
Generalized Autoregressive Conditional Heteroskedasticity
This methodology is the most widely adopted and led its creator,
Prof. Robert Engle, to the Nobel Prize in Economy in 2003.
The volatility prediction is based on
long run constant
volatility
most recent return yt+1 = ω + α˜t2 + βyt
r
previous volatility
prediction
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

23. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
GARCH Models
Generalized Autoregressive Conditional Heteroskedasticity
This methodology is the most widely adopted and led its creator,
Prof. Robert Engle, to the Nobel Prize in Economy in 2003.
The volatility prediction is based on
long run constant
volatility
most recent return yt+1 = ω + α˜t2 + βyt
r
previous volatility
prediction
The GARCH regressor is ϕt = [˜t , yt ]
r
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

24. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Linear Models
Linear Regression Models
N−1 M−1
yt+1 = r2
αi ˜t−i + βj yt−j
˜
i=0 j=0
ϕt = [˜t , . . . , ˜t−N+1 , yt , . . . , yt−M+1 ]
r r ˜ ˜
αi and βi are the parameters that must be estimated.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

25. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Linear Models
Linear Regression Models
N−1 M−1
yt+1 = r2
αi ˜t−i + βj yt−j
˜
i=0 j=0
ϕt = [˜t , . . . , ˜t−N+1 , yt , . . . , yt−M+1 ]
r r ˜ ˜
αi and βi are the parameters that must be estimated.
Moving Average Models
N−1
1
yt+1 = r2
˜t−i , ϕt = [rt , . . . , ˜t−N+1 ]
˜ r
N
i=0
1
Particular case of linear regression: αi = N, βj = 0 for each i, j.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

26. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Neural Networks
Neural Network Models
r
yt+1 = αi σ(βi ϕt − λi ) + ζ
i=1
r : number of neurons in the network
2
σ(x) = 1+e −2x
: sigmoidal function (neuron transfer function)
ϕt = [˜t , . . . , ˜t−N+1 , yt , . . . , yt−M+1 ]
r r ˜ ˜
αi , βi , λi : parameters estimated through a network training
algorithm
ζ: noise affecting the system
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

27. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Observations
These models require the selection of a specific functional form of
f0 and statistical assumptions on the noise (usually supposed to be
gaussian).
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

28. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Observations
These models require the selection of a specific functional form of
f0 and statistical assumptions on the noise (usually supposed to be
gaussian).
Search of the appropriate functional form and parameters:
complex and computationally heavy
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

29. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Observations
These models require the selection of a specific functional form of
f0 and statistical assumptions on the noise (usually supposed to be
gaussian).
Search of the appropriate functional form and parameters:
complex and computationally heavy
Wrong f0 choice ⇒ degradation in model accuracy
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

30. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Methodology
Nonlinear Set Membership models do not require the choice of a
parametric form of f0 , but more relaxed assumptions on the
analyzed system:
bound on its derivatives
bound on the noise affecting the system
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

31. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Methodology
Nonlinear Set Membership models do not require the choice of a
parametric form of f0 , but more relaxed assumptions on the
analyzed system:
bound on its derivatives
bound on the noise affecting the system
Advantages:
avoid the complexity/accuracy problems posed by the choice
of the model function and of the parameters.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

32. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Methodology
Nonlinear Set Membership models do not require the choice of a
parametric form of f0 , but more relaxed assumptions on the
analyzed system:
bound on its derivatives
bound on the noise affecting the system
Advantages:
avoid the complexity/accuracy problems posed by the choice
of the model function and of the parameters.
NSM Local Approach: check if a given model can be improved
by identifying a NSM model to forecast its residual process.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

33. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Models
1
yt+1 = (f (ϕt ) + f (ϕt )),
2
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

34. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Models
1
yt+1 = (f (ϕt ) + f (ϕt )),
2
f (ϕT ) = min (˜k+1 +
y k + γ ϕT − ϕk )
˜
k=1,...,T −1
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

35. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Models
1
yt+1 = (f (ϕt ) + f (ϕt )),
2
f (ϕT ) = min (˜k+1 +
y k + γ ϕT − ϕk )
˜
k=1,...,T −1
f (ϕT ) = max (˜k+1 −
y k − γ ϕT − ϕk )
˜
k=1,...,T −1
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

36. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Models
1
yt+1 = (f (ϕt ) + f (ϕt )),
2
f (ϕT ) = min (˜k+1 +
y k + γ ϕT − ϕk )
˜
k=1,...,T −1
f (ϕT ) = max (˜k+1 −
y k − γ ϕT − ϕk )
˜
k=1,...,T −1
where γ (gradient) and (noise) bounds are derived from past
measured data through a validation procedure.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

37. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
NSM Models
1
yt+1 = (f (ϕt ) + f (ϕt )),
2
f (ϕT ) = min (˜k+1 +
y k + γ ϕT − ϕk )
˜
k=1,...,T −1
f (ϕT ) = max (˜k+1 −
y k − γ ϕT − ϕk )
˜
k=1,...,T −1
where γ (gradient) and (noise) bounds are derived from past
measured data through a validation procedure.
NSM Regressor: ϕt = [˜t , . . . , ˜t−N+1 , yt , . . . , yt−M+1 ]
r r ˜ ˜
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

38. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

39. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Example
Available
measurements: Let’s assume
t ϕt
˜ yt+1
˜ γ = 0.5, r = 0.2
1 [3, 3] 3 ϕ4 = [2, 1].
˜
2 [1, 3] 4 How to determine the
3 [3, 2] 5 value of y5 ?
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

40. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Example
1) compute t
t yt
˜ t
2 3 0.6
3 4 0.8
4 5 1.0
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

41. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Example
1) compute 2) compute ϕ4 − ϕt
˜
t
t yt
˜ t t ϕt
˜ ϕ4 − ϕt
˜
2 3 0.6 1 [3, 3] 2.24
3 4 0.8 2 [1, 3] 2.24
4 5 1.0 3 [3, 2] 1.41
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

42. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Example
1) compute 2) compute ϕ4 − ϕt
˜
t
t yt
˜ t t ϕt
˜ ϕ4 − ϕt
˜
2 3 0.6 1 [3, 3] 2.24
3 4 0.8 2 [1, 3] 2.24
4 5 1.0 3 [3, 2] 1.41
f (ϕ4 ) = min (˜k+1 +
y k + γ ϕ4 − ϕk )
˜
k=1,...,3
f (ϕ4 ) = max (˜k+1 −
y k − γ ϕ4 − ϕk )
˜
k=1,...,3
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

43. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Example
f (ϕ4 ) = min (4.72, 5.92, 6.71) = 4.72
f (ϕ4 ) = max (1.28, 2.08, 3.30) = 3.30
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

44. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models
Example
f (ϕ4 ) = min (4.72, 5.92, 6.71) = 4.72
f (ϕ4 ) = max (1.28, 2.08, 3.30) = 3.30
The NSM prediction for y5 value will be
1
y5 = (f (ϕ4 ) + f (ϕ4 )) = 4.01.
2
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

45. Outline
Introduction
Prediction Models
Volatility Models
Results
Modeling GUI
Conclusions
Volatility Models - Nonlinear Set Membership
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

46. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Models Results
Models are evaluated on real financial time series:
FDAX
IBM
both in terms of predictive performance and by simulating an
investment strategy.
IBM Dataset
The IBM dataset is composed of 2248 daily closure prices, from
2000 to 2009.
Identification dataset: samples 1 to 1500.
Validation dataset: samples 1501 to 2248.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

47. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Results Evaluation
Trivial Models
Persistent Model
yt+1 = yt ,
˜
Constant Model
yt+1 = const,
Exact Model
yt+1 = yt+1
˜
These models are used as terms of comparisons.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

48. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
IBM Volatility
Performance Evaluation
Model RMSE R2MZ
Persistent 10.66 × 10−4 2.84%
GARCH 7.82 × 10−4 12.20%
MAV 7.74 × 10−4 13.59%
NN 7.68 × 10−4 14.03%
NSM 7.86 × 10−4 12.77%
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

49. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
IBM Volatility
Performance Evaluation
Model RMSE R2MZ
Persistent 10.66 × 10−4 2.84%
GARCH 7.82 × 10−4 12.20%
MAV 7.74 × 10−4 13.59%
NN 7.68 × 10−4 14.03%
NSM 7.86 × 10−4 12.77%
RMSE (Root Mean Squared Error)
n
t=1 (˜t
y − yt )2
RMSE =
n
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

50. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
IBM Volatility
Performance Evaluation
Model RMSE R2MZ
Persistent 10.66 × 10−4 2.84%
GARCH 7.82 × 10−4 12.20%
MAV 7.74 × 10−4 13.59%
NN 7.68 × 10−4 14.03%
NSM 7.86 × 10−4 12.77%
R2MZ (Mincer Zarnowitz’s Regression R 2 )
It is widely adopted in econometrics to assess
the practical utility of the volatility model.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

51. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Investment Strategy
Scenario
An investor can choose among a risk free asset which gives a
constant return and a risky asset.
The composition of the investor’s portfolio can be changed every
day.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

52. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Investment Strategy
Scenario
An investor can choose among a risk free asset which gives a
constant return and a risky asset.
The composition of the investor’s portfolio can be changed every
day.
Investment Strategy
The investor accepts a certain level of volatility for its portfolio if
there is the opportunity of an higher profit.
predicted volatility ⇒ risky asset weight
predicted volatility ⇒ risky asset weight
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

53. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Investment Strategy Results
Strategy Profit (×10−3 ) ∆(×10−3 ) Risk (×10−3 ) Profit
Risk
Constant 65.7 — 142 0.47
Exact Vol 163 97.3 141 1.16
Persistent 54.4 −11.3 348 0.16
GARCH 110 44.3 158 0.70
MAV 126 60.3 179 0.70
NN 115 49.3 162 0.71
NSM 152 86.3 216 0.70
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

54. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Investment Strategy Results
Strategy Profit (×10−3 ) ∆(×10−3 ) Risk (×10−3 ) Profit
Risk
Constant 65.7 — 142 0.47
Exact Vol 163 97.3 141 1.16
Persistent 54.4 −11.3 348 0.16
GARCH 110 44.3 158 0.70
MAV 126 60.3 179 0.70
NN 115 49.3 162 0.71
NSM 152 86.3 216 0.70
Profit: mean portfolio return
Profit refers to the annualized mean portfolio return.
For example the NSM strategy shows
about a +15% annual portfolio variation.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

55. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Investment Strategy Results
Strategy Profit (×10−3 ) ∆(×10−3 ) Risk (×10−3 ) Profit
Risk
Constant 65.7 — 142 0.47
Exact Vol 163 97.3 141 1.16
Persistent 54.4 −11.3 348 0.16
GARCH 110 44.3 158 0.70
MAV 126 60.3 179 0.70
NN 115 49.3 162 0.71
NSM 152 86.3 216 0.70
Profit: mean portfolio return
∆: improvement with respect to the constant strategy
Profit refers to the annualized mean portfolio return.
For example the NSM strategy shows
about a +15% annual portfolio variation.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

56. Outline
Introduction
Prediction Models Volatility Prediction
Results Investment Strategy
Modeling GUI
Conclusions
Investment Strategy Results
Strategy Profit (×10−3 ) ∆(×10−3 ) Risk (×10−3 ) Profit
Risk
Constant 65.7 — 142 0.47
Exact Vol 163 97.3 141 1.16
Persistent 54.4 −11.3 348 0.16
GARCH 110 44.3 158 0.70
MAV 126 60.3 179 0.70
NN 115 49.3 162 0.71
NSM 152 86.3 216 0.70
Profit: mean portfolio return
∆: improvement with respect to the constant strategy
Risk: portfolio return standard deviation
Profit refers to the annualized mean portfolio return.
For example the NSM strategy shows
about a +15% annual portfolio variation.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

57. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Data Load GUI
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

58. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Model Identification GUI
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

59. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Automatic Model Identification GUI
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

60. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Display Results GUI
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

61. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
GARCH, MAV, NSM and NN models show significant
improvements with respect to the persistent model and to
constant volatility.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

62. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
GARCH, MAV, NSM and NN models show significant
improvements with respect to the persistent model and to
constant volatility.
NSM optimality analysis, based on local approach, indicates
that GARCH models performance can not be significantly
improved.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

63. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
GARCH, MAV, NSM and NN models show significant
improvements with respect to the persistent model and to
constant volatility.
NSM optimality analysis, based on local approach, indicates
that GARCH models performance can not be significantly
improved.
NN models often produce unstable results in presence of
volatility dynamics very different from the ones on which they
are trained.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

64. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
GARCH, MAV, NSM and NN models show significant
improvements with respect to the persistent model and to
constant volatility.
NSM optimality analysis, based on local approach, indicates
that GARCH models performance can not be significantly
improved.
NN models often produce unstable results in presence of
volatility dynamics very different from the ones on which they
are trained.
NSM models are able to produce robust results even in
presence of extreme volatility variations.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

65. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
All the experiments have been implemented and executed in
Matlab, the development of the GUI resulted into about 2500
lines of Matlab code.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

66. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
All the experiments have been implemented and executed in
Matlab, the development of the GUI resulted into about 2500
lines of Matlab code.
More than 30 prediction models have been identified and
evaluated on the different datasets, relying on different
volatility measures proposed in financial literature.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

67. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
All the experiments have been implemented and executed in
Matlab, the development of the GUI resulted into about 2500
lines of Matlab code.
More than 30 prediction models have been identified and
evaluated on the different datasets, relying on different
volatility measures proposed in financial literature.
Future developments: try different regressor forms, apply the
models to a larger number of markets and timeframes.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

68. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Conclusions
All the experiments have been implemented and executed in
Matlab, the development of the GUI resulted into about 2500
lines of Matlab code.
More than 30 prediction models have been identified and
evaluated on the different datasets, relying on different
volatility measures proposed in financial literature.
Future developments: try different regressor forms, apply the
models to a larger number of markets and timeframes.
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke

69. Outline
Introduction
Prediction Models
Results
Modeling GUI
Conclusions
Thank You
Matteo Ainardi Nonlinear Models for Volatility Prediction in the Financial Marke