fractals in finance and risk
TRANSCRIPT
-
8/16/2019 Fractals in Finance and Risk
1/14
Fractals in Finance and
Risk
By: Will Brennan
-
8/16/2019 Fractals in Finance and Risk
2/14
Why does it matter?
Finance played a crucial role in thedevelopment of fractal theory
Fractals are used in nance tomake predictions as to the risk
involved for particular stocks.
-
8/16/2019 Fractals in Finance and Risk
3/14
The Current Model
Bronian Motiondiscovered !y "ouis
Bachalier in #$%% &Theoriede la speculation'.
Theory as later
developed !y (l!ert)instein* +ean ,errin* and-or!ert Weiner
-
8/16/2019 Fractals in Finance and Risk
4/14
Bronian Motion
http:classes.yale.eduFractalsRandFrac
BronianBronian/.html
The Mathematical formula !ehind
Bronian Motion: 0d1i0 2 &dti'#.3
http://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.htmlhttp://classes.yale.edu/Fractals/RandFrac/Brownian/Brownian3.html
-
8/16/2019 Fractals in Finance and Risk
5/14
-
8/16/2019 Fractals in Finance and Risk
6/14
( ,ro!lem )mer5es7.
8oever* hen the 5raph isplotted !y successive prices*
di9erences emer5e !eteen stockand Bronian Motion.
-
8/16/2019 Fractals in Finance and Risk
7/14
(n (lternate Method?
While the Bronian Motion model can !eadusted to t o!served data* the BM modelis not useful in predictin5 data.
(nother method is !ased on the o!servationthat stocks are statistically self;scalin5. Themethod is to input a simple al5orithm thatprovides the same scalin5* and then o!serveho many features follo automatically.
-
8/16/2019 Fractals in Finance and Risk
8/14
Cartoons aren
-
8/16/2019 Fractals in Finance and Risk
9/14
4tep #:6nitiator and
=enerator
dt1 = 4/9 - 0 = 4/9, dY
1 = 2/3 - 0 = 2/3, so dY
1 = (dt
1)1/2
dt2 = 5/9 - 4/9 = 1/9, dY
2 = 1/3 - 2/3 = -1/3, so -dY
2 = (dt
2)1/2
dt3 = 1 - 5/9 = 4/9, dY3 = 1 - 1/3 = 2/3, so dY3 = (dt3)1/2
All 3 segments of the Cartoon
Satsf! the "ondton
#dY# = (dt
)1/2
-
8/16/2019 Fractals in Finance and Risk
10/14
4tep 3: =enerate>
-
8/16/2019 Fractals in Finance and Risk
11/14
4tep /: Randomie
6n order to make more realistic*introduce randomness in thedirection of the linear se5ments
-
8/16/2019 Fractals in Finance and Risk
12/14
The Final Cartoon
-
8/16/2019 Fractals in Finance and Risk
13/14
Money mimics Cartoons
When this necartoon is placed
alon5sidenancial data*they are very
similar in termsof lar5e umpsand correlation.
-
8/16/2019 Fractals in Finance and Risk
14/14
Conclusion
Throu5h utiliin5 a cartoon* asu@cient fractal model is a!le to
make up for the failin5s of theBronian Motion model* alloin5for investors to predict nancial
risk.