Falsifying generalized wiener processes
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Falsifying Generalized Wiener Processes. Melvin J. Hinich. Applied Research Laboratories University of Texas at Austin. [email protected] http://web.austin.utexas.edu/hinich/. Black-Scholes Model. The Black-Scholes-Merton model is a central tool for

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Falsifying Generalized Wiener Processes

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Falsifying generalized wiener processes

Falsifying Generalized Wiener Processes

Melvin J. Hinich

Applied Research Laboratories

University of Texas at Austin

[email protected]

http://web.austin.utexas.edu/hinich/


Black scholes model

Black-Scholes Model

The Black-Scholes-Merton model is a central tool for

pricing & hedging options & other derivatives securities.

The model employs a Wiener process

At present the derivatives business has become a more

than 415 trillion US$ market.

It has been implicated in the present world wide

financial crisis.

(portfolio.com/news-markets/national-news/portfolio/2008/02/19/)


Generalized wiener process gwp

Generalized Wiener process(GWP)

bandlimited filter

non-gaussian i.i.d variates

fixed sampling rate


Bandlimited filter

Bandlimited Filter

Nyquist sampling rate


Falsifying generalized wiener processes

The generalized Wiener process (GWP) is linear

It is time reversiblesince the distribution of

is the same as the distribution of


The trispectrum

The Trispectrum

The principal domain of the trispectrum

in the cube of indices where


Falsifying generalized wiener processes

Normalized trispectrum

is the spectrum of

For the linear process GWP


Trispectrum based tests of linearity time reversibility

Trispectrum Based Tests of Linearity & Time Reversibility

The trispectrum version of the Hinich-Rothman (1998)

time reversibility test & the Hinich (1982) linearity test

can be used falsify the validity of the GWP model.

DFT


Estimating the trispectrum

Estimating the Trispectrum

Estimated normalized trispectrum


Testing linearity of a gwp

Testing Linearity of a GWP

Under this null hypothesis that the observed values of

are generated by a GWP when 0 < c < 1/3

Then

has a uniform (0,1) distribution


Testing time reversibility of a gwp

Testing Time Reversibility of a GWP

has a uniform (0,1) distribution


Statistics of the 4 nyse returns

Statistics of the 4 NYSE Returns


Falsifying generalized wiener processes

Statistics after 10% Trimming of the Australian Returns


Nonlinearity test for nyse returns 73 trifreqs

Nonlinearity Test for NYSE Returns 73 Trifreqs


Falsifying generalized wiener processes

Nonlinearity Test Results for AU Returns 2,920 Trifreqs


Time reversibility test results

Time Reversibility Test Results

All TR p-values are < e-05


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