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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

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


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


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






Time reversibility test results
Time Reversibility Test Results

All TR p-values are < e-05


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