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Falsifying Generalized Wiener Processes

Falsifying Generalized Wiener Processes. Melvin J. Hinich. Applied Research Laboratories University of Texas at Austin. hinich@austin.utexas.edu. 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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  1. Falsifying Generalized Wiener Processes Melvin J. Hinich Applied Research Laboratories University of Texas at Austin hinich@austin.utexas.edu http://web.austin.utexas.edu/hinich/

  2. 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/)

  3. Generalized Wiener process(GWP) bandlimited filter non-gaussian i.i.d variates fixed sampling rate

  4. Bandlimited Filter Nyquist sampling rate

  5. The generalized Wiener process (GWP) is linear It is time reversiblesince the distribution of is the same as the distribution of

  6. The Trispectrum The principal domain of the trispectrum in the cube of indices where

  7. Normalized trispectrum is the spectrum of For the linear process GWP

  8. 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

  9. Estimating the Trispectrum Estimated normalized trispectrum

  10. 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

  11. Testing Time Reversibility of a GWP has a uniform (0,1) distribution

  12. Statistics of the 4 NYSE Returns

  13. Statistics after 10% Trimming of the Australian Returns

  14. Nonlinearity Test for NYSE Returns 73 Trifreqs

  15. Nonlinearity Test Results for AU Returns 2,920 Trifreqs

  16. Time Reversibility Test Results All TR p-values are < e-05

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