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analysis assumed assumption asymptotically Bachelier behavior Brownian motion buyer centimes closing prices coefficient common stock contango Cootner correlogram corresponding dispersion dividends economic empirical equal equation estimate exercised expected value Expiring Figure filter formula frequency function futures contract Gaussian given graphs hypothesis increase independent interval investor kurtosis leverage log-normal distribution logarithmic Mandelbrot market prices mathematical expectation mean method month monthly negative normal distribution NYSE observed option at 50 Osborne paper parameters period positive premium price changes price movements price series profit purchase puts and calls random variables random walk random walk hypothesis ratio relative risk sample segment selling serial correlation spread stable Paretian stable Paretian distributions standard deviation statistical stock market stock prices Table theory tion trading transactions trend true price U.S. Steel variance volume Weber-Fechner law week weekly zero