History 230Robert Brown, 1828: Experimental study of the motion of particlessuspended in a liquid (AlbertEinstein, 1905 and Marian vonSmoluchowski, 1906). The motion (stochastic process) became known asBrownian motion.
Louis Bachelier,Théorie de la Speculation, 1900:Sfollows aBrownian motion such as:
BUT aBrownian motion and hereforeS, may become negative.This difficulty is easily eliminated by assuming that thelogarithm ofS,rather thanSitself, follows a Brownian motion.In this case wesay thatSfollows a geometric Brownian motion.tt tttdWdtdS SdWdtSdσμσμ+=⇔+=00lnttdWdtdSσμ+=Derivative securities: Options - Black-Scholes model