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Unformatted text preview: 1 OPTION VALUATION NBA 673 March 10, 2006 2 Evolution of Stock Prices 3 Stock Price Evolution Model We will model the evolution of prices in the interval [t,T]. We divide this into small intervals of equal length . 4 Stock Price Evolution Model (2) Three assumptions: (1) r(i ) are i.i.d.; (2) E[r(i )]= ; (3) Var[r(i )]= 2 . Consequences: (1) E[Z(T)] = T; (2) Var[Z(T)] = 2 T. (3) Returns are normally distributed. (4) Prices are lognormally distributed. 5 Normal vs. LogNormal108642 2 4 6 8 10 0.02 0.04 0.06 0.08 Normal pdf 1 2 3 4 5 6 7 8 9 10 0.2 0.4 0.6 0.8 LogNormal pdf 6 BlackScholes Formulas 7 Bernoulli Random Variable Two possible outcomes, one has probability 0 < p < 1, the other has probability 1 p. The outcomes could be interpreted as yes & no, 1 & 0, left & right, up & down. before after yes, 1, right, up no, 0, left, down 8 Binomial Distribution...
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 Spring '06
 JANOSI,TIBOR

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