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Unformatted text preview: Option Pricing formula based on a NonGaussian Option Pricing formula based on a NonGaussian Stock Price Model Stock Price Model Xin Li Xin Li Physics Department, NC State Univ. Physics Department, NC State Univ. Preliminary result of Option Pricing Partial differential Equation based on lognormal distribution Derivation of price of European call option based on lognormal distribution Introduction to Volatility smile Tsallis Stock Price model Tsallis distribution Derivation of Partial differential Equation and stock price based on Tsallis distribution Derivation of option pricing formula based on Tsallis distribution Empirical Result of the Tsallis Stock model Topic OutLine Topic OutLine Preliminary result of Option pricing Preliminary result of Option pricing Partial differential equation of european call option [1] dS Sdt Sd = + (1) 2 2 2 2 1 ( ) 2 f f f f df S S dt S d t S S S = + + + Consider a Portfolio short 1 option and buy share, then after time interval the price change of the portfolio must equal to riskneutral increase which leads to: f S S S t 2 2 2 2 1 2 f f f rS S rf t S S + + = 2 2 2 2 1 ( ) ( ) 2 f f f f f f f S S S t S t r f S t S t S S S S 8  + =  + + + = + 8 (3) (2) (4) Preliminary result of Option pricing...
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This note was uploaded on 08/01/2008 for the course ST 810J taught by Professor Bloomfield during the Fall '07 term at N.C. State.
 Fall '07
 BLOOMFIELD

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