Discrete Time vs Continuous Time Stock-price Dynamics and Implications for Option Pricing

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Asadzadeh, Ilnaz | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 43598 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra; Zamani, Shiva
Abstract:
In the present paper we construct stock price processes with the same marginal log- normal law as that of a geometric Brownian motion and also with the same transition density (and returns’ distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes differ from Black and Scholes’, in that option prices can be either arbitrarily close to the option intrinsic value or arbitrarily close to the underlying stock price. We also explain that this is due to the particular way one models the stock-price process in between the grid time instants which are relevant for trading
Keywords:
Fractional Black-Scholes Model ; Stochastic Differential Equation ; Markov Process ; Probability Density Function ; Fokker-Planck Equation ; Trading Time Gride ; Exponential Family ; Market Incompleteness