A derivation of the the black-scholes equation using martingales

Title: A derivation of the the black-scholes equation using martingales
Creator: Nyarko , Ebenezer Narh
Subject: Mathematical models
Date Issued: 2018
Date: 2018
Type: Thesis
Type: Masters
Type: MSc
Identifier: http://hdl.handle.net/10353/14572
Identifier: vital:40016
Description: This work focuses on the application of stochastic differential equations, with martingales, in finance. The emphasis is on the derivation of the Black-Scholes model for the valuation of options. A theoretical framework in stochastic analysis, together with Itô calculus (Kiyoshi Itô), is explored. The Girsanov Theorem is applied in order to transform a modelled stochastic equation based, on predetermined stock and bond prices, into equivalent martingale measures. A replication strategy is then adopted to solve the two equations analytically, by finding the natural logarithm of the expectation of the solution to the stochastic models. We finally compute the resulting solution based on a standard, normal distribution to get the desired outcome of the Black-Scholes model.
Format: 57 leaves
Format: pdf
Publisher: University of Fort Hare
Publisher: Faculty of Science and Agriculture
Language: English
Rights: University of Fort Hare

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