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has been cited by the following article:

• TITLE: Stochastic Ito-Calculus and Numerical Approximations for Asset Price Forecasting in the Nigerian Stock Market

  AUTHORS: Thomas Chinwe Urama, Patrick Oseloka Ezepue

  KEYWORDS: Ito-Calculus, Brownian Motion, Volatility, Black-Scholes, Stochastic Equations, Numerical Simulation, Convergence, Euler-Maruyama, Financial Assets Pricing

  JOURNAL NAME: Journal of Mathematical Finance, Vol.8 No.4, November 12, 2018

  ABSTRACT: Predicting prices of financial assets have always been topical in finance. This conceptual paper considers the seminal paper by Black-Scholes [1], how to determine the parameters of the geometric Brownian motion, and their use in forecasting stock prices, especially for cases where analytic solutions are not feasible. Generally describing stock market dynamics and heuristic modelling of derivative prices in the Nigerian Stock Market (NSM), the paper particularly uses data on the stock prices of a Nigerian bank to develop the stochastic calculus foundations of such modelling. The bank stock prices are part of daily closing stock prices of 82 stocks listed and fully traded in the NSM between 3 August 2009 and 26 August 2013, which support wider heuristic modelling foreshadowed by the paper. Technically, the paper considers the use of accurate numerical approximation method to simulate nonlinear solutions to stochastic differential Equations (SDE) resulting from asset prices. Importantly, the paper illustrates the workings of the standard Black-Scholes results as a preparation for more detailed empirical modelling of some candidate derivative pricing formulae in the Nigerian Stock Market (NSM). It particularly illustrates the dual use of the BS [1] model and the Euler-Maruyama (EM) model for pricing, respectively, the derivative and underlying assets in a financial market, for example the NSM. The paper will help the Nigerian Stock Exchange to use derivatives to deepen the NSM. The specific objectives of the paper and the notes on policy implications provide the rudiments of theory and follow-on heuristics for this goal. Also, academics and practitioners can use the results as starting points for enhancing the research and practice of derivative pricing in the NSM and other emerging markets, for sectors and products of interest to them. The novelty of this line of work is that it has not been done so far in the NSM, and wider emerging African markets.