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.
Highlights
Stochastic calculus deals with random motion of asset prices in financial engineering
Following the formal approval for derivatives trading in Nigeria, there is a need for research in key aspects of financial engineering that use data from Nigerian financial markets, for example the Nigerian Stock Market, and key sectors of the market, say, the banking sector
This paper uses them in form of Euler-Maruyama approximations of drift and volatility parameters, μ and σ associated with future stock prices, based on the Black-Scholes formula and other models for option pricing
Summary
Stochastic calculus deals with random motion of asset prices in financial engineering It is useful in estimating the price of the underlying assets and in finding the equilibrium price of stock options [2]. This problem is not addressed satisfactorily in the Nigerian financial markets as far as derivative trading and asset pricing is concerned. Following the formal approval for derivatives trading in Nigeria, there is a need for research in key aspects of financial engineering that use data from Nigerian financial markets, for example the Nigerian Stock Market, and key sectors of the market, say, the banking sector This paper fills this need, and is the first attempt known to the authors to do so since the said CBN approval
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