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

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Document pages: 28 pages

Abstract: Predicting prices of financial assets have always been topical in finance. Thisconceptual paper considers the seminal paper by Black-Scholes [1], how todetermine the parameters of the geometric Brownian motion, and their use inforecasting stock prices, especially for cases where analytic solutions are notfeasible. Generally describing stock market dynamics and heuristic modellingof derivative prices in the Nigerian Stock Market (NSM), the paper particularlyuses data on the stock prices of a Nigerian bank to develop the stochasticcalculus foundations of such modelling. The bank stock prices are part ofdaily closing stock prices of 82 stocks listed and fully traded in the NSM between3 August 2009 and 26 August 2013, which support wider heuristicmodelling foreshadowed by the paper. Technically, the paper considers theuse of accurate numerical approximation method to simulate nonlinear solutionsto stochastic differential Equations (SDE) resulting from asset prices.Importantly, the paper illustrates the workings of the standard Black-Scholesresults as a preparation for more detailed empirical modelling of some candidatederivative pricing formulae in the Nigerian Stock Market (NSM). Itparticularly illustrates the dual use of the BS [1] model and the Euler-Maruyama(EM) model for pricing, respectively, the derivative and underlying assets in afinancial market, for example the NSM. The paper will help the NigerianStock Exchange to use derivatives to deepen the NSM. The specific objectivesof the paper and the notes on policy implications provide the rudiments oftheory and follow-on heuristics for this goal. Also, academics and practitionerscan use the results as starting points for enhancing the research andpractice 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 isthat it has not been done so far in the NSM, and wider emerging Africanmarkets.

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