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.