Stochastic calculus and derivatives pricing in the Nigerian stock market

Led by the Central Bank of Nigeria (CBN) and the Nigerian Stock Exchange (NSE), policy makers, investors and other stakeholders in the Nigerian Stock Market consider the introduction of derivative products in Nigerian capital markets essential for their investment and risk management needs. This research foregrounds these interests through detailed theoretical and empirical review of derivative pricing models. The specific objectives of the research include: 1) To explore the key stochastic calculus models used in pricing and trading financial derivatives (e.g. the Black-Scholes model and its extensions); 2) To examine the investment objectives fulfilled by derivatives; 3) To investigate the links between the stylized facts in the Nigerian Stock Market (NSM), the risk management techniques to be adopted, and the workings of the pricing models; and 4) To apply the research results to the NSM, by comparing the investment performance of selected derivative pricing models under different market scenarios, represented by the stylized facts of the underlying assets and market characteristics of the NSM. The foundational concepts that underpin the research include: stochastic calculus models of derivative pricing, especially the Black-Scholes (1973) model; its extensions; the practitioners’ Ad-Hoc Black Scholes models, which directly support proposed derivative products in the NSM; and Random Matric Theory (RMT). RMT correlates market data from the NSM and Johannesburg Stock Exchange (JSE) and facilitates possible simulation of non-existing derivative prices in the NSM, from those in the JSE. Furthermore, the research explores in detail the workings of different derivative pricing models, for example various structures for the Ad-Hoc Black Scholes models, using selected underlying asset prices, to determine the applicability of the models in the NSM. The key research findings include: 1) ways to estimate the parameters of the stochastic calculus models; 2) exploring the benefits of introducing pioneer derivative products in the NSM, including risk hedging, arbitrage, and price speculation; 3) using NSM stylized facts to calibrate selected derivative pricing models; and 4) explaining how the results could be used in future experimental modelling to compare the investment performance of selected models. By way of contributions to knowledge, this is the first study known to the researcher that provides in-depth review of the theoretical and empirical underpinnings of derivative pricing possible in the NSM. This forms the basis for the Black Scholes approach to asset pricing of European option contract, which is the kind of call/put option contract that is being adopted in the NSM. The research provides the initial foundations for effective derivatives trading in the NSM. By explaining the heuristics for developing derivative products in the NSM from JSE information, the research will support future work in this important area of study.