Pricing of options using the black and scholes model the Case of Nairobi stock exchange stocks

Abstract

The objectives of this research were, first , to determine the level of stock volatility, for the period 1997 to 2000, on the Nairobi Stock Exchange and identify securities that warrant hedging through the use of options. Having assessed the volatilities, the second objective was to determine the range of exercise prices, for individual stocks, that would generate in-the-money European options. Thirdly, the research sought to determine whether the world re-known Black and Scholes option pricing model could be used to value options on stocks quoted on the Nairobi Stock Exchange. The level of stock volatility on the Nairobi Stock Exchange was determined using the expected returns and monthly share price movements for each stock. Exercise price ranges were determined using a mathematical model described in detail in the research paper. Having collated all the data required to use the Black and Scholes model, option values were determined using a Black and Scholes computation software, derivagem. The expected returns for stocks in the four years under review were markedly poor, which is perhaps expected, in view of the downturn in the Kenyan economy in the said period, mirrored in the performance of the Exchange. Stock volatilities - were significant for all stocks on the Exchange with the exception of Kapchorua Tea Company, Limuru Tea Company and Regent Undervalued Assets Africa Fund. The latter did not trade while for Kapchorua Tea Company and Limuru Tea Company, monthly share prices remained virtually the same during the period of study. The mathematically determined exercise price ranges were fairly reasonable in Views of the fact that they fell within actual share price movements in the periods under review and were in tandem with the individual volatilities of the stocks, that is the higher the volatility, the wider the range of mathematically derived exercise ranges and vice versa. The research indicates that the Black and Scholes option pricing model can be used to determine option values and ranges for in-the -money options for stocks quoted on the Nairobi Stock Exchange. All the data required to use the model was based on secondary market data, with stock volatility and exercise price ranges being determined mathematically using historical data. The study gives useful insight into the performance of the Exchange (in specific, returns and volatilities of stocks quoted thereon) and offers to investors and fund managers an alternative means of managing the risks of their quoted investments, by hedging through the use of options. To the regulatory authority, the study gives the practical ties of pricing options in a Kenyan context, which will be crucial in order to effectively establish the options exchange (fourth segment) in Kenya. Being a pioneer study in option pricing, the study opens an avenue for further extensive research by Kenya's academia.