No abstract

Proximate analysis of twenty fruits and vegetable waste from Nairobi County was evaluated. They were obtained from Kangemi and Wakulima markets. Standard procedures were used for the analysis of crude fat, protein, fiber, carbohydrates, moisture, ash, nitrogen-free extract and energy. The results obtained revealed that moisture content was in the range of 82.8 to 95.86% apart from sweet potato and banana which was 62.05 and 74.30% respectively. Protein range was between 0.57 to 3.49% with high-fat content being recorded in avocado at 9.03%. The ash content was highest in comfrey at 3.46% and lowest in mango at 0.44%. The carbohydrate level obtained by the difference method was lowest in courgette at 1.99% with crude fiber ranging from 0.69 to 2.73%. The total calculated energy ranged from 1.94 to 39.98 Kcal/100g. The macro-nutrient concentrations were 3.59 and 1.53% for potassium and calcium respectively. Lead, iron and zinc were detected at 15.1±3.6, 3742±235 and 176±11 ppm respectively. There is the presence of proximate properties in the edible portion of wasted fruits and vegetable and therefore, this study recommends proper fruits and vegetable handling during harvest, transportation, storage and marketing. Besides, the unavoidable waste should be used as biomass in energy production to deal with landfilling issues in the market places.

Precise recognition of a time series path is important to policy makers, statisticians, economists, traders, hedgers and speculators alike. The correct time series path is also a key ingredient in pricing models. This study uses daily futures prices of crude oil and other distillate fuels. This paper considers the statistical properties of energy futures and spot prices and investigates the trends that underlie the price dynamics in order to gain further insights into possible nuances of price discovery and energy market dynamics. The family of ARMA-GARCH models was explored. The trends depict time varying variability and persistence of oil price shocks. The return series conform to a constant mean model with GARCH variance.

How much to spend on an option contract is the main problem at the task of pricing options. This become more complex when it comes to projecting the future possible price of the option. This is attainable if one knows the probabilities of prices either increasing, decreasing or remaining the same. Every investor wishes to make profit on whatever amount they put in the stock exchange and thus the need for a good formula that give a very good approximations to the market prices. This paper aims at introducing the concept of pricing options by using numerical methods. In particular, we focus on the pricing of a European put option which lead us to having American put option curve using Trinomial lattice model. In Trinomial method, the concept of a random walk is used in the simulation of the path followed by the underlying stock price. The explicit price of the European put option is known. Therefore at the end of the paper, the numerical prices obtained by the Black Scholes equation will be compared to the numerical prices obtained using Trinomial and Binomial methods.

This study attempts to put forward a framework that can be utilized to model the dynamics of the underlying returns on asset. The intention is to probe the dynamic connection between volatility of stock returns and trading volume of the Nairobi Securities Exchange (NSE20) index. The consequence of incorporating trading volume in the equation for conditional variance of the generalized autoregressive conditional heteroscedasticity (GARCH) model on volatility persistence is investigated. Further, this study brings into play GARCH, GARCH-M, and EGARCH models conditioned to normal, student-t and generalized error distributions to model the dynamic structure of the NSE20 index for the period 2 January 2001 to 31 December 2017. The results disclose some well-known stylized facts of returns on stock, for instance, volatility clustering, heavy tails, leverage effects, and leptokurtic distribution. The estimates of parameters of the three models, that is, GARCH (1, 1), GARCH-M (1, 1), and EGARCH models report that the correlation between stock returns volatility and trading volume is positive and statistically significant. Moreover, estimates of the coefficients of EGARCH (1, 1) model report an increased measure of persistence on volatility as well as volatility asymmetry and the absence of leverage effect in the returned volatility. Also, the estimates of GARCH (1, 1) and GARCH-M (1, 1) parameters report that volatility persistence dwindles after trading volume is incorporated in the equation for the conditional variance.