Human activities lead to the emission of carbon and carbon equivalents into the atmosphere which leads to climate change. Some of the negative impacts of climate change include increased frequency of flooding and drought. These lead to loss of soil and crucial soil nutrients which affects agricultural production leading to food insecurity, increased poverty, and may have a significant impact on the quality of life. The majority of Africa’s population are smallholder rain-dependent farmers. Their success depends on actual rainfall (amount and distribution) whose variability is projected to increase due to climate change. As the impact of climate change is felt, the inhabitants’ activities may further exacerbate land degradation through unsustainable agricultural practices. To escape from these adverse impacts requires investment. To this end, climate finance has been offering funds for investments in climate-smart agricultural projects. This has the possibility of enhancing Africa’s adaptive capacity, food security and economic growth. This thesis estimates weather-related yield risk in agriculture and the possible use of climate finance instruments for risk weather management. First, the global climate finance landscape was reviewed. This provided an overview of the available financing mechanisms, the sources of climate finance and the overall distribution of the finances across the various regions and sectors. It also highlighted the opportunities and challenges faced by climate finance investments as well as the innovative approaches that have been adopted to tap the available climate risk finance. Upon establishing the current climate finance landscape and the approaches adopted for climate risk management in agriculture, this study estimated the probable risk in Kenya's agriculture as a result of weather events such as drought. To achieve this, the national annual maize yield data from 1961 to 2014 was utilised. The yield variation was calculated by comparing the actual yield with the average expected yield. First, the average yield for each year was defined as a 5-year running mean of yields for the interval comprising of 2 years before and 2 years after the year under consideration (t-2 to t+2). This was then compared against the actual yield to obtain the yield variation. The results were fitted to a probability distribution and the Value at Risk (VaR) method was used to estimate the agricultural drought risk. The study finds the risk of yield loss due to drought to be high especially for the 50 and 100-year return period which was an estimated loss of approximately 24%. In the 1980s, yield losses of approximately 20% were experienced affecting over half a million people. These results provide information on drought risk and the possible associated losses which could be useful for drought risk management. This information is relevant to financial institutions when pricing financial products for farmers and to the government for estimating the financial resources required to manage the impacts of drought. After estimating the agricultural yield risk due to weather changes, the viability of Index Based Weather Derivative as a risk management tool against drought losses for maize farmers in Western Kenya was evaluated. To this end, option contract prices were estimated using the growing period rainfall and a Standardised Precipitation Evapotranspiration Index (SPEI). Burn analysis and the equilibrium pricing models were also used. The study finds that farmers would have benefitted if they had hedged against drought using option contracts. Specifically, at a strike level of 1 and 4, the positive pay-outs would have been in 41 and 18 seasons out of the 108 seasons during the period under study. Further research is recommended regarding the use of market price-based models to price SPEI based weather derivatives. An analysis of the efficiency of Weather Derivatives (WD) in hedging against drought risk exposure by maize farmers in Kenya was undertaken. A put option with the Standard Precipitation Evapotranspiration Index (SPEI) as the underlying index was assumed to have been bought by the farmers to hedge against income variations due to drought. The study finds that the option contracts do not efficiently hedge against drought risk in Kenya’s agriculture. This is probably because the level of risk in Kenya’s agriculture is higher than that which would be effectively covered by option contracts. It is recommended that further studies should be conducted to establish the factors that may affect the efficiency of option contracts in hedging against drought risk. Finally, this study evaluated Kenya’s readiness for climate finance. This is based on the premise that the level of a country’s readiness greatly influences the amount of climate finance that it mobilises. It was found that Kenya has instituted legislation and policies aimed at enhancing climate finance readiness. While these have been meticulously and pragmatically formulated, the implementation and effectiveness could not be confirmed. There is a need for measures that enhance data availability which would make it easier to evaluate the performance of the implemented measures. As a result of this study, the application of VaR for risk estimation in agricultural production is better understood. Similarly, in terms of financial risk management of weather-related risk in agriculture, the viability of SPEI drought index in pricing option contracts, as well as the efficiency of weather derivatives in hedging drought risks, are better understood. This study offers insights for investors and policymakers who wish to use financial instruments to manage weather risks in agriculture.