Philip Ngare

On Modelling and Pricing Rainfall Derivatives with Seasonality

Abstract We are interested in pricing rainfall options written on precipitation at specific locations. We assume the existence of a tradeable financial instrument in the market whose price process is affected by the quantity of rainfall. We then construct a suitable ‘Markovian gamma’ model for the rainfall process which accounts for the seasonal change of precipitation and show how maximum likelihood estimators can be obtained for its parameters. We derive optimal strategies for exponential utility from terminal wealth and determine the utility indifference price of the claim. The method is illustrated with actual measured data on rainfall from a location in Kenya and spot prices of Kenyan electricity companies.

Utility indifference pricing of derivatives written on industrial loss indices

We consider the problem of pricing derivatives written on some industrial loss index via utility indifference pricing. The industrial loss index is modeled by a compound Poisson process and the insurer can adjust her portfolio by choosing the risk loading, which in turn determines the demand. We compute the price of a CAT (spread) option written on that index using utility indifference pricing and present numerical examples.

Interest rate risk management for commercial banks in Kenya

We show empirically that banks exposure to interest rate risk or income gap determines the structure of the balance sheet. In particular, we show that in Kenya, commercial banks typically retain a large exposure to interest rates that can be predicted through the income gap. We also establish the sensitivity of income gaps to market interest rates as determined by the Central Bank of Kenya (CBK) through treasury instruments. Quantitatively, a 200 basis point change in CBK rates would lead to a change of net income equivalent to 0.4% of total assets of the bank.

A Poisson-Gamma Model for Zero Inflated Rainfall Data

Rainfall modeling is significant for prediction and forecasting purposes in agriculture, weather derivatives, hydrology, and risk and disaster preparedness. Normally two models are used to model the rainfall process as a chain dependent process representing the occurrence and intensity of rainfall. Such two models help in understanding the physical features and dynamics of rainfall process. However rainfall data is zero inflated and exhibits overdispersion which is always underestimated by such models. In this study we have modeled the two processes simultaneously as a compound Poisson process. The rainfall events are modeled as a Poisson process while the intensity of each rainfall event is Gamma distributed. We minimize overdispersion by introducing the dispersion parameter in the model implemented through Tweedie distributions. Simulated rainfall data from the model shows a resemblance of the actual rainfall data in terms of seasonal variation, means, variance, and magnitude. The model also provides mechanisms for small but important properties of the rainfall process. The model developed can be used in forecasting and predicting rainfall amounts and occurrences which is important in weather derivatives, agriculture, hydrology, and prediction of drought and flood occurrences.

Regime-Switching Temperature Dynamics Model for Weather Derivatives

Weather is a key production factor in agricultural crop production and at the same time the most significant and least controllable source of peril in agriculture. These effects of weather on agricultural crop production have triggered a widespread support for weather derivatives as a means of mitigating the risk associated with climate change on agriculture. However, these products are faced with basis risk as a result of poor design and modelling of the underlying weather variable (temperature). In order to circumvent these problems, a novel time-varying mean-reversion Levy regime-switching model is used to model the dynamics of the deseasonalized temperature dynamics. Using plots and test statistics, it is observed that the residuals of the deseasonalized temperature data are not normally distributed. To model the nonnormality in the residuals, we propose using the hyperbolic distribution to capture the semiheavy tails and skewness in the empirical distributions of the residuals for the shifted regime. The proposed regime-switching model has a mean-reverting heteroskedastic process in the base regime and a Levy process in the shifted regime. By using the Expectation-Maximization algorithm, the parameters of the proposed model are estimated. The proposed model is flexible as it modelled the deseasonalized temperature data accurately.

LÉVY PROCESS BASED ORNSTEIN-UHLENBECK TEMPERATURE MODEL WITH TIME VARYING SPEED OF MEAN REVERSION

In this study we develop a Lévy process driven Ornstein-Uhlenbeck daily temperature model. The model takes into account a timedependent speed of mean reversion. It is statistically demonstrated that historical data and temperature differences are not normally distributed and hence we have argued against modeling temperature residuals as a Wiener process rather we have used the normal inverse Gaussian distribution which can ably describe skewed and heavy tailed data. Neural networks have been applied to estimate parameters of the detrended and deseasonalized temperature data because there is no prior knowledge on the nature of the function that describes the speed of mean reversion in the model. Nelson Christopher Dzupire, Philip Ngare and Leo Odongo 200

Determinants of Mobile Money Remittance in East Africa

Globally, remittances represent an important flow of international financial resources. In the East African trading bloc, the dynamic population movements between countries has led to widespread distribution of population across the region. This has driven the demand for migrant workers to send money home. Mobile money has seen a rapid growth within individual East African countries with Kenya, Tanzania and Uganda topping the global volume of mobile money transfers. One would expect the Mobile Money Remittance within the East African region to follow a similar trend being an extension of the local service. However, its uptake across borders appears to be slow. This study seeks to identify the consumer determinants that affect the uptake of the service. The study is based on the Technology Acceptance Model which gathers insight through the lens of usefulness, ease of use, perceived cost, availability of alternatives and risk perception. Once the data was collected a Cronbach alpha was applied to ensure their reliability for the purpose. The research showed that Perceived Usefulness and Perceived Ease of Use are key drivers for the mobile international remittance. This could be expected given the mobile money background of the users. In addition, the Perceived Cost of International Mobile Remittance is a key driver of behavioral intent. There was little evidence to show that Attractiveness of Alternatives and Perceived risk actually discouraged users from using International Mobile Remittances.