Stochastic models in finance
- Authors: Mazengera, Hassan
- Date: 2017
- Subjects: Finance -- Mathematical models , C++ (Computer program language) , GARCH model , Lebesgue-Radon-Nikodym theorems , Radon measures , Stochastic models , Stochastic processes , Stochastic processes -- Computer programs , Martingales (Mathematics) , Pricing -- Mathematical models
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/162724 , vital:40976
- Description: Stochastic models for pricing financial securities are developed. First, we consider the Black Scholes model, which is a classic example of a complete market model and finally focus on Lévy driven models. Jumps may render the market incomplete and are induced in a model by inclusion of a Poisson process. Lévy driven models are more realistic in modelling of asset price dynamics than the Black Scholes model. Martingales are central in pricing, especially of derivatives and we give them the desired attention in the context of pricing. There are an increasing number of important pricing models where analytical solutions are not available hence computational methods come in handy, see Broadie and Glasserman (1997). It is also important to note that computational methods are also applicable to models with analytical solutions. We computationally value selected stochastic financial models using C++. Computational methods are also used to value or price complex financial instruments such as path dependent derivatives. This pricing procedure is applied in the computational valuation of a stochastic (revenue based) loan contract. Derivatives with simple pay of functions and models with analytical solutions are considered for illustrative purposes. The Black-Scholes P.D.E is complex to solve analytically and finite difference methods are widely used. Explicit finite difference scheme is considered in this thesis for computational valuation of derivatives that are modelled by the Black-Scholes P.D.E. Stochastic modelling of asset prices is important for the valuation of derivatives: Gaussian, exponential and gamma variates are simulated for the valuation purposes.
- Full Text:
- Date Issued: 2017
- Authors: Mazengera, Hassan
- Date: 2017
- Subjects: Finance -- Mathematical models , C++ (Computer program language) , GARCH model , Lebesgue-Radon-Nikodym theorems , Radon measures , Stochastic models , Stochastic processes , Stochastic processes -- Computer programs , Martingales (Mathematics) , Pricing -- Mathematical models
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/162724 , vital:40976
- Description: Stochastic models for pricing financial securities are developed. First, we consider the Black Scholes model, which is a classic example of a complete market model and finally focus on Lévy driven models. Jumps may render the market incomplete and are induced in a model by inclusion of a Poisson process. Lévy driven models are more realistic in modelling of asset price dynamics than the Black Scholes model. Martingales are central in pricing, especially of derivatives and we give them the desired attention in the context of pricing. There are an increasing number of important pricing models where analytical solutions are not available hence computational methods come in handy, see Broadie and Glasserman (1997). It is also important to note that computational methods are also applicable to models with analytical solutions. We computationally value selected stochastic financial models using C++. Computational methods are also used to value or price complex financial instruments such as path dependent derivatives. This pricing procedure is applied in the computational valuation of a stochastic (revenue based) loan contract. Derivatives with simple pay of functions and models with analytical solutions are considered for illustrative purposes. The Black-Scholes P.D.E is complex to solve analytically and finite difference methods are widely used. Explicit finite difference scheme is considered in this thesis for computational valuation of derivatives that are modelled by the Black-Scholes P.D.E. Stochastic modelling of asset prices is important for the valuation of derivatives: Gaussian, exponential and gamma variates are simulated for the valuation purposes.
- Full Text:
- Date Issued: 2017
Analysis of food value chains in smallholder crop and livestock enterprises in Eastern Cape Province of South Africa
- Authors: Muchara, Binganidzo
- Date: 2011
- Subjects: Agricultural industries -- South Africa -- Eastern Cape , Food industry and trade -- South Africa -- Eastern Cape , Food supply -- South Africa -- Eastern Cape , Farms, Small -- South Africa -- Eastern Cape , Stochastic processes , Agriculture -- South Africa -- Eastern Cape , Business enterprises -- South Africa -- Eastern Cape , Livestock -- South Africa -- Eastern Cape , Crops -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MSc Agric (Agricultural Economics)
- Identifier: vital:11158 , http://hdl.handle.net/10353/d1000983 , Agricultural industries -- South Africa -- Eastern Cape , Food industry and trade -- South Africa -- Eastern Cape , Food supply -- South Africa -- Eastern Cape , Farms, Small -- South Africa -- Eastern Cape , Stochastic processes , Agriculture -- South Africa -- Eastern Cape , Business enterprises -- South Africa -- Eastern Cape , Livestock -- South Africa -- Eastern Cape , Crops -- South Africa -- Eastern Cape
- Description: The study was conducted in Mbozi and Ciko villages in Mbhashe Local Municipality of the Eastern Cape Province of South Africa. Two irrigation projects in the area were studied. Consumers and agricultural commodity traders in Willowvale Town, Dutywa, Butterworth and East London were also interviewed. The major objective of the study is to profile and map cabbage, maize and cattle food value chains broadly, and to understand their nature, constraints and opportunities in smallholder agriculture. A multi-stage random sampling procedure was used in which the first stage involved selecting the local government areas. This was followed by the selection of the district and then the respondents. A total of 168 participants were sampled in the proportion of 82 smallholder farmers, 41 consumers, 26 hawkers and 20 agricultural commodity traders. Focus group discussions and key informant interviews were also used during the data collection process. Value Chain mapping was done using the commodity based approach. All value chains under study indicated that they are short and commodities were transacted in unprocessed form. As cabbages and maize move from the farm to retail outlets, value addition start to take place through transportation to the market and processing in supermarkets. The cattle value chain however does not have a forward linkage beyond the two administrative boundaries of the two communities. Less than 3% of the farmers traded livestock, and this was mostly through private sales to neighbours. The farmers‘ major goal in agricultural production is assumed to be an important aspect in lengthening the value chain. As such, results of a Pearson‘s correlation exercise indicated that there is a significant relationship at 0.05% level between goals of the farmers and the village of origin. Some factors that showed significance (p=0.05) in influencing farmers‘ goals are membership of an irrigation project and household sources of income. An analysis of determinants of technical efficiency at farm level was performed using the stochastic frontier model for cabbage, maize and cattle enterprises. The results showed that rainfall adequacy, input costs, market channels and quantity sold are important determinants of cabbage production efficiency. On the other hand, maize production efficiency is positively determined by market price, area under production and rainfall adequacy. Market related variables are major drivers of the cattle value chain efficiency and these include cattle prices, market satisfaction, market channel and farm labour.
- Full Text:
- Date Issued: 2011
- Authors: Muchara, Binganidzo
- Date: 2011
- Subjects: Agricultural industries -- South Africa -- Eastern Cape , Food industry and trade -- South Africa -- Eastern Cape , Food supply -- South Africa -- Eastern Cape , Farms, Small -- South Africa -- Eastern Cape , Stochastic processes , Agriculture -- South Africa -- Eastern Cape , Business enterprises -- South Africa -- Eastern Cape , Livestock -- South Africa -- Eastern Cape , Crops -- South Africa -- Eastern Cape
- Language: English
- Type: Thesis , Masters , MSc Agric (Agricultural Economics)
- Identifier: vital:11158 , http://hdl.handle.net/10353/d1000983 , Agricultural industries -- South Africa -- Eastern Cape , Food industry and trade -- South Africa -- Eastern Cape , Food supply -- South Africa -- Eastern Cape , Farms, Small -- South Africa -- Eastern Cape , Stochastic processes , Agriculture -- South Africa -- Eastern Cape , Business enterprises -- South Africa -- Eastern Cape , Livestock -- South Africa -- Eastern Cape , Crops -- South Africa -- Eastern Cape
- Description: The study was conducted in Mbozi and Ciko villages in Mbhashe Local Municipality of the Eastern Cape Province of South Africa. Two irrigation projects in the area were studied. Consumers and agricultural commodity traders in Willowvale Town, Dutywa, Butterworth and East London were also interviewed. The major objective of the study is to profile and map cabbage, maize and cattle food value chains broadly, and to understand their nature, constraints and opportunities in smallholder agriculture. A multi-stage random sampling procedure was used in which the first stage involved selecting the local government areas. This was followed by the selection of the district and then the respondents. A total of 168 participants were sampled in the proportion of 82 smallholder farmers, 41 consumers, 26 hawkers and 20 agricultural commodity traders. Focus group discussions and key informant interviews were also used during the data collection process. Value Chain mapping was done using the commodity based approach. All value chains under study indicated that they are short and commodities were transacted in unprocessed form. As cabbages and maize move from the farm to retail outlets, value addition start to take place through transportation to the market and processing in supermarkets. The cattle value chain however does not have a forward linkage beyond the two administrative boundaries of the two communities. Less than 3% of the farmers traded livestock, and this was mostly through private sales to neighbours. The farmers‘ major goal in agricultural production is assumed to be an important aspect in lengthening the value chain. As such, results of a Pearson‘s correlation exercise indicated that there is a significant relationship at 0.05% level between goals of the farmers and the village of origin. Some factors that showed significance (p=0.05) in influencing farmers‘ goals are membership of an irrigation project and household sources of income. An analysis of determinants of technical efficiency at farm level was performed using the stochastic frontier model for cabbage, maize and cattle enterprises. The results showed that rainfall adequacy, input costs, market channels and quantity sold are important determinants of cabbage production efficiency. On the other hand, maize production efficiency is positively determined by market price, area under production and rainfall adequacy. Market related variables are major drivers of the cattle value chain efficiency and these include cattle prices, market satisfaction, market channel and farm labour.
- Full Text:
- Date Issued: 2011
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