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
Connection management applications for high-speed audio networking
- Authors: Sibanda, Phathisile
- Date: 2008 , 2008-03-12
- Subjects: Flash (Computer file) , Computer networks , Computer networks -- Management , Digital communications , Computer sound processing , Sound -- Recording and reproducing -- Digital techniques , Broadcast data systems , C# (Computer program language) , C++ (Computer program language) , ActionScript (Computer program language)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4634 , http://hdl.handle.net/10962/d1006532 , Flash (Computer file) , Computer networks , Computer networks -- Management , Digital communications , Computer sound processing , Sound -- Recording and reproducing -- Digital techniques , Broadcast data systems , C# (Computer program language) , C++ (Computer program language) , ActionScript (Computer program language)
- Description: Traditionally, connection management applications (referred to as patchbays) for high-speed audio networking, are predominantly developed using third-generation languages such as C, C# and C++. Due to the rapid increase in distributed audio/video network usage in the world today, connection management applications that control signal routing over these networks have also evolved in complexity to accommodate more functionality. As the result, high-speed audio networking application developers require a tool that will enable them to develop complex connection management applications easily and within the shortest possible time. In addition, this tool should provide them with the reliability and flexibility required to develop applications controlling signal routing in networks carrying real-time data. High-speed audio networks are used for various purposes that include audio/video production and broadcasting. This investigation evaluates the possibility of using Adobe Flash Professional 8, using ActionScript 2.0, for developing connection management applications. Three patchbays, namely the Broadcast patchbay, the Project studio patchbay, and the Hospitality/Convention Centre patchbay were developed and tested for connection management in three sound installation networks, namely the Broadcast network, the Project studio network, and the Hospitality/Convention Centre network. Findings indicate that complex connection management applications can effectively be implemented using the Adobe Flash IDE and ActionScript 2.0.
- Full Text:
- Date Issued: 2008
- Authors: Sibanda, Phathisile
- Date: 2008 , 2008-03-12
- Subjects: Flash (Computer file) , Computer networks , Computer networks -- Management , Digital communications , Computer sound processing , Sound -- Recording and reproducing -- Digital techniques , Broadcast data systems , C# (Computer program language) , C++ (Computer program language) , ActionScript (Computer program language)
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:4634 , http://hdl.handle.net/10962/d1006532 , Flash (Computer file) , Computer networks , Computer networks -- Management , Digital communications , Computer sound processing , Sound -- Recording and reproducing -- Digital techniques , Broadcast data systems , C# (Computer program language) , C++ (Computer program language) , ActionScript (Computer program language)
- Description: Traditionally, connection management applications (referred to as patchbays) for high-speed audio networking, are predominantly developed using third-generation languages such as C, C# and C++. Due to the rapid increase in distributed audio/video network usage in the world today, connection management applications that control signal routing over these networks have also evolved in complexity to accommodate more functionality. As the result, high-speed audio networking application developers require a tool that will enable them to develop complex connection management applications easily and within the shortest possible time. In addition, this tool should provide them with the reliability and flexibility required to develop applications controlling signal routing in networks carrying real-time data. High-speed audio networks are used for various purposes that include audio/video production and broadcasting. This investigation evaluates the possibility of using Adobe Flash Professional 8, using ActionScript 2.0, for developing connection management applications. Three patchbays, namely the Broadcast patchbay, the Project studio patchbay, and the Hospitality/Convention Centre patchbay were developed and tested for connection management in three sound installation networks, namely the Broadcast network, the Project studio network, and the Hospitality/Convention Centre network. Findings indicate that complex connection management applications can effectively be implemented using the Adobe Flash IDE and ActionScript 2.0.
- Full Text:
- Date Issued: 2008
Pricing exotic options using C++
- Authors: Nhongo, Tawuya D R
- Date: 2007
- Subjects: C++ (Computer program language) , Monte Carlo method , Simulation methods , Options (Finance) -- Mathematical models , Pricing -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5577 , http://hdl.handle.net/10962/d1008373 , C++ (Computer program language) , Monte Carlo method , Simulation methods , Options (Finance) -- Mathematical models , Pricing -- Mathematical models
- Description: This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.
- Full Text:
- Date Issued: 2007
- Authors: Nhongo, Tawuya D R
- Date: 2007
- Subjects: C++ (Computer program language) , Monte Carlo method , Simulation methods , Options (Finance) -- Mathematical models , Pricing -- Mathematical models
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5577 , http://hdl.handle.net/10962/d1008373 , C++ (Computer program language) , Monte Carlo method , Simulation methods , Options (Finance) -- Mathematical models , Pricing -- Mathematical models
- Description: This document demonstrates the use of the C++ programming language as a simulation tool in the efficient pricing of exotic European options. Extensions to the basic problem of simulation pricing are undertaken including variance reduction by conditional expectation, control and antithetic variates. Ultimately we were able to produce a modularized, easily extend-able program which effectively makes use of Monte Carlo simulation techniques to price lookback, Asian and barrier exotic options. Theories of variance reduction were validated except in cases where we used control variates in combination with the other variance reduction techniques in which case we observed increased variance. Again, the main aim of this half thesis was to produce a C++ program which would produce stable pricings of exotic options.
- Full Text:
- Date Issued: 2007
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