Stochastic volatility modeling of the Ornstein Uhlenbeck type : pricing and calibration
- Authors: Marshall, Jean-Pierre
- Date: 2010-02-23T10:22:16Z
- Subjects: Stochastic processes , Lévy processes , Gaussian processes , Ornstein-Uhlenbeck process , Options (Finance) , Prices
- Type: Thesis
- Identifier: uj:6632 , http://hdl.handle.net/10210/3033
- Description: M.Sc.
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- Authors: Marshall, Jean-Pierre
- Date: 2010-02-23T10:22:16Z
- Subjects: Stochastic processes , Lévy processes , Gaussian processes , Ornstein-Uhlenbeck process , Options (Finance) , Prices
- Type: Thesis
- Identifier: uj:6632 , http://hdl.handle.net/10210/3033
- Description: M.Sc.
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Survival analysis and its stochastic process approach with application to diabetes data
- Authors: Gatabazi, Paul
- Date: 2016
- Subjects: Stochastic processes , Survival analysis (Biometry) , Estimation theory , Regression analysis , Diabetes
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/84616 , uj:19242
- Description: Abstract: Survival analysis also called time to event analysis aims at making inferences on the life time or the time elapsed between the recruitment of subjects or the onset of observations, until the occurrence of some event of interest. Methods used in general statistical analysis, in particular in regression analysis, are not directly applicable to survival data due to censoring and truncation. This study reviewed nonparametric, semi-parametric, and briefly parametric methods used in classical survival analysis, namely the Kaplan-Meier estimation, the Nelson-Aalen estimation, and the Cox proportional hazards regression model. Furthermore, the study applied the theory of counting processes and martingales to model the hazard function conditional to covariates using relative risk model and the Aalen additive risk model. This study used data collected at Kigali University Teaching Hospital on 933 diabetic patients admitted or visited the hospital during the period from the 1st January 2008 to the 31st December 2013. The results revealed that the hazard of death from diabetes, for this data, is higher in male patients as compared to female patients; it is higher in older patients compared to relatively younger ones; it is also higher in rural compared to urban patients. Patients treated using placebo had a better survival outcome than those on conventional diabetes medications. Probably, they were much healthier than those on the other three medications. Patients with normal weight, overweight, and obesity were found to have a higher hazard of death from diabetes compared to underweight patients. Patients with type II diabetes had a higher hazard of death as compared to those with type I diabetes. Finally, patients with moderately high to high blood pressure had a higher hazard of death compared to patients with low or normal blood pressure. These results were not found in a single model, but are a summary of findings obtained in several models used... , M.Sc. (Mathematical Statistics)
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- Authors: Gatabazi, Paul
- Date: 2016
- Subjects: Stochastic processes , Survival analysis (Biometry) , Estimation theory , Regression analysis , Diabetes
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/84616 , uj:19242
- Description: Abstract: Survival analysis also called time to event analysis aims at making inferences on the life time or the time elapsed between the recruitment of subjects or the onset of observations, until the occurrence of some event of interest. Methods used in general statistical analysis, in particular in regression analysis, are not directly applicable to survival data due to censoring and truncation. This study reviewed nonparametric, semi-parametric, and briefly parametric methods used in classical survival analysis, namely the Kaplan-Meier estimation, the Nelson-Aalen estimation, and the Cox proportional hazards regression model. Furthermore, the study applied the theory of counting processes and martingales to model the hazard function conditional to covariates using relative risk model and the Aalen additive risk model. This study used data collected at Kigali University Teaching Hospital on 933 diabetic patients admitted or visited the hospital during the period from the 1st January 2008 to the 31st December 2013. The results revealed that the hazard of death from diabetes, for this data, is higher in male patients as compared to female patients; it is higher in older patients compared to relatively younger ones; it is also higher in rural compared to urban patients. Patients treated using placebo had a better survival outcome than those on conventional diabetes medications. Probably, they were much healthier than those on the other three medications. Patients with normal weight, overweight, and obesity were found to have a higher hazard of death from diabetes compared to underweight patients. Patients with type II diabetes had a higher hazard of death as compared to those with type I diabetes. Finally, patients with moderately high to high blood pressure had a higher hazard of death compared to patients with low or normal blood pressure. These results were not found in a single model, but are a summary of findings obtained in several models used... , M.Sc. (Mathematical Statistics)
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The application of frequency domain techniques in the multivariable modelling and control of an airframe
- Authors: Muller, Rocco Martin
- Date: 2014-06-04
- Subjects: Airframes , Domain structure , Rotors (Helicopters) , Stochastic processes
- Type: Thesis
- Identifier: uj:11409 , http://hdl.handle.net/10210/11047
- Description: M.Ing. (Electrical and Electronic Engineering) , This treatise presents an investigation into the application of multivariable frequency domain techniques in the modelling and control of a helicopter aircraft in forward flight. The presentation is structured in the following sectioned format: I Hypotheses are stated which deal with the use of linear, multivariable, frequency domain theory in the modelling and control of helicopter aircraft. II The stated hypotheses are investigated by the application of relevant theories and techniques to a reference case plant - a single rotor helicopter in forward flight. III Conclusions drawn from the results are used to assess the validity of the hypotheses. The subject matter of the presentation may be summarized as follows: The hypotheses are initially placed in perspective by a discussion of the incentives for their formulation. In essence, the hypotheses state that helicopter dynamics, in a multivariable systems characterization, can be modelled and an appropriate flight control system designed by the use of linear frequency domain theory. The plant in reference to which the hypotheses are investigated is a single rotor utility helicopter - the Aerospatiale Alouette III. A single flight condition - a typical cruising condition - is considered. A comprehensive, nonlinear digital computer simulation of the aircraft is used as a substitute for the actual plant in the execution of the modelling and control design processes. The plant is modelled in terms of a linear model structure, in the form of the frequency response function, by linearization of its highly nonlinear dynamics about an operating point (datum flight condition). The frequency response function model parameters are identified by power spectral density analysis procedures. This method, based on random signal excitation of the plant, provides a valuable quantitative measure of the accuracy of the linearization performed in the identification. The measure, the coherence function, is used as a criterion for the robustness required of a control system of which the design is based on a linear model of a nonlinear plant.
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- Authors: Muller, Rocco Martin
- Date: 2014-06-04
- Subjects: Airframes , Domain structure , Rotors (Helicopters) , Stochastic processes
- Type: Thesis
- Identifier: uj:11409 , http://hdl.handle.net/10210/11047
- Description: M.Ing. (Electrical and Electronic Engineering) , This treatise presents an investigation into the application of multivariable frequency domain techniques in the modelling and control of a helicopter aircraft in forward flight. The presentation is structured in the following sectioned format: I Hypotheses are stated which deal with the use of linear, multivariable, frequency domain theory in the modelling and control of helicopter aircraft. II The stated hypotheses are investigated by the application of relevant theories and techniques to a reference case plant - a single rotor helicopter in forward flight. III Conclusions drawn from the results are used to assess the validity of the hypotheses. The subject matter of the presentation may be summarized as follows: The hypotheses are initially placed in perspective by a discussion of the incentives for their formulation. In essence, the hypotheses state that helicopter dynamics, in a multivariable systems characterization, can be modelled and an appropriate flight control system designed by the use of linear frequency domain theory. The plant in reference to which the hypotheses are investigated is a single rotor utility helicopter - the Aerospatiale Alouette III. A single flight condition - a typical cruising condition - is considered. A comprehensive, nonlinear digital computer simulation of the aircraft is used as a substitute for the actual plant in the execution of the modelling and control design processes. The plant is modelled in terms of a linear model structure, in the form of the frequency response function, by linearization of its highly nonlinear dynamics about an operating point (datum flight condition). The frequency response function model parameters are identified by power spectral density analysis procedures. This method, based on random signal excitation of the plant, provides a valuable quantitative measure of the accuracy of the linearization performed in the identification. The measure, the coherence function, is used as a criterion for the robustness required of a control system of which the design is based on a linear model of a nonlinear plant.
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Modelling a random cash flow of an asset using the Semi-Markovian model
- Authors: Mishindo, Leon Mbucici
- Date: 2016
- Subjects: Markov processes , Stochastic processes , Cash flow , Finance - Mathematical models
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/245887 , uj:25478
- Description: M.Com. , Abstract: In this dissertation, we have used a semi-Markovian model to calculate the conditional higher moments of any order of the present value of cash flows generated by an investment, taking into account the state of the market. With the force of interest following a stochastic process, we give an example to illustrate our results. In this work we assume that the state of economy explains the state of a country’s finances. This state is perceptible on the basis of certain indicators such as the index of a stock market. In South Africa it is the All Share Index (ALSI) that we have taken into consideration. We have observed the daily series of the ALSI index for the period from 6 December 1994 to 6 September 2014. We have further subdivided this period into two sub-periods. The first sub-period runs from December 6, 1994 to December 31, 2007 coinciding with the period before the global financial crisis and the second sub-period runs from January 1, 2008 to September 6, 2014, and relates to the post-crisis period. We have found that the daily average of the index for the pre-crisis is much lower than the daily average for the post-crisis period. Consequently, we assumed that each of these two periods put the South African economy in a particular state. Symbolically we denote state1 to represent the pre-crisis state, corresponding to the low level of the index and state0 for which the index has a high average. The consideration of South African data to conduct this study is essentially judged by the importance of its economy on the African continent. Moreover, this study established a multi-state model based on a semi-Markov approach that calculates the moments of any order of the present value of a given cash-flow. As results we found explicit formulas for the first two moments for the compound renewal sums with discounted cash flows, for a random interest rate. We observe that the length of stay in a state has a positive influence on the current value of moments in state 0. Instead In the state 1 when the length of stay increases, the present value of moments shows a slight downward trend. In additional to the above findings, when considering time, the current values of moments of order 1 are growing except in the case where the interest rate is lower in state 1. But when the interest rate increases the present value of moments also increases, even when the length of stays increasing this cause moments to increase. When the interest rate is lower, the moments of order 2 decrease with time regardless of the state in which we stand. The length of stay has the same effect on the moments, it positively influences the moments of order 2 in the state 0,..
- Full Text:
- Authors: Mishindo, Leon Mbucici
- Date: 2016
- Subjects: Markov processes , Stochastic processes , Cash flow , Finance - Mathematical models
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/245887 , uj:25478
- Description: M.Com. , Abstract: In this dissertation, we have used a semi-Markovian model to calculate the conditional higher moments of any order of the present value of cash flows generated by an investment, taking into account the state of the market. With the force of interest following a stochastic process, we give an example to illustrate our results. In this work we assume that the state of economy explains the state of a country’s finances. This state is perceptible on the basis of certain indicators such as the index of a stock market. In South Africa it is the All Share Index (ALSI) that we have taken into consideration. We have observed the daily series of the ALSI index for the period from 6 December 1994 to 6 September 2014. We have further subdivided this period into two sub-periods. The first sub-period runs from December 6, 1994 to December 31, 2007 coinciding with the period before the global financial crisis and the second sub-period runs from January 1, 2008 to September 6, 2014, and relates to the post-crisis period. We have found that the daily average of the index for the pre-crisis is much lower than the daily average for the post-crisis period. Consequently, we assumed that each of these two periods put the South African economy in a particular state. Symbolically we denote state1 to represent the pre-crisis state, corresponding to the low level of the index and state0 for which the index has a high average. The consideration of South African data to conduct this study is essentially judged by the importance of its economy on the African continent. Moreover, this study established a multi-state model based on a semi-Markov approach that calculates the moments of any order of the present value of a given cash-flow. As results we found explicit formulas for the first two moments for the compound renewal sums with discounted cash flows, for a random interest rate. We observe that the length of stay in a state has a positive influence on the current value of moments in state 0. Instead In the state 1 when the length of stay increases, the present value of moments shows a slight downward trend. In additional to the above findings, when considering time, the current values of moments of order 1 are growing except in the case where the interest rate is lower in state 1. But when the interest rate increases the present value of moments also increases, even when the length of stays increasing this cause moments to increase. When the interest rate is lower, the moments of order 2 decrease with time regardless of the state in which we stand. The length of stay has the same effect on the moments, it positively influences the moments of order 2 in the state 0,..
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