Ruin probability for heterogeneous loans
- Authors: Mashimbye, Felicia
- Date: 2020
- Subjects: Probabilities , Bank loans
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/451947 , uj:39845
- Description: Abstract: This study examines the impact of losses and defaults using ruin theory and uses a heterogeneous portfolio of loans extending specifically to banking institutions. Simply put, this study focuses on the time at which default occurs in order to assist banks to detect defaults before they occur. This is done through the Sparre Anderson Model and the associated ruin probabilities linked to the stochastic flows of heterogeneous loans. The dissertation derives the Cramér-Lundberg-type bounds for ruin probability (through the Sparre Anderson Model) while also determining the impact of changing the interest rate, time to maturity and probability of default of different loan sizes. In addition, the Cramér-Lundberg-type bounds are derived to determine the lower and upper ruin probability bounds. The time of ruin is analysed through the Laplace Transform. The results show that if the adjustment coefficient declines, the ruin probability will increase, resulting in an increase in the probability of default. The values of 𝐶− and 𝐶+ (the upper and lower bound, respectively) are meaningful in deriving the bounds for ruin probability. This dissertation finds that obtaining the value of the adjustment coefficient makes it possible to determine the constants of the bounds which are a risk measure for the default exposure of loans. Increasing the premium increases the probability of default. This means that financial institutions should apply caution when increasing their premiums. , M.Com. (Financial Economics)
- Full Text:
- Authors: Mashimbye, Felicia
- Date: 2020
- Subjects: Probabilities , Bank loans
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/451947 , uj:39845
- Description: Abstract: This study examines the impact of losses and defaults using ruin theory and uses a heterogeneous portfolio of loans extending specifically to banking institutions. Simply put, this study focuses on the time at which default occurs in order to assist banks to detect defaults before they occur. This is done through the Sparre Anderson Model and the associated ruin probabilities linked to the stochastic flows of heterogeneous loans. The dissertation derives the Cramér-Lundberg-type bounds for ruin probability (through the Sparre Anderson Model) while also determining the impact of changing the interest rate, time to maturity and probability of default of different loan sizes. In addition, the Cramér-Lundberg-type bounds are derived to determine the lower and upper ruin probability bounds. The time of ruin is analysed through the Laplace Transform. The results show that if the adjustment coefficient declines, the ruin probability will increase, resulting in an increase in the probability of default. The values of 𝐶− and 𝐶+ (the upper and lower bound, respectively) are meaningful in deriving the bounds for ruin probability. This dissertation finds that obtaining the value of the adjustment coefficient makes it possible to determine the constants of the bounds which are a risk measure for the default exposure of loans. Increasing the premium increases the probability of default. This means that financial institutions should apply caution when increasing their premiums. , M.Com. (Financial Economics)
- Full Text:
Linear predictor of discounted aggregated cash flows with dependent inter-occurrence time
- Authors: Shipalana, Peace Victory
- Date: 2019
- Subjects: Finance - Mathematical models , Accounting - Mathematical models , Copulas (Mathematical statistics) , Portfolio management
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/403013 , uj:33751
- Description: Abstract : In this minor dissertation we derive the first two moments and a linear predictor of the compound discounted renewal aggregate cash flows when taking into account dependence within the inter-occurrence times. To illustrate our results, we use specific mixtures of exponential distributions to define the Archimedean copula, the dependence structure between the cash flow inter-occurrence times. The Ho-Lee interest rate model is used to show that the formulas derived can be calculated. , M.Com. (Financial Economics)
- Full Text:
- Authors: Shipalana, Peace Victory
- Date: 2019
- Subjects: Finance - Mathematical models , Accounting - Mathematical models , Copulas (Mathematical statistics) , Portfolio management
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/403013 , uj:33751
- Description: Abstract : In this minor dissertation we derive the first two moments and a linear predictor of the compound discounted renewal aggregate cash flows when taking into account dependence within the inter-occurrence times. To illustrate our results, we use specific mixtures of exponential distributions to define the Archimedean copula, the dependence structure between the cash flow inter-occurrence times. The Ho-Lee interest rate model is used to show that the formulas derived can be calculated. , M.Com. (Financial Economics)
- Full Text:
Modelling credit scoring with data limitations : logistic vs Bayesian linear techniques
- Authors: Ncapai, Thamsanqa Herbert
- Date: 2019
- Subjects: Credit scoring systems , Financial economics , Bayesian statistical theory
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/414262 , uj:34932
- Description: Abstract: The South African banking sector has been faced with many different challenges in recent years, driven by the slow growth of the economy. This among other factors has forced the South African banking sector to explore growth opportunities in other countries on the African continent. The drive for growth on the African continent has brought different changes for banks looking to provide loans in these countries. One particular challenge during the credit scoring process has been the banks' ability to distinguish between good and bad customers who require a loan. Considering that a key income for retail banking results mainly in their ability to provide loans, this dissertation explores an alternative to credit scoring for banks that are looking to move into an environment with data limitations. The objective of this dissertation is to ascertain if the Bayesian approach can improve banks’ ability to properly distinguish between bad and good customers applying for credit when working with data limitations. This approach is compared to the logistic regression approach currently used by the bank under study. Data was obtained from a South African Bank with exposure to Botswana overdraft accounts for retail lending from 2014 to 2017, with only 964 accounts. The MCMC procedure in SAS was used to build the Bayesian model and was compared to the bank's logistic regression model. The RMSE and graphical representation of the actuals vs predicted defaults were used as performance measures to compare the two models. The logistic regression model was found to be better at predicting default than the Bayesian model, when based on RMSE. If we consider the graphical representation, we can identify that the Bayesian model is more stable than the logistic regression model. However, the Bayesian logistic regression model did not outperform the bank's logistic regression model. , M.Com. (Financial Economics)
- Full Text:
- Authors: Ncapai, Thamsanqa Herbert
- Date: 2019
- Subjects: Credit scoring systems , Financial economics , Bayesian statistical theory
- Language: English
- Type: Masters (Thesis)
- Identifier: http://hdl.handle.net/10210/414262 , uj:34932
- Description: Abstract: The South African banking sector has been faced with many different challenges in recent years, driven by the slow growth of the economy. This among other factors has forced the South African banking sector to explore growth opportunities in other countries on the African continent. The drive for growth on the African continent has brought different changes for banks looking to provide loans in these countries. One particular challenge during the credit scoring process has been the banks' ability to distinguish between good and bad customers who require a loan. Considering that a key income for retail banking results mainly in their ability to provide loans, this dissertation explores an alternative to credit scoring for banks that are looking to move into an environment with data limitations. The objective of this dissertation is to ascertain if the Bayesian approach can improve banks’ ability to properly distinguish between bad and good customers applying for credit when working with data limitations. This approach is compared to the logistic regression approach currently used by the bank under study. Data was obtained from a South African Bank with exposure to Botswana overdraft accounts for retail lending from 2014 to 2017, with only 964 accounts. The MCMC procedure in SAS was used to build the Bayesian model and was compared to the bank's logistic regression model. The RMSE and graphical representation of the actuals vs predicted defaults were used as performance measures to compare the two models. The logistic regression model was found to be better at predicting default than the Bayesian model, when based on RMSE. If we consider the graphical representation, we can identify that the Bayesian model is more stable than the logistic regression model. However, the Bayesian logistic regression model did not outperform the bank's logistic regression model. , M.Com. (Financial Economics)
- Full Text:
- «
- ‹
- 1
- ›
- »