Victor Gumbo
National University of Science & Technology, Finance, Faculty Member
- I am a seasoned modeling analyst in the areas of Basel II/III-IFRS 9 risk modeling, tariff modeling, revenue modeling, customer lifetime value and market mix modeling.edit
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In this study, we design stepwise ordinary least squares regression models using various amalgamations of firm features, loan characteristics and macroeconomic variables to forecast workout recovery rates for defaulted bank loans for... more
In this study, we design stepwise ordinary least squares regression models using various amalgamations of firm features, loan characteristics and macroeconomic variables to forecast workout recovery rates for defaulted bank loans for private non-financial corporates under downturn conditions in Zimbabwe. Our principal aim is to identify and interpret the determinants of recovery rates for private firm defaulted bank loans. For suitability and efficacy purposes, we adopt a unique real-life data set of defaulted bank loans for private non-financial firms pooled from a major anonymous Zimbabwean commercial bank. Our empirical results show that the firm size, the collateral value, the exposure at default, the earnings before interest and tax/total assets ratio, the length of the workout process, the total debt/total assets ratio, the ratio of (current assets–current liabilities)/total assets, the inflation rate, the interest rate and the real gross domestic product growth rate are the s...
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Online transaction services have been in use in the banking environment for the past few decades. Their use is attracting more and more organisations due to the convenience that they offer to customers as well as the efficiency offered to... more
Online transaction services have been in use in the banking environment for the past few decades. Their use is attracting more and more organisations due to the convenience that they offer to customers as well as the efficiency offered to banks. The adoption and use of online transactions in banks has been generally accepted in many parts of the world. However, there has been little information on the adoption and use of online transactions in Zimbabwe in general and in Gwanda in particular. The study thus sought to find out the adoption and use of online transactions in retail banks in Gwanda town in Zimbabwe. The adoption and use of online transactions was also explored in terms of gender and age differences. In this study, the online transactions examined were Internet Banking, Automated Teller Machines (ATM) and Mobile Banking. The study took an exploratory and mixed methods approach where interviews and questionnaires were used to collect data. The results revealed that althoug...
The estimation of Basel II/III risk parameters (PD, LGD, EAD, M) is an important task in banking and other credit providers. These parameters are used on one hand as inputs to credit portfolio models, and on the other hand, to compute... more
The estimation of Basel II/III risk parameters (PD, LGD, EAD, M) is an important task in banking and other credit providers. These parameters are used on one hand as inputs to credit portfolio models, and on the other hand, to compute risk-weighted assets, regulatory, economic and other capital. EAD modeling for the credit card portfolio presents some challenges driven by the characteristics of the portfolio. We seek to demonstrate some practical techniques for the estimation of EAD for Credit Card, mostly based on the work by G. Moral [G. Moral, EAD Estimates for Facilities with Explicit Limits, Chapter X of The Basel II Risk Parameters, Bernd Engelmann and Robert Rauhmeier, Springer, Berlin, Heidelberg, 2006].
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Technological advancements have altered the manner in which individuals conduct their personal and business affairs. This has prompted banks to realise the need to switch to online banking in an effort to increase customer satisfaction.... more
Technological advancements have altered the manner in which individuals conduct their personal and business affairs. This has prompted banks to realise the need to switch to online banking in an effort to increase customer satisfaction. In order to do this, banks have introduced the use of online transaction platforms to connect with their customers. Therefore the objective of this study was to find out the rate of adoption and the level of customer satisfaction with the online transaction platforms in commercial banks in Zimbabwe and how gender influences them. The study also sought to determine the factors influencing customer satisfaction in banks and how gender and age influences them. A sample of 268 customers was used. The online transaction platforms studied in this Paper were Internet banking, Automated Teller Machines, Mobile banking and Point of Sale. The study revealed that the adoption of online transaction platforms was relatively due to continued use of branch banking....
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The paper investigated the role of location on the performance attributes of manufacturing Small, Micro and Medium Enterprises (SMMEs) in South Africa’s second-largest province of KwaZulu Natal (KZN). Panel data from 191 SMMEs covering... more
The paper investigated the role of location on the performance attributes of manufacturing Small, Micro and Medium Enterprises (SMMEs) in South Africa’s second-largest province of KwaZulu Natal (KZN). Panel data from 191 SMMEs covering three years between 2015 and 2017 were analysed using R software. The results utilising the Random Effects Within-Between (REWB) technique show that SMMEs in KZN have related characteristics but the extent to which they influence performance is moderated by location. The findings also indicate that the use of digital media and liability registration negatively affects the performance of urban-based, with no effect on rural-based enterprises. Based on the findings, it was recommended that SMMEs in KZN should focus on productivity, permanent employees, temporary employees and total assets to drive performance despite their locations. Based on this study, the government has an informed basis for the development of effective interventions for SMMEs in the...
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The emergence of machine learning algorithms presents the opportunity for a variety of stakeholders to perform advanced predictive analytics and to make informed decisions. However, to date there have been few studies in developing... more
The emergence of machine learning algorithms presents the opportunity for a variety of stakeholders to perform advanced predictive analytics and to make informed decisions. However, to date there have been few studies in developing countries that evaluate the performance of such algorithms—with the result that pertinent stakeholders lack an informed basis for selecting appropriate techniques for modelling tasks. This study aims to address this gap by evaluating the performance of three machine learning techniques: ordinary least squares (OLS), least absolute shrinkage and selection operator (LASSO), and artificial neural networks (ANNs). These techniques are evaluated in respect of their ability to perform predictive modelling of the sales performance of small, medium and micro enterprises (SMMEs) engaged in manufacturing. The evaluation finds that the ANNs algorithm’s performance is far superior to that of the other two techniques, OLS and LASSO, in predicting the SMMEs’ sales perf...
The main objective of this work is to construct and implement a LIBOR market model and a Swaptions market model for the South African market.In his Thesis, Victor Gumbo starts by recapitulating the basic theory of arbitrage pricing,... more
The main objective of this work is to construct and implement a LIBOR market model and a Swaptions market model for the South African market.In his Thesis, Victor Gumbo starts by recapitulating the basic theory of arbitrage pricing, forward measures and term structure models for zero-coupon bonds. He goes on to describe and analyze the LIBOR market models. Apart from the standard models, he goes on to discusses market practice and provides numerous formulae for pricing as well as terminal measure existence. In Chapter 3, he gives a similar outline for Swap Market models. It should be emphasized that these models are quite complicated from a theoretical point of view but Victor manages to give an extremely pedagical account of this difficult theory.
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Prediction of financial distress for lending institutions has been a major concern since the financial crisis of 2008. The motivation for empirical research in bank bankruptcy prediction is clear — the early detection of financial... more
Prediction of financial distress for lending institutions has been a major concern since the financial crisis of 2008. The motivation for empirical research in bank bankruptcy prediction is clear — the early detection of financial distress and the use of corrective measures are preferable to protection under bankruptcy law. If it is possible to recognize failing banks in advance, then appropriate action can be taken to reverse the process before it is too late. This study uses panel multi-state Markov (MSM) chains to build a predictive model for financial distress of banks in Zimbabwe. Microeconomic factors and the CAMELS ratings were used in the construction of the MSM model. Distress probabilities were calculated using hazard ratios found by MSM and then the Altman [Formula: see text]-Scores were generated for each bank as a means of validating the built MSM model. The scores generated were very similar to the current CAMELS ratings.
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Banks play a vital role in the financial system of any country. This study aims to examine the financial performance of eleven banks in Botswana for the period 2015 to 2019 using Return on Assets (ROA), Return on Equity (ROE), and... more
Banks play a vital role in the financial system of any country. This study aims to examine the financial performance of eleven banks in Botswana for the period 2015 to 2019 using Return on Assets (ROA), Return on Equity (ROE), and Cost-to-Income (C_I) ratio as the financial measures (dependent variables), and fifteen other ratios (independent variables) as the drivers of financial performance. ROA was used to measure the internal-based performance of banks, ROE was used to study and understand the amount of a bank’s income that is returned as shareholders’ equity, and C_I ratio was used to study and understand the productivity and efficiency of banks. The data were obtained from the financial statements and annual reports of the banks under study. The study employed correlation and multiple regression analysis and it was established that the most significant driver of a bank’s ROA and ROE is the “interest income on loans over average total assets” (II_AVG_TA) ratio. However, this ra...
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Portfolio insurance is a critical component of portfolio management. Constant proportion portfolio insurance (CPPI) is one of the most popular and widely used portfolio insurance approaches. Recent years have witnessed increased... more
Portfolio insurance is a critical component of portfolio management. Constant proportion portfolio insurance (CPPI) is one of the most popular and widely used portfolio insurance approaches. Recent years have witnessed increased application of CPPI. The notion of CPPI limits the downside risk of a portfolio when markets are bearish whilst maintaining its upside potential when markets are bullish. The practice behind CPPI is to shift financial resources between risky and risk-free asset classes. Conceptually, the cushion plays a central role in the dynamics of CPPI. Portfolio insurance is currently based on stochastic finance theory. Probability theory recognises randomness as the only important form of indeterminacy in asset pricing. However, recent research through uncertainty theory led to the birth of uncertain finance theory. Uncertainty theory proposes that uncertainty is the only legitimate form of indeterminacy which should be taken into account in asset pricing. Therefore, i...
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The main objective of the study is to determine a country beta model for Zimbabwe based on six economic fundamentals; namely political risk, GDP deflator, FDI inflows, current account, external debt and GDP per capita. The country beta... more
The main objective of the study is to determine a country beta model for Zimbabwe based on six economic fundamentals; namely political risk, GDP deflator, FDI inflows, current account, external debt and GDP per capita. The country beta model is useful for predicting country risk. Logistic multiple regression analysis was employed in order to develop the beta model.
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Previous studies in both developed and developing economies have reported that firm growth declines with firm age and size. However, review of literature showed that there are limited studies to empirically assess the validity of this... more
Previous studies in both developed and developing economies have reported that firm growth declines with firm age and size. However, review of literature showed that there are limited studies to empirically assess the validity of this fact on firm growth in developing countries. As such, this paper assesses the role of firm size and age on firm growth in KwaZulu Natal, South Africa. The study employed a unique balanced three-year panel dataset of 191 manufacturing Small Medium and Micro Enterprises (SMMEs) in the province. As expected, the results showed a negative relationship between firm growth and size especially in the short term. However, contrary to the wider body of literature, the study established a positive relationship between firm age and growth. The study also established that older firms grow faster than their younger counterparts despite their size. On the other hand, small sized firms despite their age grow faster than large firms when employment and total assets we...
This study brings novelty to the area of corporate distress modelling in Zimbabwe by exploring company-specific indicators of corporate distress, unlike most of the previous studies, which used financial performance indicators. Using a... more
This study brings novelty to the area of corporate distress modelling in Zimbabwe by exploring company-specific indicators of corporate distress, unlike most of the previous studies, which used financial performance indicators. Using a binary logistic regression on a time series dataset collated between 2010 and 2017, this study establishes book value, book value per share, average debt to equity and equity per share as very significant determinants of corporate distress on the Zimbabwe Stock Exchange (ZSE). Future studies incorporating artificial intelligence and a combination of both the traditional financial ratios and market-based indicators is recommended to expand the scope of the study.
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The main aim of this study was to empirically assess the main microeconomic factors that affect a bank's performance. The objectives were to ascertain if there is a relationship between the performance variables with the microeconomic... more
The main aim of this study was to empirically assess the main microeconomic factors that affect a bank's performance. The objectives were to ascertain if there is a relationship between the performance variables with the microeconomic variables, determine those that are significant and their impact on the performance of banks in Zimbabwe. An econometric model was built from balanced panel data and the Arellano-Bond estimation procedure was employed. The empirical analysis was carried out on a sample of 17 banks that were operational in the years 2010 to 2017 in Zimbabwe. Return on Assets (ROA), Return on Equity (ROE) and Net Interest Margin (NIM) were used as the performance indicators in the analysis. The results indicate the main microeconomic factors to be those attributed to growth, credit risk, capitalisation, managerial efficiency, liquidity and diversification in the Zimbabwean financial institutions. Performance in these institutions is generally good as measured by posi...
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The introduction of the Internet has led to the development of new technologies and applications that have been adopted by organisations and their users to enable them to survive in this age of technology. Online technologies have... more
The introduction of the Internet has led to the development of new technologies and applications that have been adopted by organisations and their users to enable them to survive in this age of technology. Online technologies have penetrated Zimbabwe, particularly in the retail industry, however, little research has been done to link the research results to theory particularly the technology adoption theories. Therefore the objective of this study was to explore the current extent of adoption of online transaction platforms in the retail industry in Zimbabwe. Furthermore, this paper purposed to determine the extent of this adoption on the Technology Adoption Curve. The online transaction platforms studied were Internet banking, Automated Teller Machines, Mobile banking, Point of Sale and Mobile money. The study took a mixed method approach where both qualitative and quantitative strategies were used. A three-sample dataset comprising of 268 bank and supermarket customers, 56 bank ma...
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Inclusive financial systems allow broad access to financial services without price barriers to their use and are likely to benefit poor people and other disadvantaged groups. In Zimbabwe, little research has been done on financial... more
Inclusive financial systems allow broad access to financial services without price barriers to their use and are likely to benefit poor people and other disadvantaged groups. In Zimbabwe, little research has been done on financial inclusion since it is still a relatively new concept and hence no model has been developed to date. Therefore the purpose of this study is to explore the current extent of financial inclusion and to develop a model for financial inclusion for Zimbabwe’s retail industry. A sample of 16 bank managers and 4 supermarket managers were interviewed. The results indicated that although the retail industry had embraced some of the financial inclusion initiatives, other initiatives were still not being accepted. The resultant model was developed from the identified factors influencing financial inclusion in the study borrowing ideas from the 5Ps of financial inclusion identified in the mid 2010s.
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Inclusive financial systems allow broad access to financial services without price barriers to their use and are likely to benefit poor people and other disadvantaged groups. In Zimbabwe, little research has been done on financial... more
Inclusive financial systems allow broad access to financial services without price barriers to their use and are likely to benefit poor people and other disadvantaged groups. In Zimbabwe, little research has been done on financial inclusion since it is still a relatively new concept and hence no model has been developed to date. Therefore the purpose of this study is to explore the current extent of financial inclusion and to develop a model for financial inclusion for Zimbabwe’s retail industry. A sample of 16 bank managers and 4 supermarket managers were interviewed. The results indicated that although the retail industry had embraced some of the financial inclusion initiatives, other initiatives were still not being accepted. The resultant model was developed from the identified factors influencing financial inclusion in the study borrowing ideas from the 5Ps of financial inclusion identified in the mid 2010s.
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The retail industry in Zimbabwe has embraced the use of a variety of technologies in order to survive in this ever changing technological era. However, little research has been done on the adoption and use of these technologies and no... more
The retail industry in Zimbabwe has embraced the use of a variety of technologies in order to survive in this ever changing technological era. However, little research has been done on the adoption and use of these technologies and no model has been developed to date. The aim of this paper was to develop a model best suited to the Zimbabwean retail industry in order to enhance the successful adoption and use of online transaction platforms. The online transaction platforms used to develop the model were Internet banking, Automated Teller Machines, Mobile banking and Point of Sale. A three-sample dataset comprising of 268 bank and supermarket customers, 56 bank managers and 31 supermarket managers was used. Pearson’s correlation coefficient was used to determine the relationship between the given factors influencing adoption and use of online transaction platforms and the constructs perceived ease of use and perceived usefulness. The resultant TAMZIM model borrowed ideas from the Tec...
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The research examines the long run relationship between money market interest rates and stock market returns in Zimbabwe from April 2009 to December 2013. The estimation model controls for money supply growth rate, inflation, volume of... more
The research examines the long run relationship between money market interest rates and stock market returns in Zimbabwe from April 2009 to December 2013. The estimation model controls for money supply growth rate, inflation, volume of manufacturing index, crude oil price and political stability. All the variables were tested for unit root using augmented Dickey-Fuller test before Johansen cointegration tests. Based on vector error correlation Granger causality tests, findings show evidence of strong and statistically significant inverse causal relationship between money market interest and stock market returns. Findings also show existence of short run causality that runs from stock market returns to money market interest rates. This is believed to be caused by the passive nature of money market in Zimbabwe and non-functionality of Reserve Bank of Zimbabwe in controlling interest rates through monetary policy. There is therefore need to implement robust and pragmatic macroeconomic ...
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Capital Adequacy Ratio (CAR) plays a very important role in the financial success of banks and acts as a buffer to prevent and absorb any unexpected losses. This study examines explanatory variables that influence CAR for nine banks in... more
Capital Adequacy Ratio (CAR) plays a very important role in the financial success of banks and acts as a buffer to prevent and absorb any unexpected losses. This study examines explanatory variables that influence CAR for nine banks in Botswana. Multiple linear regression was used for analysis, with CAR as the dependent variable and thirteen financial ratios as the independent variables. The study period is 2015-2019. Based on the data for this period, it was established that out of the thirteen financial ratios utilised, only four were found to have significant impact on the CAR of the nine banks under study, which are: Asset to Equity Ratio (A E), Return on Equity (ROE), Non-Performing Loans Ratio (NPL RATIO) and the Cost-to-Income Ratio (C I). The A E Ratio was found to be the most influential driver of the CAR and the NPL Ratio was found to be the least influential driver of the CAR for the banks under study.
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Probability of Default (PD) is a financial term describing the likelihood of default over a particular time horizon. This concept has attracted a lot of interest ever since the late 1960 " s and has been extended to the banking sector to... more
Probability of Default (PD) is a financial term describing the likelihood of default over a particular time horizon. This concept has attracted a lot of interest ever since the late 1960 " s and has been extended to the banking sector to predict probability of failure as well as bank performance ratings. We derive the probability of bankruptcy and bank ratings in a Zimbabwean context based on data between 2009 and 2013, inclusive. We build a model to predict the probability of bank failure twelve months in advance for Zimbabwean banks based on twelve micro factors. Further, we build the corresponding rating model. The empirical analysis revealed that the warning signal so developed produced a robust result with a high prediction accuracy of 92.31% compared to 60% of the Altman " s Z Score model.
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This study reviews futures contracts on a contract design approach basis. Drawing from the literature and using indicative empirics, it assesses the futures contract specifications that would enable success once the recently re-launched... more
This study reviews futures contracts on a contract design approach basis. Drawing from the literature and using indicative empirics, it assesses the futures contract specifications that would enable success once the recently re-launched commodity exchange of Zombabwe (Comez) begins trading. The study highlights a primary point that while the commodity characteristics may be suitable, coupled with a very strong and supportive economic and policy environment, failure to design appropriate futures contracts may result in poor participation by market participants thereby rendering the exchange untenable.
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The research examines the long run relationship between money market interest rates and stock market returns in Zimbabwe from April 2009 to December 2013. The estimation model controls for money supply growth rate, inflation, volume of... more
The research examines the long run relationship between money market interest rates and stock market returns in Zimbabwe from April 2009 to December 2013. The estimation model controls for money supply growth rate, inflation, volume of manufacturing index, crude oil price and political stability. All the variables were tested for unit root using augmented Dickey-Fuller test before Johansen cointegration tests. Based on vector error correlation Granger causality tests, findings show evidence of strong and statistically significant inverse causal relationship between money market interest and stock market returns. Findings also show existence of short run causality that runs from stock market returns to money market interest rates. This is believed to be caused by the passive nature of money market in Zimbabwe and non-functionality of Reserve Bank of Zimbabwe in controlling interest rates through monetary policy. There is therefore need to implement robust and pragmatic macroeconomic policies like the repo market to reactivate the money market.
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In [4], the authors propose a portfolio optimization model under concave transaction costs employing" absolute deviation" a.<; a mea.<; ure of risk as out lined in [3]. It is further shown in [3], by applying the model to... more
In [4], the authors propose a portfolio optimization model under concave transaction costs employing" absolute deviation" a.<; a mea.<; ure of risk as out lined in [3]. It is further shown in [3], by applying the model to historical data of NIKKEI 225, that the" mean-absolute ...
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Portfolio insurance is a critical component of portfolio management. Constant proportion portfolio insurance (CPPI) is one of the most popular and widely used portfolio insurance approaches. Recent years have witnessed increased... more
Portfolio insurance is a critical component of portfolio management. Constant proportion portfolio insurance (CPPI) is one of the most popular and widely used portfolio insurance approaches. Recent years have witnessed increased application of CPPI. The notion of CPPI limits the downside risk of a portfolio when markets are bearish whilst maintaining its upside potential when markets are bullish. The practice behind CPPI is to shift financial resources between risky and risk-free asset classes. Conceptually, the cushion plays a central role in the dynamics of CPPI. Portfolio insurance is currently based on stochastic finance theory. Probability theory recognises randomness as the only important form of indeterminacy in asset pricing. However, recent research through uncertainty theory led to the birth of uncertain finance theory. Uncertainty theory proposes that uncertainty is the only legitimate form of indeterminacy which should be taken into account in asset pricing. Therefore, it is in the best interest of this research paper to analyse portfolio insurance in uncertain markets. In continuous time diffusion models, CPPI techniques are not exposed to gap risk. However, in practical reality CPPI approaches are exposed to gap risk. To model the dynamics of CPPI, the study adopts jump-diffusion models where the value of the underlying portfolio exhibits sudden significant downward shocks. The aim of this research paper is to quantify gap risk for CPPI strategies in uncertain markets using the investment risk index. The study also analyses the relationship between a predetermined participation rate, , and the value of the portfolio. The importance of in CPPI is also examined.
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The estimation of Basel II/III risk parameters (PD, LGD, EAD, M) is an important task in banking and other credit providers. These parameters are used on one hand as inputs to credit portfolio models, and on the other hand, to compute... more
The estimation of Basel II/III risk parameters (PD, LGD, EAD, M) is an important task in banking and other credit providers. These parameters are used on one hand as inputs to credit portfolio models, and on the other hand, to compute risk-weighted assets, regulatory, economic and other capital. EAD modeling for the credit card portfolio presents some challenges driven by the characteristics of the portfolio. We seek to demonstrate some practical techniques for the estimation of EAD for Credit Card, mostly based on the work by [1].
Research Interests:
The main objective of the study is to determine a country beta model for Zimbabwe based on six economic fundamentals; namely political risk, GDP deflator, FDI inflows, current account, external debt and GDP per capita. The country beta... more
The main objective of the study is to determine a country beta model for Zimbabwe based on six economic fundamentals; namely political risk, GDP deflator, FDI inflows, current account, external debt and GDP per capita. The country beta model is useful for predicting country risk. Logistic multiple regression analysis was employed in order to develop the beta model.
Research Interests:
Following the recent financial crises, there has been a proliferation of new risk management and portfolio construction approaches. These approaches all endeavour to better quantify and manage risk by accounting for the stylised facts of... more
Following the recent financial crises, there has been a proliferation of new risk management and
portfolio construction approaches. These approaches all endeavour to better quantify and manage
risk by accounting for the stylised facts of financial time series mainly heavy and skewed tails, volatility
clustering and converging correlations. Capturing all these stylised facts in a coherent
framework has proved to be an elusive and knotty task. We here propose a pure econometric
framework that captures all the stylised facts satisfactorily. We use three data sets to show how
the approach is implemented in VaR forecasting and correlation analysis. We show how an investment
portfolio can be constructed in order to optimise reserve capital holding. The approach
employed is linear programming (LP) computable, satisfies second degree stochastic dominance
and outperforms the general mean/VaR quadratic optimisation to arrive at efficient asset allocation.
Keywords
VaR, Stylised Facts, Volatility Clustering, Leptokurtic Returns, Converging Correlation
portfolio construction approaches. These approaches all endeavour to better quantify and manage
risk by accounting for the stylised facts of financial time series mainly heavy and skewed tails, volatility
clustering and converging correlations. Capturing all these stylised facts in a coherent
framework has proved to be an elusive and knotty task. We here propose a pure econometric
framework that captures all the stylised facts satisfactorily. We use three data sets to show how
the approach is implemented in VaR forecasting and correlation analysis. We show how an investment
portfolio can be constructed in order to optimise reserve capital holding. The approach
employed is linear programming (LP) computable, satisfies second degree stochastic dominance
and outperforms the general mean/VaR quadratic optimisation to arrive at efficient asset allocation.
Keywords
VaR, Stylised Facts, Volatility Clustering, Leptokurtic Returns, Converging Correlation
Research Interests:
It is possible to construct an arbitrage-free interest rate model in which the LIBOR rates follow a log-normal process leading to Black-type pricing formulae for caps and floors. The key to their approach is to start directly with... more
It is possible to construct an arbitrage-free interest rate model in which the LIBOR rates follow a log-normal process
leading to Black-type pricing formulae for caps and floors. The key to their approach is to start directly with modeling
observed market rates, LIBOR rates in this case, instead of instantaneous spot rates or forward rates. This model is
known as the LIBOR Market Model. We formulate the SAFEX-JIBAR market model based on the fact that the forward
JIBAR rates follow a log-normal process. Formulae of the Black-type are deduced.
leading to Black-type pricing formulae for caps and floors. The key to their approach is to start directly with modeling
observed market rates, LIBOR rates in this case, instead of instantaneous spot rates or forward rates. This model is
known as the LIBOR Market Model. We formulate the SAFEX-JIBAR market model based on the fact that the forward
JIBAR rates follow a log-normal process. Formulae of the Black-type are deduced.