Defaultable bond pricing under the jump diffusion model with copula dependence structure

We study the pricing of a defaultable bond under various dependence structure captured by copulas. For that purpose, we use a bivariate jump-diffusion process to represent a bond issuer’s default intensity and the market short rate of interest. We assume that each jump of both variables occur simultaneously, and that their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process and three copulas, which are a Farlie-Gumbel- Morgenstern copula, a Gaussian copula, and a Student t-copula are used, respectively. We use the joint Laplace transform of the integrated risk processes to obtain the expression of the defaultable bond price with copula-dependent jump sizes. Assuming exponential marginal distributions, we compute the zero coupon defaultable bond prices and their yields using the three copulas to illustrate the bond. We found that the bond price values are the lowest under the Student-t copula, suggesting that a dependence structure under the Student-t copula could be a suitable candidate to depict a riskier environment. Additionally, the hypothetical term structure of interest rates under the risky environment are also upward sloping, albeit with yields greater than 100%, reflecting a higher compensation required by investors to lend funds for a longer period when the financial market is volatile

Students’ Inclination towards English Language as Medium of Instruction in the Teaching of Science and Mathematics

AbstractMalay language, the national language of Malaysia has been the medium of instruction for Science and Mathematics for the past four and a half decades in Malaysia. The government however changed the medium of instruction of these subjects to English in January 2003. The “Teaching and Learning of Science and Mathematics in English” (PPSMI) policy was implemented in all primary and secondary schools. It aims to improve the English language proficiency among students as well as the learning and achievement level in science and mathematics. This paper presents findings of the study on students’ inclination towards English language as medium of instruction in teaching and learning of Science and Mathematics in Higher Learning Institutions in Malaysia. The respondents were 291 undergraduate students from the Faculty of Science and Technology (FST) and Faculty of Education (FPEND) of Universiti Kebangsaan Malaysia (UKM). A questionnaire pertaining to students’ inclination was used as research instrument. Using descriptive statistics, ANOVA and t-test, the study found that undergraduate students of FST and FPEND had an inclination towards English as medium of instruction in the teaching and learning of Science and Mathematics. Using the Post-Hoc test, it is found that Indian students and students from other races than Malay and Chinese have greater inclination towards English as medium of instruction in teaching and learning of Science and Mathematics in UKM for both faculties. However, FST students who studied in Mandarin and Tamil at pre-university level (STPM) had higher inclination compared to those who used Malay language or even English

Modelling multivariate dependence structures in insurance and credit risk via copulas

Thesis by publication."A thesis submitted to Macquarie University for the degree of Doctor of Philosophy, Department of Applied Finance & Actuarial Studies, Faculty of Business & Economics"."November 2014".Bibliography: pages 159-165.1. Introduction -- 2. Neumann series on the recursive moments of copula-dependent aggregate discounted claims -- 3. A multivariate jump diffusion process for counterparty risk in CDS rates -- 4. Jump diffusion model with copula dependence structure in defaultable bond pricing -- 5. Conclusion -- Appendices.This PhD thesis seeks to offer a new framework that accommodates dependency in pricing an insurance portfolio following the renewal risk model, corporate bonds, as well as credit default swaps (CDS). This will be achieved by combining the approach and methodology of actuarial science with stochastic processes and probability theories, as well as employing a hint of the integral calculus used in the electromagnetic and viscoelasticity fields.This thesis is a collection of three papers, which are presented in Chapters 2, 3 and 4. While Chapters 3 and 4 can be read in conjunction with each other, Chapter 2 can be read in isolation because it presents a completely different perspective of insurance to the financial perspective taken in the other two articles (Chapter 3 and 4). Nevertheless, the three papers share the same scope, which is the use of copula to capture the dependency between variables. In total, four copulas are explored: the Farlie-Gumbel-Morgenstern (FGM) copula, Gumbel copula, Gaussian copula and Student-t copula. However, only three copulas are compared in each working paper. The first article in Chapter 2 models a continuous time renewal risk process, and uses copulas to capture the dependence structure between the claims inter-arrival time and discounted claims size. The second and third articles work under the framework of a reduced form model and use various copulas to capture the dependence structure between the jump sizes of the intensity processes, each of which is represented by a jump diffusion process.Taking the insurance perspective, the first article - titled Neumann Series on the Recursive Moments of Copula-Dependent Aggregate Discounted Claims - studies the recursive moments of aggregate discounted claims, where the dependence between the interclaim time and the subsequent claim size is considered. Using the general expression for the mth order moment proposed in [1] which takes the form of the Volterra Integral Equation (VIE), we used the method of successive approximation to derive the Neumann series of the recursive moments. We then compute the first two moments of aggregate discounted claims, i.e. its mean and variance, based on the Neumann series expression where the dependence structure is captured by the FGM copula, Gaussian copula and Gumbel copula, with exponential marginal distributions. Insurance premium calculations with their figures are also illustrated.The second work – titled A multivariate jump diffusion process for counterparty risk in CDS rates – considers counterparty risk in CDS rates. To do so, it uses a multivariate jump diffusion process for obligors’ default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process and three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas are used. This project applies copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [2] and the martingale methodology in [3] are used. The survival/default probability is computed using the three copulas and exponential marginal distributions, and the results are applied to calculate CDS rates, assuming deterministic rate of interest and recovery rate. Sensitivity analysis for the CDS rates were also conducted by changing the relevant parameters and providing their figures.The final article – titled Jump diffusion model with copula dependence structure in defaultable bond pricing – studies the pricing of a defaultable bond under various copulas. For that purpose, it used a bivariate jump diffusion process for a bond issuer’s default intensity and the short rate of interest. We assume the jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process and three copulas – FGM copula, Gaussian copula and Student-t copula are used, respectively. The joint Laplace transform for the variables’ integrated processes is derived to provide the expression for defaultable bond price, using copula-dependent jump sizes. Once again, we apply the piecewise deterministic Markov process (PDMP) theory developed in [2] and the martingale methodology in [3]. Zero coupon defaultable bond prices and their yield are computed using the three copulas and exponential marginal distributions. The model is then used to calibrate zero coupon bonds on one-day basis as well as for an extended period of one year. Calibration results show that the Student-t copula provides the best fit relative to the other two copulas.Mode of access: World wide web1 online resource (xxii, 165 pages) colour illustration

Neumann series on the recursive moments of copula-dependent aggregate discounted claims

We study the recursive moments of aggregate discounted claims, where the dependence between the inter-claim time and the subsequent claim size is considered. Using the general expression for the m-th order moment proposed by Léveillé and Garrido (Scand. Actuar. J. 2001, 2, 98–110), which takes the form of the Volterra integral equation (VIE), we used the method of successive approximation to derive the Neumann series of the recursive moments. We then compute the first two moments of aggregate discounted claims, i.e., its mean and variance, based on the Neumann series expression, where the dependence structure is captured by a Farlie–Gumbel–Morgenstern (FGM) copula, a Gaussian copula and a Gumbel copula with exponential marginal distributions. Insurance premium calculations with their figures are also illustrated.16 page(s

A Multivariate jump diffusion process for counterparty risk in CDS rates

We consider counterparty risk in CDS rates. To do so, we use a multivariate jump diffusion process for obligors' default intensity, where jumps (i.e. magnitude of contribution of primary events to default intensities) occur simultaneously and their sizes are dependent. For these simultaneous jumps and their sizes, a homogeneous Poisson process. We apply copula-dependent default intensities of multivariate Cox process to derive the joint Laplace transform that provides us with joint survival/default probability and other relevant joint probabilities. For that purpose, the piecewise deterministic Markov process (PDMP) theory developed in [7] and the martingale methodology in [6] are used. We compute survival/default probability using three copulas, which are Farlie-Gumbel-Morgenstern (FGM), Gaussian and Student-t copulas, with exponential marginal distributions. We then apply the results to calculate CDS rates assuming deterministic rate of interest and recovery rate. We also conduct sensitivity analysis for the CDS rates by changing the relevant parameters and provide their figures.23 page(s

Jump diffusion transition intensities in life insurance and disability annuity

We study the effects of jump diffusion transition intensities on a life insurance and disability annuity. To do so, we use a multi-states Markov chain with multiple decrement. Assuming independent statewise intensities, we evaluate the prospective reserve for this scheme where the insured life is in Active or Disabled state at inception, respectively. We also examine the components of the prospective reserves by changing the relevant parameters of the transition intensities, which are the jump size, the average frequency of jumps as well as the diffusion parameters, assuming deterministic rate of interest. The computation of the reserve sensitivity with their figures are provided.12 page(s

The Effect of minimum wage policy on Malaysia’s CPI & PPI: an intervention analysis

The minimum wage policy in Malaysia has been debatable due to contradicting perspectives among consumers and producers. While the consumers believe that the minimum wage policy is important to support their increasing cost of living, this policy has raised concerns among producers as they believe that this intervention might increase the cost of production, especially to producers who have been paying wages lesser than the policy’s rate. Hence it is important to numerically assess the impact of the policy on Malaysia’s consumer price index (CPI) and producer price index (PPI). To achieve this main objective, we built an intervention model using time series analysis and multiple linear regression. Based on both analyses, we conclude that only the PPI shows significant changes following the minimum wage policy implementation, whereby a decrease of 97.3% occurred in every month of 2014. However, there was no significant effect on the CPI during the first year of its establishment. Our 3 months forecast for the year 2018 also shows that the forecast of both indices is within the 95% confidence interval, which could imply that both indices are following the same fundamental structure during the 3 months period, despite the change in the Malaysian government ruling party

Comparison of performance between MARKOWITZ model and enhanced index tracking model

The rapid growth of exchange-traded fund (ETF) in Malaysia and recommendation of investment professionals raise doubt on whether a portfolio which tracks the performance of an index will perform better than a carefully built portfolio, such as the one built by using the classical Markowitz Model. Thus, the composition of an optimal portfolio built based on the Markowitz model and enhanced index tracking model using the data of finance, plantation and industrial indices of the Malaysian stock market from 2012-2017 will be investigated. Comparisons are made on their risk-adjusted performance using expected return, the Sharpe ratio and information ratio. The study found that the Markowitz portfolio includes only 31.43% to 33.33% of the respective index components inside the portfolio built. Overall, the Markowitz model outperforms the enhanced index tracking model in constructing an optimal portfolio with a higher expected return, Sharpe ratio and information ratio in finance and industrial sectors

A Review of statistical methods used for intervention evaluation

The adopted United Nations General Assembly through Resolution A/RES/74/299 “Improving global road safety” with the Decade of Action for Road Safety 2021-2030 targets to prevent at least 50% of road deaths and injuries by 2030. The global plan called for a holistic approach to road safety and continued improvements in the vehicles and road, enhancement of laws and law enforcement; and provision of timely, life-saving emergency care for the injured. Various road safety interventions and programs have been implemented worldwide with the aim to reduce fatalities and injuries. The importance of evaluating the impact of intervention through sound statistical approaches is definite. As intervention could be conducted in many ways, so can the methods. By design, randomized control trials hold the gold standard in intervention evaluation. However, there are many circumstances where it is not feasible, and researchers opted for a quasi-experimental approach especially when it involves ethical or financial constraints. This paper reviews three approaches used for intervention evaluation: the difference-in-differences method, segmented regression of interrupted time series, and interventional autoregressive integrated moving average, in the field of road safety. The aim is to review the methods used for intervention evaluation or program effectiveness. The Scopus database and available research reports from World Health Organization and related agencies were used to search for available pieces of literature for the year 2013 onwards

Talent management and public service competitiveness in Malaysia

Public service organizations in Malaysia must improve their performance and competitiveness to safeguard themselves against the potential negative consequences of their modest decline in these areas. Previous studies have recognized that talent management can significantly influence an organization's performance, but theoretical and empirical research on this relationship remains limited within public service organizations. Therefore, this research aimed to explore and understand the interplay among talent, talent management, and competitiveness within the context of the Malaysian public service sector. Following a qualitative approach, interviews were conducted with 10 Malaysian public servants from the Public Sector Key Position (JUSA) level. The interview transcripts were subsequently analyzed using ATLAS.ti 9 software. The study's findings revealed that talent management and talent constitute a core strategy for competitiveness in the Malaysian public service. Clear definitions of these concepts are vital in facilitating a more profound understanding of this strategy among public service organizations and their stakeholders. Consequently, the refinement and elaboration of definitions are essential to ensure clarity and consensus among all stakeholders, thus preventing confusion and misunderstandings in the future. Lastly, the definition process enables public service organizations to develop more precise definitions based on their specific context and scope