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Compound distributions for financial returns.

ABSTRACT: In this paper, we propose six Student's t based compound distributions where the scale parameter is randomized using functional forms of the half normal, Fréchet, Lomax, Burr III, inverse gamma and generalized gamma distributions. For each of the proposed distribution, we give expressions for the probability density function, cumulative distribution function, moments and characteristic function. GARCH models with innovations taken to follow the compound distributions are fitted to the data using the method of maximum likelihood. For the sample data considered, we see that all but two of the proposed distributions perform better than two popular distributions. Finally, we perform a simulation study to examine the accuracy of the best performing model.

SUBMITTER: Afuecheta E

PROVIDER: S-EPMC7531861 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Compound distributions for financial returns.

Afuecheta Emmanuel E Semeyutin Artur A Chan Stephen S Nadarajah Saralees S Andrés Pérez Ruiz Diego D

PloS one 20201002 10

In this paper, we propose six Student's t based compound distributions where the scale parameter is randomized using functional forms of the half normal, Fréchet, Lomax, Burr III, inverse gamma and generalized gamma distributions. For each of the proposed distribution, we give expressions for the probability density function, cumulative distribution function, moments and characteristic function. GARCH models with innovations taken to follow the compound distributions are fitted to the data using ...[more]

PMID: 33006975

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Project description:BackgroundEmpirical studies and population-level policy simulations show the importance of voluntary medical male circumcision (VMMC) in generalized epidemics. This paper complements available scenario-based studies (projecting costs and outcomes over some policy period, typically spanning decades) by adopting an incremental approach-analyzing the expected consequences of circumcising one male individual with specific characteristics in a specific year. This approach yields more precise estimates of VMMC's cost-effectiveness and identifies the outcomes of current investments in VMMC (e.g., within a fiscal budget period) rather than of investments spread over the entire policy period.Methods/findingsThe model has three components. We adapted the ASSA2008 model, a demographic and epidemiological model of the HIV epidemic in South Africa, to analyze the impact of one VMMC on HIV incidence over time and across the population. A costing module tracked the costs of VMMC and the resulting financial savings owing to reduced HIV incidence over time. Then, we used several financial indicators to assess the cost-effectiveness of and financial return on investments in VMMC. One circumcision of a young man up to age 20 prevents on average over 0.2 HIV infections, but this effect declines steeply with age, e.g., to 0.08 by age 30. Net financial savings from one VMMC at age 20 are estimated at US$617 at a discount rate of 5% and are lower for circumcisions both at younger ages (because the savings occur later and are discounted more) and at older ages (because male circumcision becomes less effective). Investments in male circumcision carry a financial rate of return of up to 14.5% (for circumcisions at age 20). The cost of a male circumcision is refinanced fastest, after 13 y, for circumcisions at ages 20 to 25. Principal limitations of the analysis arise from the long time (decades) over which the effects of VMMC unfold-the results are therefore sensitive to the discount rate applied, and more generally to the future course of the epidemic and of HIV/AIDS-related policies pursued by the government.ConclusionsVMMC in South Africa is highly effective in reducing both HIV incidence and the financial costs of the HIV response. The return on investment is highest if males are circumcised between ages 20 and 25, but this return on investment declines steeply with age.

Project description:Background:Based on the Minorities' Diminished Returns (MDRs) framework, indicators of high socioeconomic status (SES), such as high maternal educational attainment, show weaker protective effects on various developmental, behavioral, and health outcomes for Black than White families. As a result of these MDRs, families and individuals with high educational attainment still report high levels of depression, smoking, obesity, and chronic disease. Limited knowledge exists on MDRs of maternal education on indicators of wealth such as home ownership and home value. Aims:Built on the MDRs framework, we tested the hypothesis of whether the effects of maternal educational attainment at birth on home ownership and home value, as proxies of wealth, vary between Black and White families. We hypothesized that: 1) high maternal education would be associated with more wealth 15 years later, and 2) compared to Whites, Blacks would be less likely to accumulate wealth (own a house) across all educational levels, given a weaker boosting effect of maternal educational attainment on wealth for Black than White families. Methods:The Fragile Families and Child Well-being Study, is a 15-year follow up study of a random sample of births in cities larger than 200,000 population in the US. A total number of 2004 White or Black youth were included and were followed from birth to the age of 15. The predictor of interest was maternal educational attainment at birth, treated as a categorical variable (college graduation). The outcomes were home ownership and home value (worth - owed) 15 years later, as proxies of wealth. Logistic and linear regression were used for data analysis. Results:High maternal education at birth was associated with home ownership and higher value of owned home at age 15. We also found that maternal educational attainment at birth and race interact with each other, suggesting that the effects of high maternal educational attainment at birth on home ownership/value at age 15 were weaker for Black than White families. Conclusions:Diminished returns of maternal educational attainment at birth on wealth accumulation in Black families may be a mechanism that contributes to racial health disparities in high socioeconomic status and also poor outcomes of high SES Black families. That is, a smaller effect of maternal educational attainment on changing the real lives of Black than White youth may be one of the mechanisms by which health remains worse than expected in high SES Black families. Not all of the health, behavioral, and developmental disparities are due to the racial gap in SES but also diminishing returns of socioeconomic status indicators such as maternal educational attainment for racial minorities. Research should study how social stratification, discriminatory mortgage and banking, residential segregation, family formation, employment, and occupational prestige reduce Black families' ability to mobilize their human capital and secure tangible economic and non-economic outcomes.

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Compound distributions for financial returns.

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Compound distributions for financial returns.

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