Probabilistic Modeling of Financial Uncertainties

Introduction

In recent years, there have been advancements in the efficiency improvement of computational algorithms for financial risk modeling (Ramachandran & Chang, 2014; Zhang et al., 2018), development of new methodologies for tackling financial prediction in the era of Big Data (Jeon et al., 2018) and the introduction of emerging technologies and platforms (Chang et al., 2012; Chang et al., 2017) such as cloud that can benefit financial modeling and prediction. There are numerous studies that have proved the assumption of normal distribution in financial asset returns wrong. In recent decades, there have been numerous research works and case studies that have verified the fact that financial applications entail heavy-tail distribution. This is where deviation from the mean is far greater than normal distribution. Moreover, understanding the implications of heavy-tail distributions is crucial, specifically when assessing financial risk. The key to financial risk assessment is to maximise the profit and/or return on investment whilst minimizing the potential realistic risks. Risks have impact, likelihood or probability which will assist us in calculating the risk value. However, catastrophes usually ensue upon convergence of the most extreme events and therefore calculating the probability of risk manifestation is the key to an informed decision making. We should also note that heavy tailed and super heavy tailed distributions do not only appear in financial settings, and they also exist in a variety of other applications and domains, including but not limited to environment and weather data, electronic engineering for instance heavy tailed noise, hospital patients’ stay statistics and others. In financial applications, Bayesian Networks (BNs) and copulas are two common approaches to modeling joint uncertainties with probability distributions. In particular, copulas have acclaimed more popularity; this is due to fact that with copula we can approximate the probability distribution of the data with heavy tail, which is in fact very common in financial applications (Ibragimov & Prokhorov, 2017).