I. Stochastic Models and Processes · 28. août 2024

Skewness and kurtosis are essential measures that help describe the shape of a data distribution. While both are moments * of the distribution, they serve different purposes and utilize different mathematical approaches to capture unique aspects of data behavior. A particularly interesting point of differentiation between these two metrics is the power to which the deviations from the mean are raised: skewness uses the third power, while kurtosis uses the fourth power. But why is this the case?...

III. Quantitative Finance Applications · 19. avril 2024

Understanding the probability of events like bond defaults requires recognizing that individual likelihoods, or marginal distributions, don't inherently reveal the likelihood of multiple bonds defaulting simultaneously. Even if two sets of bonds have identical marginal probabilities, their joint probabilities can differ significantly based on default correlations. Marginal distributions describe individual behavior without considering other variables.

III. Quantitative Finance Applications · 09. février 2024

Sklar's Theorem, a pivotal concept since 1959, separates the modeling of individual behaviors and dependencies in multivariate analysis, reshaping risk management and probabilistic modeling. It states that any multivariate distribution can be expressed via a copula linking its univariate marginal distributions. This theorem allows the copula to remain constant despite changes in individual distributions, enabling flexible and accurate modeling of complex dependencies.