Abstract
This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally—but perhaps most importantly—(v) “radical complexity” that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models. Some open questions and future research directions are outlined.
Highlights
This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and —but perhaps most importantly—(v) “radical complexity” that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models
Gives an optimal, mathematically rigorous, recipe to tweak the value of the eigenvalues so that the resulting “cleaned” covariance matrix is as close as possible to the “true” one in the absence of any prior information on the direction of the eigenvectors
In the case of copulas, one interesting stylised fact is the way the probability that two assets have returns simultaneously smaller than their respective medians depends on the linear correlation between the said two assets
Summary
Harry Markowitz famously quipped that diversification is the only free lunch in finance. RMT gives an optimal, mathematically rigorous, recipe to tweak the value of the eigenvalues so that the resulting “cleaned” covariance matrix is as close as possible to the “true” (but unknown) one in the absence of any prior information on the direction of the eigenvectors. Parallel to the development of descriptive and predictive models, the introduction of standardised instruments that hedge against such correlation jumps would clearly serve a purpose This is especially true in the current environment [21] where inflation fears could trigger another inversion of the equity/bond correlation structure, which would be possibly devastating for many strategies that—implicitly or explicitly—rely on persistent negative correlations.
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