The theory of multilayer networks is in its early stages, and its development provides powerful and vital methods for understanding complex systems. Multilayer networks, in their multiplex form, have been introduced within the last three years to analysing the structure of financial systems, and existing studies have modelled and evaluated interdependencies of different type among financial institutions. The empirical studies, however, have considered the multiplex structure rather as an ensemble of single layer networks than as an interconnected multiplex or multilayer network. No mechanism of multichannel contagion has been modelled and empirically evaluated, and no multichannel stabilisation strategies for pre-emptive contagion containment have been designed. This paper formulates an interconnected multilayer structure, and a contagion mechanism among financial institutions due to bilateral exposures arising from institutions activity within different interconnected markets that compose the overall financial market. We introduce structural measures of absolute systemic risk and resilience, and relative systemic-risk indexes. The multiple-market systemic risk and resilience allow comparing the structural (in)stability of different financial system or the same system in different periods. The relative systemic-risk indexes of institutions acting in multiple markets allow comparing the institutions according to their relative contributions to overall structural instability within the same period. Based on the contagion mechanism and systemic-risk quantification, this study designs minimum-cost stabilisation strategies that act simultaneously on different markets and their interconnections, in order to effectively contain potential contagion progressing through the overall structure. The empirical analysis uses granular data now available at the Bank of England.
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