Abstract: The failing bank can lead to the potential collapse of the whole financial system,sophisticated financial instruments based on the assumption of stable equilibria in economic systems was seen as a major cause of the 2008 financial crisis. Contagion risk and the scale of systemic breakdown in the financial system are the key concern for effective macro prudential oversight. Recently these insights from the study of complex networks have been applied to the financial system.
Some simulation-based studies of financial contagion risk on the framework of complex networks models are mainly concerned in this paper. Banks are the nodes, inter-connected if financial flows and exposures exist among them. One of the key problems in this paper is that of understanding the role of the network structure in relation to the contagion effect.
We apply techniques from cascade dynamics on complex networks of Watts, which gives a degree distribution p_k and the average degree of the networkz.An bank is called vulnerable if their threshold φ is smaller than the inverse of their degree k, i.e.φ≤1/k, such that one infected neighbor suffices to attain the threshold. Starting from a small number of failed banks, the aim is to characterize the probability that failures propagate at the systemic level as a function of some relevant parameters, like the connectivity of the network and the net capital of banks. In numerical simulations, it can be found that while greater connectivity helps lower the probability of contagion, it can also increase its spread in the event of problems occurring. Greater connectivity does not only create more channels through which contagion can spread but also improves counteracting risk-sharing benefits.
Most importantly, the proposed methodology can be employed in many segments of the entire financial system, providing a useful tool in the hands of regulatory authorities in assessing more accurate estimates of systemic risk. It is investigated that how several new mathematical modeling approaches represented by the analytical framework of Gleeson may be applied. Overall goal will be to develop a comprehensive toolkit of computational algorithms that will include network simulation methods, analytic results for several models, plus statistical and graphical methods.

Key words: contagion risk, cascade dynamics, complex networks, financial networks, random graphs, connectivity