Research

My research is in financial engineering, Monte Carlo simulation, and Financial systemic risk. My current main research interest is to study the Financial Systemic Risk and Contagion Effects.

Financial Systemic Risk and Contagion Effects

• The study of contagion in financial systems is very topical in light of the recent global credit crisis and the resultant damage inflicted on financial institutions.

• "Contagion" refers to the spread of defaults through a system of financial institutions, with each successive default causing increasing pressure on the remaining components of the system.

• The term "systemic risk" refers to the contagion-induced threat to the financial system as a whole, due to the default of one (or more) of its component institutions.

• Motivation: It is widely held that financial systems, defined for example as the collection of banks and financial institutions in a developed country, can be modeled as a random network of nodes or vertices with stylized balance sheets, connected by directed links or edges that represent exposures ("inter-bank loans"), each edge with a positive weight that represents the size of the exposure. If ever a node becomes "insolvent" and ceases to operate as a bank, it will create balance sheet shocks to other nodes, creating the potential of chains of insolvency that we will call "default cascades".

• Financial networks are difficult to observe because interbank data is often not publicly available, but studies have indicated that they share characteristics of other types of technological and social networks, such as the world wide web and Facebook. For example, the degree distributions of financial networks are thought to be "fat-tailed" since a significant number of banks are very highly connected.

• A less studied feature observed in financial networks (and as it happens, also the world wide web) is that they are highly "dis-assortative". This refers to the property that any bank's counterparties (i.e. their graph neighbours) have a tendency to be banks of an opposite character. For example, it is observed that small banks tend to link preferentially to large banks rather than other small banks.

• Commonly, social networks are observed to be assortative rather than disassortative. Structural characteristics such as degree distribution and assortativity are felt to be highly relevant to the propagation of contagion in networks but the nature of such relationships is far from clear.

Relevant Literatures:

• • Studies on Financial Systems

    1. Eisenberg, L. and Noe, T. H. 2001 Systemic risk in financial systems,Management Science, 47, (2) 236–249. EisenbergNoe01

    2. C. Upper. Simulation methods to assess the danger of contagion in interbank markets. J. Financial Stability, 2011.Upper Review Paper

    3. FINANCIAL STABILITY REVIEW JUNE 2012: Financial Stability Review

    4. Bisias, Dimitrios, Flood, Mark D., Lo, Andrew W. and Valavanis, Stavros, A Survey of Systemic Risk Analytics (January 11, 2012). U.S. Department of Treasury, Office of Financial Research No. 0001. Risk Analytics

    5. Nier, E., Yang, J., Yorulmazer, T., and Alentorn, A. 2007 Network models and financial stability, J. Economic Dynamics & Control, 31, 2033–2060. Nieretal07

• • • New Research on Financial Networks

• • 1. P. Gai and S. Kapadia. Contagion in financial networks. Proceedings of the Royal Society A, 466(2120):2401–2423, 2010.GaiKapadia10

    2. R. Cont, A. Moussa, and E. B. Santos. Network Structure and Systemic Risk in Banking Systems. SSRN eLibrary, 2010.ContMoussaSantos10

    3. H. Amini, R. Cont, and A. Minca. Resilience to contagion in financial networks. Working paper: arXiv:1112.5687v1 [q-fin.RM], December 2011.AminiContMinca11

    4. P. Gai, A. Haldane, S. Kapadia, “Complexity, Concentration and Contagion”, Journal of Monetary Economics, 58, 2011. GaiHaldaneKapadia11

    5. J. P. Gleeson, T. R. Hurd, S. Melnik, and A. Hackett. Systemic risk in banking networks without Monte Carlo simulation. In E. Kranakis, editor, Advances in Network Analysis and its Applications, volume 18 of Mathematics in Industry. Springer Verlag, Berlin Heidelberg New York, June 2012.Gleeson et al

    6. T. R. Hurd, James Gleeson "A framework for analyzing contagion in banking networks", working paper, June 2011 Hurd Gleeson

    7. R. M. May and N. Arinaminpathy. Systemic risk: the dynamics of model banking systems. Journal of The Royal Society Interface, 7(46):823–838, 2010.ArinMay10.pdf

My prior and ongoing research interests also include: American option pricing, stochastic volatility models, volatility derivatives, optimal mean-reversion pairs trading, nested simulation, multi-level Monte Carlo simulation, and Risk management for equity-linked derivatives and variable annuities.

In particular, there are several research themes that I am interested in (some current and future projects are listed):

Stochastic processes in finance and risk management

• Martingale property in time-homogeneous diffusion models and time-changed Levy models.

• Probability density function for correlated stochastic volatility models.

• Moment explosion behaviors of stock prices under various stochastic models.

• Asymptotics of the implied volatility in large maturity or large strike case.

• Option pricing under GARCH model, in particular the Heston-Nandi (2000) GARCH model

Robust pricing methods in finance and risk management

Efficient Monte Carlo simulation methods in finance and risk management