Modelling of contagion in financial markets

Empirical studies provide evidence of contagion effects in equity markets: e.g. shocks in USA stocks induce self-excitation events (further jumps for the US index) and mutual excitation events (in external markets). Modeling such interconnected phenomena is a cutting-edge research area in Finance/Economics. Mutual-excitation implies clustering of financial shocks, and particular dependency structures across markets. Joint time/space propagation of crisis is of key interest. Widely used Stochastic Volatility (SV) models cannot induce such dependencies; new paradigms are required.
State-of-art models build upon the Hawkes process - used in epidemiology, earthquake modeling - known to induce mutually-exciting effects. Influential works proposed relevant models in Finance. However, calibration is nonoptimal, based on Method of Moments - required moments are obtainable for simplified models restricting applicability.
The main project objectives are:
1) Model Development: state-of-art models require thorough investigation and improvements, as the area is not mature enough. E.g. models combining SV with Hawkes processes can be tried - amongst others. Models should be used for option pricing, portfolio optimization.
2) Model Calibration: Leading methodology in Computational Statistics (Hybrid Monte Carlo, Filtering) should be tried in the field, and is expected to allow full Bayesian inference for far more complex models, removing applicability barriers.