Modelling of contagion in financial markets

实证研究提供了股票市场传染效应的证据：例如，美国股票的冲击引起自激事件（美国指数进一步跃升）和相互激励事件（在外部市场）。对这种相互关联的现象进行建模是金融/经济学的前沿研究领域。相互激励意味着金融冲击的聚集，以及市场之间的特殊依赖结构。危机的联合时间/空间传播是一个关键问题。广泛使用的随机波动率（SV）模型不能诱导这种依赖性;需要新的范例。最先进的模型建立在霍克斯过程的基础上-用于流行病学，地震建模-已知诱导相互激励的影响。金融学中有影响的著作提出了相关模型。然而，基于矩量法的校准不是最佳的-简化模型的所需矩量是可获得的，限制了适用性。项目的主要目标是：1）模型开发：由于该领域还不够成熟，最先进的模型需要彻底的调查和改进。例如，可以尝试将SV与Hawkes过程相结合的模型。模型应用于期权定价、投资组合优化。2）模型校准：应在该领域尝试计算统计学中的领先方法（混合蒙特卡罗、过滤），并有望允许对复杂得多的模型进行完全贝叶斯推断，消除适用性障碍。

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.