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，美国股市的冲击引发了自激事件（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，以及整个市场的特定依赖结构。危机的时空联合传播是关键的兴趣所在。广泛使用的随机波动（SV）模型不能诱导这种依赖关系；我们需要新的范例。最先进的模型建立在霍克斯过程的基础上，霍克斯过程用于流行病学和地震建模，众所周知，霍克斯过程会产生相互刺激的效应。有影响的著作在金融学中提出了相关的模型。然而，基于矩量法的标定不是最优的，简化后的模型无法获得所需的矩量，限制了模型的适用性。主要的项目目标是：1)模型开发：由于该领域还不够成熟，需要对最先进的模型进行彻底的调查和改进。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：计算统计学中的领先方法（混合蒙特卡罗，滤波）应该在该领域进行尝试，并且有望允许对更复杂的模型进行完整的贝叶斯推理，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.