Saddlepoint Approximations for Hawkes Jump-Diffusion Processes with an Application to Risk Management*
提出基于霍克斯过程的统计模型，推导出利润与损失分布尾部的鞍点近似，用于计算考虑损失传染效应的风险度量，帮助金融机构设定资本要求和系统性风险费用。
We propose a statistical model based on Hawkes processes in which large financial losses can arise in close succession serially as well as cross-sectionally. We derive in closed form saddlepoint approximations to the tails of profit and loss distributions, both marginal and joint, and use them to construct explicit risk measure formulae that account for the fact that a given financial institution’s losses make it more likely that that institution will experience further losses, and that other financial institutions will experience losses as well. These closed-form risk measures can be used for comparative statics, parameter calibration, and setting capital requirements and potential systemic risk charges.