The VI AMMCS International Conference

Waterloo, Ontario, Canada | August 14-18, 2023

AMMCS 2023 Plenary Talk

Saddlepoint Approximations for Hawkes Jump-Diffusion Processes with an Application to Risk Management

Yacine Ait-Sahalia (Princeton University, New Jersey) with Roger J.A. Laeven

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 bank's losses make it more likely that that bank will experience further losses, and that other banks 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.
Yacine Ait-Sahalia is the Otto A. Hack 1903 Professor of Finance and Economics at Princeton University where he served as the inaugural Director of the Bendheim Center for Finance from 1998 until 2014. He was previously an Assistant Professor (1993-96), Associate Professor (1996-98) and Professor of Finance (1998) at the University of Chicago's Graduate School of Business, where he received the Emory Williams Award for Excellence in Teaching in 1995. His research contributions in financial econometrics include various methods to estimate and test continuous-time models that are sampled at discrete time intervals, including nonparametric methods, closed-form expansions for the transition density of continuous-time models and various methods to analyze high frequency data with a particular emphasis on the presence of jumps. He recently authored High Frequency Financial Econometrics with Jean Jacod, served as the editor of the Review of Financial Studies, the managing editor of the Journal of Econometrics and an associate editor for Econometrica, the Journal of Finance and the Annals of Statistics. Professor Ait-Sahalia is an elected Fellow of the Econometric Society, the Institute of Mathematical Statistics, the American Statistical Association and the Society for Financial Econometrics. He is also an Alfred P. Sloan Foundation Research Fellow, a Fellow of the Guggenheim Foundation and a Research Associate for the National Bureau of Economic Research. He received his Ph.D. in Economics from the Massachusetts Institute of Technology in 1993 and is a graduate of Ecole Polytechnique in France.