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Title: Modeling extreme negative returns using marked renewal Hawkes processes Authors:  Tom Stindl - UNSW (Australia) [presenting]
Abstract: Extreme return financial time series are often challenging to model due to the presence of heavy temporal clustering of extremes and strong bursts of return volatility. The marked self-exciting process has been used extensively to model these phenomena. However, it restricts the arrival times of exogenously driven returns to follow a Poisson process and may fail to provide an adequate fit. We introduce a modification to the marked Hawkes process by defining the arrival of exogenously driven extreme returns in terms of a renewal process. We discuss a direct likelihood evaluation approach to parameter estimation which poses some additional computational challenges but only requires quadratic computational time. As a by-product of the likelihood evaluation algorithm, we have a computationally efficient method for goodness-of-fit assessment and a simple, yet efficient procedure for future event prediction. The proposed model is applied to extreme negative returns for stocks traded on the ASX. The models identified for the stocks using in-sample data were found to be able to successfully forecast the out-of-sample risk measures such as the value at risk and expected shortfall and provides a better quality of fit than the competing Hawkes model.