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Title: Bayesian risk evaluation for long horizons Authors:  Agnieszka Borowska - Vrije Universiteit Amsterdam (Netherlands) [presenting]
Lennart Hoogerheide - Vrije Universiteit Amsterdam (Netherlands)
Siem Jan Koopman - VU University Amsterdam (Netherlands)
Abstract: An accurate and efficient approach to Bayesian estimation of two financial risk measures, Value-at-Risk and Expected Shortfall, for a given volatility model, is presented. Precise forecasts of the tail of the distribution of returns are obtained not only for the 10-days-ahead horizon required by the Basel Committee but even for long horizons, like one-month or one-year ahead. The latter has recently attracted a considerable attention due to a different character of the short term risk and the long run one. Long horizon forecasts can also be useful, e.g. for option pricing. The key insight behind the proposed importance sampling based approach is the construction of the importance densities as mixtures of Student's $t$ distributions sequentially. By oversampling the extremely negative scenarios and punishing them by lower importance weights, a much higher precision in characterising the properties of the left tail is achieved. Empirical studies of GARCH(1,1)-$t$ and GAS(1,1)-$t$ models for daily financial data show substantial accuracy gains for all the considered horizons. To illustrate the flexibility of the proposed construction method, an adjustment to the frequentist case is provided.