Bayesian Risk Forecasting for Long Horizons

Tinbergen Institute Discussion Paper 2019-018/III

40 Pages Posted: 13 Mar 2019

See all articles by Agnieszka Borowska

Agnieszka Borowska

VU University Amsterdam

Lennart F. Hoogerheide

VU University Amsterdam

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute; Aarhus University - CREATES

Date Written: January 31, 2019

Abstract

We present an accurate and efficient method for Bayesian forecasting of two financial risk measures, Value-at-Risk and Expected Shortfall, for a given volatility model. We obtain precise forecasts of the tail of the distribution of returns 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 considerable attention due to the different properties of short term risk and long run risk. The key insight behind our importance sampling based approach is the sequential construction of marginal and conditional importance densities for consecutive periods. We report substantial accuracy gains for all the considered horizons in empirical studies on two datasets of daily financial returns, including a highly volatile period of the recent financial crisis. To illustrate the flexibility of the proposed construction method, we present how it can be adjusted to the frequentist case, for which we provide counterparts of both Bayesian applications.

Keywords: Bayesian inference, forecasting, importance sampling, numerical accuracy, long run risk, Value-at-Risk, Expected Shortfall

JEL Classification: C32

Suggested Citation

Borowska, Agnieszka and Hoogerheide, Lennart F. and Koopman, Siem Jan, Bayesian Risk Forecasting for Long Horizons (January 31, 2019). Tinbergen Institute Discussion Paper 2019-018/III. Available at SSRN: https://ssrn.com/abstract=3339819 or http://dx.doi.org/10.2139/ssrn.3339819

Agnieszka Borowska (Contact Author)

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Lennart F. Hoogerheide

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Siem Jan Koopman

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31205986019 (Phone)

HOME PAGE: http://sjkoopman.net

Tinbergen Institute ( email )

Gustav Mahlerplein 117
1082 MS Amsterdam
Netherlands

HOME PAGE: http://personal.vu.nl/s.j.koopman

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

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