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Elements of Financial Risk Management, 2nd Edition by Peter Christoffersen

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2. Historical Simulation, Value-at-Risk, and Expected Shortfall
This chapter introduces the most commonly used method for computing Value-at-Risk, namely Historical Simulation (HS), and discusses the pros and cons of this method. We also consider an extension of HS, referred to as Weighted Historical Simulation (WHS). We compare HS and WHS during the 1987 crash. We then study the performance of HS during the 2008–2009 financial crisis and compare it to the RiskMetrics alternative. The inherent problems with HS highlighted in this chapter serves to motivate the dynamic risk models considered later on in the book. The second part of the chapter discusses the pros and cons of the Value-at-Risk measure itself and considers the Expected Shortfall alternative. ...

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