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A Modern Risk Management Perspective

Paolo Sironi

It does not do to leave a live dragon out of your calculations, if you live near him.

J. R. R. Tolkien (1892–1973)

This chapter discusses risk management of real products to enrich optimal portfolio choice: defining scenarios and scenario paths. It covers the parametric and historical scenario, bootstrapping and Monte Carlo methods, geometric Brownian motion (GBM) and the Hull–White one-factor model and gives scholastic examples.

INTRODUCTION

Financial markets have been characterised by a sustained path of financial innovation that, coupled with the broader market imbalances that culminated in the global financial crisis of 2007, has sparked a debate about the appropriateness of the methods dedicated to constructing optimal asset allocations. This debate questions both sides of the investment equation: the risk measure and the expected returns.

On the risk side, the commonly used measure of volatility is known to be a limiting risk management estimate, as it fails to represent the asymmetry and the long tail of potential returns. Quantitative research has investigated more refined measures of risk, such as value-at-risk (VaR) and expected shortfall (ES), in an

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