Chapter 4

Market Exposures and Factor Sensitivities

… there is not a single effect in nature, even the least that exists, such that the most ingenious theorists can arrive at a complete understanding of it. This vain presumption of understanding everything can have no other basis than never understanding anything.

Galileo Galilei, Dialogue Concerning the Two Chief World Systems

4.1. FROM VALUATION TO RESPONSES AND SENSITIVITIES

A tested and audited valuation model serves as a foundation for the second element of the risk management triad of identifying, quantifying, and managing market exposures that we set out to elucidate in the Preface. In this section we will show how to use a model to tabulate an asset's responses to large (or, more generally, finite) factor changes, as well as how to calculate the asset value's sensitivities to small (in the limit, infinitesimally small) shifts in continuous, especially market, factors and how to translate these sensitivities into equivalent variation investments (EVIs) that can be directly used for sizing hedges.

In section 3.3 we introduced the view of the valuation model as a computational engine that processes inputs to generate a value V, a relationship formalized by equation (3.2). When interested in current valuation, an analyst would ...

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