Practical Financial Optimization: Decision Making for Financial Engineers

Chapter 5

Scenario Optimization

No great deed is done by falterers who ask for certainty.

George Eliot

5.1 Preview

Scenario optimization provides powerful and flexible models for risk management in both equities and fixed-income assets, integrating in a common framework several disparate sources of risk. In this chapter we develop models that trade off reward against risk, when both measures are computed from scenario data. The scenarios describing market, credit, liquidity, actuarial, and other types of risk can be quite general. Portfolios of fixed-income, equities and derivative assets can be optimized in the same framework, and liabilities can also be incorporated. The relationships between several models are revealed.

5.2 Basics of Scenario Optimization

In Chapters 1 and 2, we argued that financial risks are multidimensional and must be managed in an integrated fashion. And yet, the two subsequent chapters (3 and 4) took the traditional silo approach and developed optimization models for managing risks for equities and fixedincome securities, respectively. By managing the risks of equities and fixed-income securities independently from each other, it was possible to use some of the simpler risk measures for the respective asset classes, as given in Chapter 2, namely the variance risk measures for equities and the duration and convexity measures for fixed-income.

Having grasped the financial optimization principles for these simpler problem classes, we can now move away from ...