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An Introduction to Financial Markets
book

An Introduction to Financial Markets

by Paolo Brandimarte
November 2017
Beginner content levelBeginner
784 pages
22h 31m
English
Wiley
Content preview from An Introduction to Financial Markets

Chapter Eleven Modeling Dynamic Uncertainty

From Chapter 8 on, we have considered static portfolio management models, where we make a decision at time t = 0 and observe the result at time t = T, the end of a predefined holding period. Representing uncertainty in this context requires the characterization of a multivariate distribution of risk factors, which is not quite trivial. However, there are even more complicated problems, calling for a dynamic characterization of uncertainty.

  • A first example is asset–liability management (ALM) problems, where we consider a sequence of time instants ti ε [0, T], i = 1, …, m, at which we must meet a possibly uncertain liability Li. We have considered simple approaches to interest rate risk management for ALM problems in Section 6.3. In these limited approaches, we actually solve a static decision problem. It may be the case that a better plan is obtained bHy a multistage decision model, but even if we do not want to pay the price of such a challenging optimization model,1 we may need to check the performance of whatever plan on a set of random scenarios for both the assets and the liabilities. Thus, we must characterize the uncertain evolution of the underlying risk factors over time, in order to generate a rich and reliable set of scenarios.
  • Another quite relevant example is provided by the need to hedge an option dynamically. In Section 2.3.4, we have considered a single-step binomial model for option pricing. Quite clearly, we need ...
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Publisher Resources

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