CHAPTER 15Scenario Generation

15.1 OVERVIEW

It is a common requirement in risk management that models, as well as being used for generating end‐of‐day prices, are required to produce hypothetical prices under a range of future possible market scenarios. The calculations that we have provided in the preceding, insofar as they have been provided not only as PV at t equals 0, but as prices of the form f left-parenthesis bold-italic x Subscript t Baseline comma t right-parenthesis, t greater-than 0, can be used in this way. In other cases, some extra work allows formulae for conditional prices of this kind to be produced.

In addition to calculating the prices under hypothetical scenarios, there is also often a need to generate the scenarios themselves under the assumption that they arise from an evolution of the market underlyings in the pricing model from time 0 to time t. Typically, we make use of the joint distribution of the (usually Gaussian) variables in the vector bold-italic x Subscript t to produce scenarios through random number generation and obtain the distribution of prices by applying . In this way we ...

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