Benchmarking with machine learning

Christian Meyer and Peter Quell

Empirical data indicate that financial markets feature several so-called stylised facts, such as changing volatilities and fat tails of return distributions. As a first step to address the aspect of changing volatility, filtered historical simulation was introduced at the end of the previous chapter. This method captures time-varying characteristics of markets by starting with the dynamics of individual risk factors. In this sense, it provides a bottom-up perspective.

In this chapter, a benchmark model for market risk will be presented that is inherently of a top-down flavour. The starting point will be the time series of profits and losses at a portfolio level, a dataset that every bank using internal models already has in stock. That implies several advantages:

    • the benchmark model is easy to implement with existing risk models;

    • since the benchmark model provides a top-down approach, it is a useful companion to other risk model validation processes; and

    • the benchmark model can focus on the distributional properties of the portfolio profit and loss in contrast to the distributional properties of risk factors.

The aim of this chapter is to find

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