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

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