Model validation is a labor-intensive profession that requires specialists who understand both quantitative finance as well as business practices. Validating a single valuation model typically requires between 3 and 6 weeks of hard work focusing on many different topics. In this first article, I would like to highlight a few ideas on how to automate such analyses.

# Data

Models need. Hence, a large portion of time in model validation is spent on managing data. To give a few examples, the validator has to make sure that the input data is of good quality, that the test data is sufficiently rich and that there are processes in place to deal with data issues. Broadly speaking, input data exists in two flavours: time series and multi-dimensional data that is not indexed primarily by time.

## Time series

Time series are overly present in finance. Valuation models typically use quotes (standardized prices of standardized contracts) as input data. Since the market changes, time series of quotes are abundant. To determine the quality of quotes one can run anomaly detection models on historical data (i.e. on time series). Many such algorithms exist. Simple ones use time series decomposition like STL to subtract the predictable part and study the distribution of the resulting residue to determine the likelihood of an outlier. More modern alternatives use machine learning algorithms. In one approach, a model is trained to detect anomalies by using labeled datasets (e.g. such as the ODDS database). Another family of solutions uses a ML model to forecast the time series. In that method, anomalies are discovered in case the prediction differs significantly from the realization.

## Data representativeness

In some cases, the time component is less (or not) important. When building regression or classification models, one often uses a large collection of samples (not indexed by time) with many features. In that case, due to the curse of dimensionality, one would need astronomical sizes of data to cover every possibility. Most often, the data is not spread homogeneously over feature space but instead is clustered into similarly looking parts. When building a model, it is important to make sure that the data for which the model is going to be used is similar to data on which the model has been trained. Hence, one needs to understand if a new data point is close to existing data. There are many clustering algorithms (like e.g. DBSCAN) that can perform this analysis generically.

# Model dependencies

A model inventory is a necessary tool in a model governance process. On top of keeping track of all the models used, it is extremely valuable to also store the dependencies between models. For instance, when computing VaR one need the historical PnL of all portfolios. If these portfolios contain derivatives, we need models to compute their net present value. All the models that are used within an enterprise can be represented as a graph where the nodes are the models while the vertices represent data. Understanding the topology makes it easier to trace back model issues.

# Benchmarking

ML can help benchmarking models. First of all, in the case of forecasting models, we can easily train alternative algorithms on the realizations. This will help you to understand the impact of changing the underlying assumptions of the model.

However, even in case such realizations are not available, we can still train a model to mimic the algorithm that is used in production. We can use such surrogate models (see e.g. this paper from our colleagues at IMEC) to detect changes in the behaviour. As an example, suppose we are monitoring a XVA model. We can train a ML algorithm to predict the changes in the XVA amounts of a portfolio when the market data changes. We can still build a model that tries to forecast the change in PnL with market data. Such model can be used to detect e.g. instabilities in the XVA computation. An additional benefit of such approach is that one can estimate the sensitivity from the calibrated model.

*Jos Gheerardyn*