Value at Riskin ja Expected Shortfallin mallintaminen k-means-pohjaisilla markkinaregiimeillä

This thesis studies historical Value at Risk (VaR) and Expected Shortfall (ES) estimation using past return observations drawn from days deemed similar to the current market state. The goal is to improve the responsiveness and accuracy of traditional historical risk estimates by partitioning data into distinct market states using unsupervised learning, specifically the k-means algorithm. Three main sets of features are presented: EWMA-based volatility estimates, vectors of returns, and vectors of absolute returns. For vector-based features, similarity is measured using the Wasserstein distance to capture differences in the empirical distribution of returns. The study uses approximately 35 years of daily data for the S&P 500 and Euro Stoxx 50 indices. Model development is conducted in-sample, and performance is assessed out-of-sample to reduce the risk of overfitting. Models are evaluated using Kupiec's proportion-of-failures test, the Christoffersen independence test, and the Expected Shortfall backtests proposed by Acerbi and Székely. The results indicate that k-means clustering can identify economically meaningful market states, such as periods of market stress, and that incorporating these states into VaR and ES estimation can improve risk estimates relative to standard Historical Simulation and the Filtered Historical Simulation (EWMA lambda = 0.94) baseline considered in this thesis, with the largest gains in the tail of the loss distribution. At the same time, the approach is data-intensive and can produce more variable risk estimates. The results also indicate that Wasserstein distance clustering of return vectors gives market states broadly similar to those from volatility clustering. More broadly, distributional-shape information helps both in identifying market states and in improving VaR and ES estimation.