Tail risk and uncertainty in financial markets

Millar, Robert ORCID: 0009-0001-4097-2715 (2024). Tail risk and uncertainty in financial markets. University of Birmingham. Ph.D.

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Abstract

This thesis explores the intricacies of managing and modelling tail risk and uncertainty in financial markets. Tail risks arise from infrequent but potentially significant events, while uncertainty refers to the unpredictable aspects of market dynamics that cannot be accounted for by standard probabilistic models. Traditional models often struggle to account for these elements, leading to inadequate investment strategies which underestimate risk. This thesis proposes a new investment framework centred around three objectives: (1) to develop forecasting methods that provide more accurate and robust predictions of asset prices and volatility, accounting for the inherent uncertainty in financial markets (2) to devise new methodologies which better predict the probability and impact of tail events (3) to create portfolio allocation algorithms which eliminate unrealistic assumptions and better reflect the complex dynamics of modern financial markets.

In addressing the first objective, this thesis critiques existing forecasting models and introduces a Bayesian approach to ARMA-GARCH modelling. This new approach incorporates prior knowledge and directly accounts for the uncertainty in financial data, offering a more robust prediction framework.

Regarding the second objective, this thesis introduces existing quantitative tools to measure financial risk and then proposes a new algorithm called the Multicanonical Sequential Monte Carlo Sampler (MSMCS), which efficiently reconstructs probability distributions to capture tail risk.

For the final objective, this thesis proposes a series of Bayesian Optimisation algorithms that address optimal portfolio allocation. These algorithms are tailored to reduce the computational intensity often associated with such tasks and to take advantage of specific characteristics of portfolio optimisation problems.

This thesis culminates in the combined application of the Bayesian ARMAGARCH models to forecast asset returns, MSMCS to assess tail risk, and Bayesian Optimisation to find an optimal portfolio allocation. The combined framework is applied to historic market data and shown to outperform various existing strategies and market indices.

This work contributes to financial mathematics by challenging conventional approaches and introducing new Bayesian-based models that more accurately reflect the complexity and inherent uncertainties of financial markets. It provides a foundation for further research and practical applications in financial forecasting models, risk assessment, and portfolio management.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):