Cryptocurrency derivatives: models and pricing methods

The rapid growth of the crypto market has led to the introduction of novel crypto derivative instruments that challenge traditional trading and valuation frameworks, given the lack of regulation, the market’s inherent fragmentation, where prices of the same underlying asset can differ substantially across independent exchanges, and the subsequent introduction of non-tradable indices. These indices provide average prices of crypto assets across exchanges and, while improving stability and reducing possible impacts of manipulation, their non-tradability and difficult replication result in market incompleteness when they are used as underlying assets in derivative instruments. This makes classical pricing models, such as Black-Scholes and its stochastic volatility and jump-diffusion extensions, less effective in derivative valuation. In light of these challenges, this thesis aims to introduce preference-dependent pricing approaches in the context of crypto trading, consolidating investor behavior, preferences and utility maximization in the absence of a single risk-neutral measure. Such methods acknowledge the heterogeneous nature of market participants and aim to incorporate their sentiments directly into pricing, offering a more reliable framework in an incomplete market. Overall, the goal of this thesis is to provide a holistic understanding of the crypto market, starting from technical foundations, classification of crypto assets, types and operations of crypto exchanges and the features and proposed valuations of crypto derivative instruments: futures, perpetual contracts and options. Finally, the introduction of preference-based pricing methods to the crypto context aims to account for the market's, as well as its investors', unique characteristics, and provide a novel contribution to research in this area.