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Implementing Neural SDEs for Data-Driven Dynamics of the Bitcoin Option Surface

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Preprints.org
DOI
10.20944/preprints202605.0049.v1

This paper presents a full implementation of data-driven modelling of the dynamics of the options on Bitcoin, using high-frequency data from the Deribit exchange. To this end, we provide a synthesis of methods established in prior papers, namely the works involving “neural SDE market models,” to build a pipeline to go from raw options quotes to a functioning non-parametric model. The options surface is decomposed into a low-dimensional latent space designed to minimise arbitrage in reconstruction and the temporal evolution of these factors are modelled with a stochastic differential equation (SDE). The drift and diffusion of the SDE are learnt from data using neural networks, thereby forming a ’Neural SDE’. These networks are constrained in order to guarantee the absence of static arbitrage and to minimise dynamic arbitrage in the resulting model. The networks are trained using a likelihood-based objective function in an SDE transition discretisation. The framework produces arbitrage-free simulations of option surfaces and enables risk management applications such as Value-at-Risk estimation and hedging applications.

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