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 option quotes to a functioning non-parametric model. The option surface is decomposed into a low-dimensional latent space designed to minimise arbitrage in reconstruction, and the temporal evolution of these factors is modelled with a stochastic differential equation (SDE). The drift and diffusion of the SDE are learned 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.
Shah et al. (Tue,) studied this question.