Bitcoin option pricing: A market attention approach

Alet Roux; Álvaro Guinea Julia

doi:10.48550/arXiv.2107.12447

Bitcoin option pricing: A market attention approach

Alet Roux, Álvaro Guinea Julia

Mathematics

Research output: Working paper

Abstract

A model is proposed for Bitcoin prices that takes into account market attention. Market attention, modeled by a mean-reverting Cox-Ingersoll-Ross processes, affects the volatility of Bitcoin returns, with some delay. The model is affine and tractable, with closed formulae for the conditional characteristic functions with respect to both the conventional and a delayed filtration. This leads to semi-closed formulae for European call and put prices. A maximum likelihood estimation procedure is provided, as well as a method for changing to a risk-neutral measure. The model compares very well against classical and attention-based models when tested on real data.

Original language	English
Publisher	arXiv
DOIs	https://doi.org/10.48550/arXiv.2107.12447
Publication status	Published - 15 Jan 2024

Keywords

Bitcoin
option pricing
Heston model
market attention
Cox-Ingersoll-Ross process

Access to Document

10.48550/arXiv.2107.12447

Cite this

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title = "Bitcoin option pricing: A market attention approach",

abstract = "A model is proposed for Bitcoin prices that takes into account market attention. Market attention, modeled by a mean-reverting Cox-Ingersoll-Ross processes, affects the volatility of Bitcoin returns, with some delay. The model is affine and tractable, with closed formulae for the conditional characteristic functions with respect to both the conventional and a delayed filtration. This leads to semi-closed formulae for European call and put prices. A maximum likelihood estimation procedure is provided, as well as a method for changing to a risk-neutral measure. The model compares very well against classical and attention-based models when tested on real data.",

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AB - A model is proposed for Bitcoin prices that takes into account market attention. Market attention, modeled by a mean-reverting Cox-Ingersoll-Ross processes, affects the volatility of Bitcoin returns, with some delay. The model is affine and tractable, with closed formulae for the conditional characteristic functions with respect to both the conventional and a delayed filtration. This leads to semi-closed formulae for European call and put prices. A maximum likelihood estimation procedure is provided, as well as a method for changing to a risk-neutral measure. The model compares very well against classical and attention-based models when tested on real data.

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