A Sentiment-Based Model for the Bitcoin: Theory, Estimation and Option Pricing

A revised version of this paper is published under the new title "Market attention and Bitcoin price modeling: theory, estimation and option pricing" in Cretarola, A., Figà-Talamanca, G. & Patacca, M. Decisions in Economics and Finance (2019).

39 Pages Posted: 27 Sep 2017 Last revised: 19 Sep 2019

See all articles by Alessandra Cretarola

Alessandra Cretarola

University of Perugia - Dipartimento di Matematica e Informatica

Gianna Figà-Talamanca

University of Perugia - Department of Economics

Marco Patacca

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV); University of Perugia - Department of Economics

Date Written: September 3, 2017

Abstract

In recent literature it is claimed that BitCoin price behaves more likely to a volatile stock asset than a currency and that changes in its price are influenced by sentiment about the BitCoin system itself; in Kristoufek the author analyses transaction based as well as popularity based potential drivers of the BitCoin price finding positive evidence. Here, we endorse this finding and consider a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as a second factor, affecting the price itself, which represents a sentiment indicator. We prove that the suggested model is arbitrage-free under a mild condition and, based on risk-neutral evaluation, we obtain a closed formula to approximate the price of European style derivatives on the BitCoin. By applying the same approximation technique to the joint likelihood of a discrete sample of the bivariate process, we are also able to fit the model to market data. This is done by using both the Volume and the number of Google searches as possible proxies for the sentiment factor. Further, the performance of the pricing formula is assessed on a sample of market option prices obtained by the Deribit website.

Keywords: BitCoin, Sentiment, Stochastic Models, Equivalent Martingale Measure, Option Pricing, Likelihood

JEL Classification: C22, C58, G02

Suggested Citation

Cretarola, Alessandra and Figà-Talamanca, Gianna and Patacca, Marco, A Sentiment-Based Model for the Bitcoin: Theory, Estimation and Option Pricing (September 3, 2017). A revised version of this paper is published under the new title "Market attention and Bitcoin price modeling: theory, estimation and option pricing" in Cretarola, A., Figà-Talamanca, G. & Patacca, M. Decisions in Economics and Finance (2019). , Available at SSRN: https://ssrn.com/abstract=3042029 or http://dx.doi.org/10.2139/ssrn.3042029

Alessandra Cretarola

University of Perugia - Dipartimento di Matematica e Informatica ( email )

Via Vanvitelli 1
Perugia, 06123
Italy

Gianna Figà-Talamanca (Contact Author)

University of Perugia - Department of Economics ( email )

via Pascoli, 20
PG 06123 Perugia, 06123
Italy

Marco Patacca

Ecole Superieure d'Ingenierie Leonard de Vinci (ESILV) ( email )

92916 Paris La Defense Cedex
France

University of Perugia - Department of Economics ( email )

via Pascoli, 20
PG 06123 Perugia, 06123
Italy

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