A Confidence-Based Model for Asset and Derivative Prices in the Bitcoin Market

An updated 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).

24 Pages Posted: 1 Feb 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

Date Written: January 10, 2017

Abstract

We endorse the idea, suggested in recent literature, that BitCoin prices are influenced by sentiment and confidence about the underlying technology; as a consequence, an excitement about the BitCoin system may propagate to BitCoin prices causing a Bubble effect, the presence of which is documented in several papers about the cryptocurrency. In this paper we develop a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as the behavior of a second factor affecting the price itself, which we name confidence indicator. The two dynamics are possibly correlated and we also take into account a delay between the confidence indicator and its delivered effect on the BitCoin price. Statistical properties of the suggested model are investigated and its arbitrage-free property is shown. Further, based on risk-neutral evaluation, a quasi-closed formula is derived for European style derivatives on the BitCoin. A short numerical application is finally provided.

Keywords: BitCoin, Sentiment, Equivalent martingale measure, Option Pricing

JEL Classification: C32,G02,G12,G13

Suggested Citation

Cretarola, Alessandra and Figà-Talamanca, Gianna, A Confidence-Based Model for Asset and Derivative Prices in the Bitcoin Market (January 10, 2017). An updated 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=2908921 or http://dx.doi.org/10.2139/ssrn.2908921

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

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