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
Date Written: January 10, 2017
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: Suggested Citation