A confidence-based model for asset and derivative prices in the BitCoin market

TL;DR

This paper introduces a continuous-time bivariate model linking Bitcoin prices with a confidence indicator, capturing sentiment effects and enabling derivative pricing, with demonstrated statistical properties and an arbitrage-free framework.

Contribution

It develops a novel bivariate model incorporating sentiment-driven confidence and price dynamics, including delay effects, and derives a quasi-closed formula for Bitcoin derivative valuation.

Findings

Model captures sentiment influence on Bitcoin prices

Statistical properties of the model are analyzed

A quasi-closed formula for derivatives is derived

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.