Everything You Always Wanted To Know About Bitcoin Modelling But Were Afraid To Ask

Dean Fantazzini
Moscow School of Economics, Moscow State University; National Research University Higher School of Economics (Moscow)

Erik Nigmatullin
Bocconi University

Vera Sukhanovskaya
Perm State University

Sergey Ivliev
Perm State University

June 12, 2016

Applied Econometrics, Forthcoming

Abstract:

Bitcoin is an open source decentralized digital currency and a payment system. It has raised a lot of attention and interest worldwide and an increasing number of articles are devoted to its operation, economics and financial viability. This article reviews the econometric and mathematical tools which have been proposed so far to model the bitcoin price and several related issues, highlighting advantages and limits. We discuss the methods employed to determine the main characteristics of bitcoin users, the models proposed to assess the bitcoin fundamental value, the econometric approaches suggested to model bitcoin price dynamics, the tests used for detecting the existence of financial bubbles in bitcoin prices and the methodologies suggested to study the price discovery at bitcoin exchanges.

Everything You Always Wanted To Know About Bitcoin Modelling But Were Afraid To Ask – Introduction

Bitcoin is an online decentralized currency that allows users to buy goods and services and execute transactions, without involving third parties. It was launched in 2009 by a person or (more likely) by a group of people operating under the name of Satoshi Nakamoto. Bitcoin belongs to the large family of “cryptocurrencies”, which are based on cryptographic methods of protection. The main characteristic of these currencies is their decentralized structure: there is no central authority which issues and regulates the currency, and transactions are executed using a peer-to-peer crypto-currency protocol without intermediaries. Introductory surveys about bitcoin structure and operation can be found in Becker et al. (2013), Segendorf (2014), Dwyer (2014), B¨ohme et al. (2015), or simply in Bitcoin (2015). Several central banks also examined bitcoin, see Velde (2013), Lo and Wang (2014), Baden and Chen (2014), Ali et al. (2014), and ECB (2012, 2015). Discussions of bitcoin as a potential alternative monetary system can be found in Rogojanu and Badea (2014) and Weber (2016), while the economics of bitcoin mining are examined in Kroll (2013). Analyses of the legal issues involved by using bitcoin can be found in Allen (2015) and Murphy et al. (2015).

The goal of this article is to review the econometric and mathematical tools which have been proposed so far to model the bitcoin price and several related issues. To our knowledge, such a review is missing in the financial literature and it can be of interest to both market professionals and researchers alike, given the early stages of the empirical literature devoted to bitcoin.

The rest of the paper is organized as follows. Section 2 introduces crypto-currencies with a particular focus on bitcoin, and briefly explains how bitcoin works. Section 3 reviews the studies devoted to the analysis of the characteristics of bitcoin users, while Section 4 discusses the main models proposed to assess the bitcoin fundamental value, ranging from market sizing to the bitcoin marginal cost of production based on electricity consumption. Section 5 describes several econometric approaches suggested to model bitcoin price dynamics, starting with cross-sectional regression models involving the majority of traded digital currencies and then moving to univariate and multivariate time series models, till models in the frequency domain. Section 6 reviews the tests employed for detecting the existence of financial bubbles in bitcoin prices and which can be broadly classified into two large families, depending on whether they are intended to detect a single bubble, or (potentially) multiple bubbles. Section 7 examines the methodologies suggested to estimate the information share of various bitcoin exchanges with respect to the information generated by the whole market, which is of great importance for both short-term traders and long-term investors who want to know which exchange reacts most quickly to new information. Section 8 briefly concludes and highlights several possible avenues for further research.

Bitcoin Modelling

Definition of Crypto-currencies and Bitcoin

2.1 How Bitcoin works

2.1.1 Digital signatures and cryptographic hash function

The Bitcoin network uses cryptography to validate transactions during the payment processing and create transaction blocks. In particular, Bitcoin relies on two cryptographic schemes: 1) digital signatures and 2) a cryptographic hash function. The first scheme allows the exchange of payment instructions between the involved parties, while the second is used to maintain the discipline when recording transactions to the public ledger (known as Blockchain). It should be noted that none of these schemes is unique to Bitcoin, since they are widely used to protect commercial and government communications. A short description of how the Bitcoin network works is reported below, while more details can be found in Becker et al. (2013), Segendorf (2014), Dwyer (2014), B¨ohme et al. (2015), or simply in Bitcoin (2015). Digital signatures are used to authenticate digital messages between a sender and a recipient, and they provide:

(i) Authentication: the receiver can verify that the message came from the sender;

(ii) Non-repudiation: the sender cannot deny having sent the message;

(iii) Integrity: the message was not altered in transit.

The use of digital signatures includes public key cryptography, where a pair of keys (open and private) are generated with certain desirable properties. A digital signature is used for signing messages: the transaction is signed using a private key, and then transferred to the Bitcoin network. All the members of the network can verify that the transaction came from the owner of the public key, by taking the message, the signature, the public key and by running a test algorithm.

Bitcoin Modelling

Bitcoin Modelling

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