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This study empirically examines interdependencies between BitCoin and altcoin markets in the short- and long-run. We apply time-series analytical mechanisms to daily data of 17 virtual currencies (BitCoin + 16 alternative virtual…
We confirm and substantially extend the recent empirical result of Andersen et al. \cite{Andersen2015}, where it is shown that the amount of risk $W$ exchanged in the E-mini S\&P futures market (i.e. price times volume times volatility)…
Understanding the emergence of universal features such as the stylized facts in markets is a long-standing challenge that has drawn much attention from economists and physicists. Most existing models, such as stochastic volatility models,…
This document analyzes price discovery in cryptocurrency markets by comparing centralized and decentralized exchanges, as well as spot and futures markets. The study focuses first on Ethereum (ETH) and then applies a similar approach to…
In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are…
It is well-known that the Black-Scholes formula has been derived under the assumption of constant volatility in stocks. In spite of evidence that this parameter is not constant, this formula is widely used by financial markets. This paper…
We analyze the market efficiency of 25 commodity futures across various groups -- metals, energies, softs, grains and other agricultural commodities. To do so, we utilize recently proposed Efficiency Index to find that the most efficient of…
Cryptocurrencies have recently experienced a new wave of price volatility and interest; activity within social media communities relating to cryptocurrencies has increased significantly. There is currently limited documented knowledge of…
Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian…
Bitcoin's price has been described as following a power law (PL) in time, $P \sim t^{\beta}$ with $\hat\beta \approx 5.7$ over 2010-2026. We test this claim using the Clauset-Shalizi-Newman protocol applied to Bitcoin's tail-relevant…
In this paper we analyzed dependencies in commodity markets investigating correlations of future contracts for commodities over the period 1998.09.01 - 2007.12.14. We constructed a minimal spanning tree based on the correlation matrix. The…
Cryptocurrencies and Bitcoin, in particular, are prone to wild swings resulting in frequent jumps in prices, making them historically popular for traders to speculate. A better understanding of these fluctuations can greatly benefit crypto…
We consider a market model that consists of financial investors and producers of a commodity. Producers optionally store some production for future sale and go short on forward contracts to hedge the uncertainty of the future commodity…
We study the relationship between price spread, volatility and trading volume. We find that spread forms as a result of interplay between order liquidity and order impact. When trading volume is small adding more liquidity helps improve…
In this study, we investigate asset price bubbles in a discrete-time, discrete-state market under model uncertainty and short sales prohibitions. Building on a new fundamental theorem of asset pricing and a superhedging duality in this…
Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of…
We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when…
In this paper, we propose and study a novel continuous-time model, based on the well-known constant elasticity of variance (CEV) model, to describe the asset price process. The basic idea is that the volatility elasticity of the CEV model…
Bitcoin is a digital financial asset that is devoid of a central authority. This makes it distinct from traditional financial assets in a number of ways. For instance, the total number of tokens is limited and it has not explicit use value.…
Extreme volatility, nonlinear dependencies, and systemic fragility are characteristics of cryptocurrency markets. The assumptions of normality and centralized control in traditional financial risk models frequently cause them to miss these…