The S&P 500 index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past years, Bitcoin has also grown in popularity and adoption. The paper aims to analyze the daily return distribution of the Bitcoin and S&P 500 index and assess their tail probabilities through two financial risk measures. As a methodology, We use Bitcoin and S&P 500 Index daily return data to fit The seven-parameter General Tempered Stable (GTS) distribution using the advanced Fast Fractional Fourier transform (FRFT) scheme developed by combining the Fast Fractional Fourier (FRFT) algorithm and the 12-point rule Composite Newton-Cotes Quadrature. The findings show that peakedness is the main characteristic of the S&P 500 return distribution, whereas heavy-tailedness is the main characteristic of the Bitcoin return distribution. The GTS distribution shows that $80.05\%$ of S&P 500 returns are within $-1.06\%$ and $1.23\%$ against only $40.32\%$ of Bitcoin returns. At a risk level ($α$), the severity of the loss ($AVaR_α(X)$) on the left side of the distribution is larger than the severity of the profit ($AVaR_{1-α}(X)$) on the right side of the distribution. Compared to the S&P 500 index, Bitcoin has $39.73\%$ more prevalence to produce high daily returns (more than $1.23\%$ or less than $-1.06\%$). The severity analysis shows that at a risk level ($α$) the average value-at-risk ($AVaR(X)$) of the bitcoin returns at one significant figure is four times larger than that of the S&P 500 index returns at the same risk.
Quoc Minh Nguyen, Dat Tran, Juho Kanniainen, Alexandros Iosifidis · 5 authors
Many cryptocurrency brokers nowadays offer a va-riety of derivative assets that allow traders to perform hedging or speculation. This paper proposes an effective algorithm based on neural networks to take advantage of these investment products. The proposed algorithm constructs a portfolio that contains a pair of negatively correlated assets. A deep neural network, which outputs the allocation weight of each asset at a time interval, is trained to maximize the Sharpe ratio. A novel loss term is proposed to regulate the network's bias towards a specific asset, thus enforcing the network to learn an allocation strategy that is close to a minimum variance strategy. Extensive experiments were conducted using data collected from Binance spanning 19 months to evaluate the effectiveness of our approach. The backtest results show that the proposed algorithm can produce neural networks that are able to make profits in different market situations.
This paper investigates portfolio management algorithm for the cryptocurrency market by using the TQC (Truncated Quantile Critics) algorithm. The study is based on the daily prices of cryptocurrencies. TQC is a deep reinforcement learning algorithm with the Actor-Critic architecture. It alleviates the overestimation problem of traditional value learning algorithm. In this paper, the data of cryptocurrencies are first processed as input to the networks. The inputs to the networks include not only the closing prices of cryptocurrencies, but also the relative strength index, moving average line, and moving average convergence divergence. Various metrics measuring algorithm returns and algorithm stability are used as evaluation criteria in this paper. In this paper, common deep reinforcement learning algorithms are compared. The experimental results show that the TQC algorithm has a highest return of 33.9 % during the test period, which is 3 %, 3 % and 15.6 % higher than A2C, PPO and DDPG respectively. And, the TQC algorithm has the highest stability of return, which is an important evaluation metric for portfolio management algorithms. Despite the high volatility of the cryptocurrency market, the performance of the TQC algorithm has remained relatively stable. This illustrates the positive effects of the TOC algorithm.
Lai Ting, M. M. Abd El‐Raouf, M. E. Bakr, Arwa M. Alsahangiti
Statistical modeling and forecasting are very important for decision-making in any field of life. This paper has two major objectives, namely, statistical modeling and forecasting of real phenomena. For covering the first aim (i.e., statistical modeling), we introduce a new probabilistic model. The new model is introduced by mixing the Dagum distribution with the weighted TX family approach. The proposed model is called the weighted TX Dagum distribution and possesses heavy-tailed characteristics. The new model is illustrated by analyzing real-life data related to Bitcoin prices. To cover the second aim (i.e., forecasting), we take into account six macroeconomic and financial indicators to investigate their impact on Bitcoin prices such as the Adaptive least absolute shrinkage and selection operator (Alasso), elastic net, and minimax concave penalty. After analyzing the data, it is found that Alasso and MCP have retained all the included predictors, except import, while Enet holds all the predictors. The root means square error and mean absolute error associated with MCP are lower than Alasso and Enet, which reveals that MCP fits the data very well as compared to rival methods.
Ze Chen, Ruichao Jiang, Javad Tavakoli, Yiqiang Q. Zhao
In this article we show that Theorem 2 in Lie et al. (2023) is incorrect. Since Wombat Exchange, a decentralized exchange, is built upon Lie et al. (2023) and Theorem 2 is fundamental to Wombat Finance, we show that an undesirable phenomenon, which we call the robbed withdrawal, can happen as a consequence.
Abstract This paper studies the optimal stopping problem under the large‐population framework. In particular, two classes of optimal stopping problems are formulated by taking into account the relative performance criteria . It is remarkable that the relative performance criteria, also understood by the Joneses preference , habit formation utility , or relative wealth concern in economics and finance, play an important role in explaining various decision behaviors such as price bubbles. By introducing such criteria in large‐population setting, a given agent can compare his individual stopping rule with the average behaviors of its cohort. The associated mean‐field games are formulated in order to derive the decentralized stopping rules. The related consistency conditions are characterized via some coupled equation system and the ‐Nash equilibrium properties are also verified. In addition, some inverse mean‐field optimal stopping problem is also introduced and discussed.
Weihao Han, David Newton, Emmanouil Platanakis, Charles Sutcliffe · 5 authors
Abstract Cryptocurrency returns are highly nonnormal, casting doubt on the standard performance metrics. We apply almost stochastic dominance, which does not require any assumption about the return distribution or degree of risk aversion. From 29 long–short cryptocurrency factor portfolios, we find eight that dominate our four benchmarks. Their returns cannot be fully explained by the three‐factor coin model of Liu et al. So we develop a new three‐factor model where momentum is replaced by a mispricing factor based on size and risk‐adjusted momentum, which significantly improves pricing performance.
Abstract Novel technologies allow cryptocurrency exchanges to offer innovative services that set them apart from other exchanges. In this paper we study the distinct features of cryptocurrency fee schedules and the implications for optimal trade execution. We formulate an optimal execution strategy that minimizes the trading fees charged by the exchange. We further provide a proof for the existence of an optimal execution strategy for this type of fee schedule. In fact, the optimal strategy involves both market and limit orders on various price levels. The optimal order distribution scheme depends on the market conditions expressed in terms of the distribution of limit order execution probabilities and the exchange's specific configuration of the fee schedule. Our results indicate that a strategy kernel with an exponentially decaying allocation of trade volume to price levels further away from the best price provides a superior performance and potential reduction of trade execution cost of more than 60%. The robustness of these results is confirmed in an empirical study. To our knowledge this is the first study of optimal trade execution that takes into consideration the full fee schedule of exchanges in general.
In response to the unprecedented uncertain rare events of the last decade, we derive an optimal portfolio choice problem in a semi-closed form by integrating price diffusion ambiguity, volatility diffusion ambiguity, and jump ambiguity occurring in the traditional stock market and the cryptocurrency market into a single framework. We reach the following conclusions in both markets: first, price diffusion and jump ambiguity mainly determine detection-error probability; second, optimal choice is more significantly affected by price diffusion ambiguity than by jump ambiguity, and trivially affected by volatility diffusion ambiguity. In addition, investors tend to be more aggressive in a stable market than in a volatile one. Next, given a larger volatility jump size, investors tend to increase their portfolio during downward price jumps and decrease it during upward price jumps. Finally, the welfare loss caused by price diffusion ambiguity is more pronounced than that caused by jump ambiguity in an incomplete market. These findings enrich the extant literature on effects of ambiguity on the traditional stock market and the evolving cryptocurrency market. The results have implications for both investors and regulators.
The study of order volumes in financial markets has shown that these display several non-trivial statistical properties. Most studies have been focused on the bulk properties of volume of incoming orders or of realized transactions rather than the dynamical aspects. The present work is a study of the dynamical properties of volume. Unlike previous works, we studied the volume available at the spread rather than the volume of incoming orders or of realized transactions. We found evidence that suggests mean reverting volume changes and strong asymmetries in the equilibrium of sell and buy orders as well as the presence of clustering.
Options play a significant role in the financial markets. These types of securities’ values are derived from other securities such as stocks or bonds and, in recent years, cryptocurrencies. There are two types of option contract structures: American and European. Uncovered, or naked, options are buying or selling options primarily on speculation, where the investor does not hold any ownership in the underlying asset, in this case stock or cryptocurrency, from which the option premium is derived. The following three strategies are buying and selling call options, put options, and straddles. Black-Scholes-Merton model is one of the first pricing models that was used to calculate the fair price for a call or a put option premium based on five variables such as current spot price (cryptocurrency), strike price, volatility, time, and risk-free rate. It’s important to reintroduce some mathematical concepts that are essential for valuating options, including the natural logarithms, probability theory, and normal distribution.
The stochastic volatility (SV) model is one of the main methods of modeling time-varying volatility.In particular, SV model is actively used in estimation and prediction of financial market volatility and option pricing.This paper attempts to model the time-varying volatility of the bitcoin market price using SV model.Hidden Markov model (HMM) is combined with the SV model to capture characteristics of regime switching of the market.The HMM is useful for recognizing patterns of time series to divide the regime of market volatility.This study estimated the volatility of bitcoin by using data from Upbit, a cryptocurrency trading site, and analyzed it by dividing the volatility regime of the market to improve the performance of the SV model.The MCMC technique is used to estimate the parameters of the SV model, and the performance of the model is verified through evaluation criteria such as MAPE and MSE.
Abstract Cryptocurrencies are notoriously difficult to value from a fundamental perspective. This valuation challenge is rooted in various debated issues in academia and the investments industry. For example, do cryptocurrencies and other cryptoassets have intrinsic value in the conventional sense? Can one appropriately regard cryptocurrencies as digital fiat currencies? What distinguishes cryptocurrencies such as bitcoin and ether from precious metals like gold from a financial perspective? How do cryptocurrencies compare to other cryptoassets in terms of pricing and valuation? This chapter aims to provide responses to these questions, discuss approaches to cryptoasset valuation, and identify areas for future research.
The study investigates the no-arbitrage parity conditions in Bitcoin spot and futures markets, focusing on the efficiency of the spot-futures (SFP) and futures spread parity (FSP) models in estimating the Bitcoin futures prices. Utilizing data from the Chicago Mercantile Exchange (CME) and Binance exchange, the research analyzes the relationship between spot and futures prices of Bitcoin, moreover, examines the relationship between intramarket Bitcoin futures contracts. The study finds that the mean pricing error of SFP is greater than FSP, indicating the greater efficiency of FSP in pricing Bitcoin futures. It also explores arbitrage opportunities by testing the equality of means of the bid-ask spread and mispricing, revealing that arbitrage opportunities are not consistently present. Few exploitable arbitrage opportunities in bullish markets are found, but overall, the arbitrage profit is not feasible when considering the costs such as bid-ask spread.
Currently the most liquidly traded options on the crypto underlying are the so-called inverse options. An inverse option contract is quoted and traded in the units of the underlying cryptocurrency. The main economic reason for popularity of inverse contracts in the crypto exchanges (such as Deribit) is that inverse contracts enable to operate without maintaining fiat cash accounts. For the theoretical part, we show that inverse options are just regular vanilla options considered under the martingale measure using the forward of the underlying as the numéraire. This measure requires an adjustment to option delta. For the empirical part, we use Deribit options data of past four years to backtest delta-hedged option strategies. We introduce USD and Coin accounting of trading Profit&Loss (P&L) which is important for designing strategies in crypto options. We show empirically that USD and Coin accounting rules are equivalent when performance is measured is Coin and USD units, respectively. We establish that the risk-premia observed in options on Deribit is negative and significant so that strategies selling volatility are expected to generate positive risk-adjusted performance in the long-term.
Exchange-traded funds (ETFs) investing in bitcoin futures contracts first listed for trading in the fall of 2021. This research evaluates the extent to which the returns of bitcoin futures and bitcoin correspond to determine if bitcoin futures provide an effective proxy for a direct bitcoin investment. A no-arbitrage framework for bitcoin futures is established, which provides the basis for the empirical analyses that follow. The empirical analyses of returns correspondence between bitcoin futures and bitcoin use daily and monthly returns to estimate single-factor asset pricing regressions, finding coefficients of expected magnitude and that bitcoin returns explain over 97% of the variation in bitcoin futures returns. This research also estimates two-factor asset pricing regressions that include a novel excess carry term. The two-factor regressions find statistically significant excess carry term coefficients and over 99% explained variation. Finding strong evidence that the returns of bitcoin futures and bitcoin closely correspond, this research concludes that bitcoin futures provide an effective proxy for a direct bitcoin investment.
Fabian E. Eska, Yanghua Shi, Erik Theissen, Marliese Uhrig‐Homburg
Abstract We analyze whether the design of cryptocurrencies helps to explain the Huge cross-sectional variation in the market values of cryptocurrencies. We propose a taxonomy of design features and Hand-collect data on these features for a sample of 79 cryptocurrencies. Using a two-stage regression approach and LASSO regressions, we find, inter alia, that forks and deviations from the design of Bitcoin are associated with lower valuation. In contrast, non-anonymous cryptocurrencies and cryptocurrencies that do not pass on any transaction fees and/or tips to agents who maintain the integrity of the network have, on average, higher market values. These results are robust to variations in the way we measure market valuation.