Financial markets, particularly cryptocurrency markets, are characterized by high volatility and sudden price jumps, making it essential to develop models that can capture these dynamics effectively. In this paper, our focus lies on the Mertonâs jump diffusion model, employing jump processes characterized by the compound Poisson process. Our primary objective is to forecast the drift and volatility of the model using a variety of methodologies. We adopt an approach that involves implementing different drift, volatility, and jump terms within the model through various machine learning techniques, traditional methods, and statistical methods on price-volume data. Additionally, we introduce a path-dependent Monte Carlo simulation to model cryptocurrency prices, taking into account the volatility and unexpected jumps in prices. The results indicate that incorporating jump processes significantly improves forecasting accuracy, especially in volatile markets. Our findings highlight the effectiveness of combining machine learning and traditional methods for more robust predictions.
We consider Geometric Mean Market Makers (G3Ms) â a special type of Decentralized Exchange â with two types of traders: liquidity takers and arbitrageurs. Liquidity takers use G3Ms to swap tokens and to speculate, while arbitrageurs exploit arbitrage opportunities arising from misalignments between the G3M's price and the external market price. We show that in continuous time, a G3M charging proportional transaction fees offers exchange rates that are of finite variation, and that the opportunity cost of providing liquidity relative to rebalancing a self-financing constant-weights portfolio is, in fact, a non-negative gain. Moreover, we demonstrate that Impermanent Loss can be super-hedged in continuous time by a model-free rebalancing strategy. We conclude with a numerical analysis discussing the approximative nature of our continuous-time results for trading in discrete time.
This paper investigates portfolio optimization methodologies and short-term investment strate-gies in the context of the cryptocurrency market, focusing on ten major cryptocurrencies from January 2020 to November 2023. We employ high frequency data and utilize the Kurtosis Mini-mization methodology, alongside other optimization strategies, to construct and evaluate port-folios under different rebalancing frequencies. The empirical analysis reveals that cryptocurren-cies exhibit significant volatility, skewness, and kurtosis, necessitating sophisticated portfolio management techniques. We find that the Kurtosis Minimization methodology consistently outperforms other optimization strategies, delivering optimal returns to investors, particularly in shorter-term investment horizons. We demonstrate the diversification benefits of integrating cryptocurrencies into multi-asset portfolios and emphasize the importance of regular portfolio rebalancing in the volatile cryptocurrency market. Our findings offer insights for portfolio man-agers and investors seeking to optimize their investment outcomes in the cryptocurrency market, highlighting the importance of risk management, diversification, and dynamic portfolio man-agement strategies.
In this paper, we describe and apply different models of portfolio construction in the selection between a small number of big-cap cryptocurrencies. Our purpose is to select the minimum riskiness between cryptocurrencies, comparing different risk measures and maximum diversification. We build our models without the constraints of the expected returns. Without relying on expected returns, we have the same condition on the comparison between them. Cryptocurrencies are not common stock or other assets indexed in the market but it is interesting to study how diversification can significantly improve investment performance. We first give the methodology to use high-frequency observation data, in the numeral approximation especially in the novel application of the Risk parity models, used with different risk measures we can achieve a very good result, from the position of gaining and variation. Since Risk parity models divide the weights of the asset in equal risk contribution proportion, it is suggested to use a small number of cryptocurrencies, otherwise their performance will be close to the uniform portfolio. To the traditional Mean Variance model, and the alternative, Expected shortfall/Conditional Value at Risk, we use three versions of Risk Parity with two different risk measures and a naive risk parity. The uniform portfolio is used as a benchmark for selection comparison with the other portfolio models. We give the conditions for the Risk Parity with the Expected shortfall/Conditional Value at Risk (CVaR) to guarantee convergence with the numerical approximation. In the end, we study the tradeoff between each model and which is more suitable for a small cryptocurrency portfolio.
Eminda Ishan De Silva, Gayithri Niluka Kuruppu, Sandun Dassanayake
Purpose The non-fungible token (NFT) market had undergone dramatic growth and a sudden decline during 2021â2022. The market experienced a surge in prices in late 2021 and early 2022, with NFTs being sold at inflated prices. Despite this, by April 2022, the market underwent a correction, and the prices of NFTs returned to more reasonable levels. This can be a result of imitating the actions or judgments of a larger group, which is not systematically proven yet. Therefore, this study systematically investigates the applicability of herding behavior in the NFT market. Design/methodology/approach This research employs cross-sectional absolute deviation (CSAD) of returns and ordinary least squares (OLS) to test herding behavior with moving time windows of 10, 20 and 30 days based on the sales data collected from public interface of OpenSea between July 1, 2021 and June 30, 2022. Additionally, NFT-related keyword usage analysis is done for the detected herding periods. Findings As per the results of the data analyzed, herding behavior was evidenced using 10-, 20- and 30-day time windows from July 1, 2021 to June 30, 2022because of media movement. The findings revealed that this behavior was present and aligned with the overall behavior of the market. Originality/value This study introduces CSAD to examine herding behavior patterns within the NFT market. Complementing this method, keyword count-based analysis is employed to identify the underlying causes of herding behavior. Through this comprehensive approach, this study not only uncovers the roots of herding behavior but also offers an assessment of the time windows during which it occurs, considering the plausible socioeconomic contexts that influence these trends.
Manoel Fernando Alonso Gadi, Maximilian Schmidt, Noah Ruemmele, MiguelâĂngel Sicilia
Stock market indices are pivotal tools for establishing market benchmarks, enabling investors to navigate risk and volatility while capitalizing on the stock market's prospects through index funds. For participants in decentralized finance (DeFi), the formulation of a token index emerges as a vital resource. Nevertheless, this endeavor is complex, encompassing challenges such as transaction fees and the variable availability of tokens, attributed to their brief history or limited liquidity. This research introduces an index tailored for the Ethereum ecosystem, the leading smart contract platform, and conducts a comparative analysis of capitalization-weighted (CW) and equal-weighted (EW) index performances. The article delineates exhaustive criteria for token eligibility, intending to serve as a comprehensive guide for fellow researchers. The results indicate a consistent superior performance of CW indices over EW indices in terms of return and risk metrics, with a 30-constituent CW index outshining its counterparts with varied constituent numbers. The recommended CW30 index demonstrates substantial advantages in comparison to established benchmarks, including prominent indices like DeFi Pulse Index (DPI) and CRypto IndeX (CRIX). Additionally, the article explores the practicality of implementing the CW30 in Layer 2 networks of the Ethereum Ecosystem, advocating for the Arbitrum infrastructure as the optimal choice for the decentralized crypto index protocol herein referred to as the Ethereum Ecosystem Index (EEI). The study's insights aspire to enrich the DeFi ecosystem, offering a nuanced understanding of network selection and a strategic framework for implementation. This research significantly enhances the existing literature on index construction and performance within the Ethereum ecosystem. To our knowledge, it represents a pioneering comprehensive analysis of an index that accurately mirrors the Ethereum market, advancing our comprehension of its intricacies and wider ramifications. Moreover, this study stands as one of the initial thorough examinations of index construction methodologies within the nascent asset class of crypto. The insights gleaned provide a pragmatic approach to index construction and introduce an index poised to serve as a benchmark for index products. In illuminating the unique facets of the Ethereum ecosystem, this research makes a substantial contribution to the current discourse on crypto, offering valuable perspectives for investors, market stakeholders, and the ongoing exploration of digital assets.
ABSTRACT Contrasting sharply with traditional money, bond, and bond futures markets, where interest rates emerge organically from participant interactions, DeFi lending platforms employ ruleâbased interest rates that are algorithmically set. Thus, the selection of an effective interest rate model (IRM) is paramount for the success of a lending protocol. This paper investigates the modeling of agents' behaviors on lending platforms and proposes a theoretical framework for formulating optimal IRMs. We show that, under perfect information, an optimal control model with a state constraint generates an optimal interest rate policy that has a shape similar to that of popular markets. Furthermore, we formally analyze interest rate policies based on PID controllers, which work efficiently based on fewer assumptions. Using public data of popular markets on the Ethereum blockchain, we analyze agents' behavior, build a realistic simulation environment, and highlight the main tradeoffs in the design of interest rates for decentralized lending platforms.
This study presents the mathematical formulations of investor sentiment for investors in cryptocurrencies. We assume that bitcoin prices are driven by investor sentiment measured in terms of Google search volume and social media posts. The current generation of retail investors uses non-traditional methods such as social media posts and Google searches to obtain information so that an increase in posts and searches on âbitcoin,â indicate positive or negative investor sentiment. Mathematical formulations describe investor sentiment separately for risk-averse, moderate risk, and risk-taking investors. Risk-averse investors are considered to be aberrant in their investment in cryptocurrencies as they are naturally resistant to high-risk investments such as cryptocurrencies. Only risk-taking investors capture the fullest extent of irrational exuberance that prevailed in the cryptocurrency markets. However, risk-takers with very high-risk tolerance, such as hedge funds, trade in investments with volatility to capitalize upon the highest market prices for cryptocurrencies. Their behavior is modeled in cryptocurrency futures and cryptocurrency call options, and cryptocurrency put options. The insight provided by this paper is that the history of cryptocurrency prices is stored in a Laplace transform so that investor sentiment is based on the trajectory of past prices for cryptocurrencies and cryptocurrency futures. For cryptocurrency options, the history of volatility of prices is embedded in the Laplace transform, with increasing volatility embedded in call option prices, and decreasing volatility embedded in put option prices.
Min-Bin Lin, Cathy YiâHsuan Chen, Wolfgang Karl HĂ€rdle
This study investigates cryptocurrency volatility dynamics, particularly focusing on Ethereum (ETH). We dissect long- and short-term volatility components to gain deeper insights into its evolution. This approach allows studying the impact of ETHâs Merge upgrade, replacing Proof-of-Work with Proof-of-Stake on September 15, 2022. Employing 29 empirical factors related to blockchain functionality and crypto market characteristics, we explore their long-term equilibrium connection with price volatility. Our findings reveal that scalability factors and wealth dis- tribution significantly influence volatility persistence, ultimately highlighting the stability-enhancing impact of Ethereumâs Merge upgrade.
This study examines the impact of incorporating cryptocurrencies into global asset portfolios using ensemble approaches and a tracing strategy. We considered cryptocurrency ratios of 1%, 3%, and 5% for including cryptocurrencies. Benchmarking was performed using classical portfolio optimization strategies such as minimum variance portfolio (MVP), maximum diversification portfolio (MDP), equal risk contribution portfolio (ERCP), and hierarchical risk parity (HRP). The ensemble methods and tracing strategies we evaluated were the equally weighted portfolio (EWP), the linear combination portfolio (LCP), the return tracing portfolio (RTP), and the return volatility tracing portfolio (RVTP). EWP averages the weights of classical methods, while LCP combines the objective functions of three optimization methods. RTP and RVTP represent tracing strategy portfolios with monthly rebalancing, selecting the best-performing portfolio based on cumulative returns or a combination of cumulative returns and annualized volatility. Our findings reveal that increasing the cryptocurrency allocation improves performance metrics in ensemble portfolios but also leads to higher risk. In addition, including cryptocurrencies reduces transaction fees, especially evident in the LCP with a 5% allocation. In the case of a 3-month RTP, HRP emerged as the preferred strategy, outperforming the use of HRP alone. In the case of a 6-month RVTP, MVP remained the preferred choice, consistently achieving lower volatility.
Ilyas Agakishiev, Wolfgang Karl HĂ€rdle, Denis Becker, Xiaorui Zuo
Abstract There are many ways to model complex time series. The simplest approach is to increase the complexity, and thus, the flexibility of the model, for the entire time series. As an example, one could use a neural network. Another solution would be to change the parameters of a model dependent on the âstateâ or âregimeâ of the time series. A typical example here would be the Hidden Markov model (HMM). This paper combines the two concepts to create a Reinforcement Learning (RL) model that adds variables that depend on the state of the time series. To test the concept, the RL model is used with cryptocurrency data to determine the share to invest into the cryptocurrency index CRIX in order to maximize wealth. The results have shown that cryptocurrency metadata is useful as supplementary data for analysis of the respective prices. The Reinforcement learning model with regimes shows potential for investment management, but comes with some caveats.
We propose a "break-even" implied volatility of a decentralized finance (defi) pool. The implied volatility is "break-even" because it is defined by the zero expected profit-and-loss of hedged liquidity providers i.e. by their expected profit (against the "buy-and-hold" benchmark) equaling their expected loss (against the same benchmark): the numerator of Rebalancing Loss a.k.a. Impermanent Loss. It depends only on the time-to-maturity and therefore forms only a curve (as opposed to the traditional surface). Similarly to traditional finance, when implied volatility is higher than realized volatility, option sellers (liquidity providers) are more likely to make money, irrespective of hedging. When approximated, this first-principles definition of implied volatility can be surprisingly (loosely) derived from the square-root market impact empirical rule in traditional finance.
To understand the disruption and implications of distributed ledger technologies for financial reporting and auditing, we analyze firm misreporting, auditor monitoring and competition, and regulatory policy in a unified model. A federated blockchain for financial reporting and auditing can improve verification efficiency not only for transactions in private databases but also for cross-chain verifications through privacy-preserving computation protocols. Despite the potential benefit of blockchains, private incentives for firms and first-mover advantages for auditors can create inefficient under-adoption or partial adoption that favors larger auditors. Although a regulator can help coordinate the adoption of technology, endogenous choice of transaction partners by firms can still lead to adoption failure. Our model also provides an initial framework for further studies of the costs and implications of the use of distributed ledgers and secure multiparty computation in financial reporting, including the positive spillover to discretionary auditing and who should bear the cost of adoption. This paper was accepted by David Simchi-Levi, finance. Funding: The authors gratefully acknowledge research support from the FinTech Laboratory at J. Mack Robinson College of Business at Georgia State University, the Center for Research in Security Prices at the University of Chicago, the Ripple University Blockchain Research Initiative, and the Smith AI Initiative for Capital Market Research at the University of Maryland. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.02577 .
Mustafa Kamal, Sabir Ali Siddiqui, Nayabuddin, Afaf Alrashidi · 11 authors
The study and investigation of the behavior of monetary phenomena is an interesting subject for actuaries and practitioners. In the recent age and development in the monetary and financial phenomena, cryptocurrency has gained much attention from actuaries. Over the past decade, several research studies have emerged on modeling and forecasting cryptocurrency exchange rates. This paper also contributes to the modeling of cryptocurrency exchange rates using a new version of the Logistic distribution, namely, a new cotangent-Logistic distribution. The mathematical properties and estimators of the new cotangent-logistic distribution's parameters are obtained. We illustrate the new cotangent-Logistic distribution using two financial data sets representing the log-returns of the Bitcoin and Ethereum prices. We compare the new cotangent-Logistic distribution with the baseline Logistic distribution and its modified version. Using the p-value and three other statistical tests, we show that the new cotangent-Logistic distribution repeatedly provides the optimal fit to cryptocurrency exchange rates.
Sulalitha Bowala, A. Thavaneswaran, Ruppa K. Thulasiram, Thimani Ranathungage · 5 authors
Recently there has been a growing interest in constructing portfolios with stocks and cryptocurrencies. As cryptocurrency prices increase over the years, there is a growing interest in investing in cryptocurrencies, along with diversifying portfolios by adding multiple cryptocurrencies to the existing portfolios. Even though investing in cryptocurrency leads to high returns, it also leads to high risk due to the high un-certainty of cryptocurrency price changes. Thus, more robust risk measures have been introduced to capture market risk and avoid investment loss, along with different types of portfolios to mitigate risks. Many portfolio techniques assume asset returns are normally distributed with constant variance. However, these assumptions are violated in many cases. Unlike the existing work, this study investigates the recently proposed data-driven exponentially weighted moving average (DDEWMA) covariance model to estimate the variance-covariance matrix for high frequency (hourly data) cryptocurrency returns in Markowitz portfolio optimization. The experimental results show that for high-frequency data, the DDEWMA approach outperforms the existing portfolio optimization model that uses the empirical variance-covariance matrix. Improvements have been identified in terms of the Sharpe ratio as well as risks (volatility, mean absolute deviation (MAD), Value-at-Risk (VaR), and Expected shortfall (ES)).
Valuation of Bitcoin, Ethereum, and other cryptoassets is a challenge for the investment industry. We review the tools available to value cryptoassets, and in doing so, we aim to help practitioners better understand the dynamics of cryptoassets.
Adithya Bhaskara, Rafael Frongillo, Lindgren, Elias, Maneesha Papireddygari
Liquidity provisioning in automated market makers is the practice of recruiting third-party liquidity providers (LPs) to contribute assets to the market in exchange for fees skimmed off of trades. This paper introduces a general framework for liquidity provisioning in cost function prediction markets. Our most general protocol allows LPs to submit or update an arbitrary cost function that specifies their liquidity over the entire price space. We show that our protocol encapsulates several notions of running market makers in parallel, which we prove to be equivalent. We also recover existing protocols from decentralized finance as special cases. In our protocol, liquidity can be expressed as a matrix-valued function, which we argue is necessary with three or more securities. Due to this inherent multidimensionality, the design of trading fees with three or more securities is nontrivial: we show that natural axioms on the design of these fees are incompatible.
Abstract Cryptocurrencies and Bitcoin, in particular, are prone to wild swings resulting in frequent jumps in prices, making them historically popular for traders to speculate. It is claimed in recent literature that Bitcoin price is influenced by sentiment about the Bitcoin system. Transaction, as well as the popularity, have shown positive evidence as potential drivers of Bitcoin price. This study introduces a bivariate jump-diffusion model to capture the dynamics of Bitcoin prices and the Bitcoin sentiment indicator, integrating trading volumes or Google search trends with Bitcoin price movements. We derive a closed-form solution for the Bitcoin price and the associated BlackâScholes equation for Bitcoin option valuation. The resulting partial differential equation for Bitcoin options is solved using an artificial neural network, and the model is validated with data from highly volatile stocks. We further test the modelâs robustness across a broad spectrum of parameters, comparing the results to those obtained through Monte Carlo simulations. Our findings demonstrate the modelâs practical significance in accurately predicting Bitcoin price movements and option values, providing a reliable tool for traders, analysts, and risk managers in the cryptocurrency market.