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.
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.
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.
Lai Ting, M. M. Abd ElâRaouf, 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 largeâpopulation 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 largeâpopulation setting, a given agent can compare his individual stopping rule with the average behaviors of its cohort. The associated meanâfield games are formulated in order to derive the decentralized stopping rules. The related consistency conditions are characterized via some coupled equation system and the âNash equilibrium properties are also verified. In addition, some inverse meanâfield 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 longâshort cryptocurrency factor portfolios, we find eight that dominate our four benchmarks. Their returns cannot be fully explained by the threeâfactor coin model of Liu et al. So we develop a new threeâfactor model where momentum is replaced by a mispricing factor based on size and riskâadjusted 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.
Roberto Mota Navarro, F. Leyvraz, HernĂĄn Larralde
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.
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.