Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. This article shows how to build a simple and precise estimator of the jump activity index of a semimartingale observed at a high frequency by comparing different multipowers. The novel methodology allows to infer whether a discretely observed process contains a continuous martingale component. The empirical part of the article undertakes a nonparametric analysis of the jump activity of bitcoin and shows that bitcoin is a pure jump process with high jump activity, which is critically different from conventional currencies that include a Brownian motion component.
This paper aims at identifying a validated risk model for the cryptocurrency market. We propose a stochastic volatility model with co-jumps in return and volatility (SVCJ) to highlight the role of jumps in returns and volatility in affecting Value-at-Risk (VaR) and Expected Shortfall (ES) in cryptocurrency market. Validation results based on backtesting show that SVCJ model is superior in terms of statistical accuracy of VaR and ES estimates, compared to alternative models such as TGARCH (Threshold GARCH) volatility and RiskMetrics models. The results imply that for the cryptocurrency market, the best performing model is a stochastic process that accounts for both jumps in returns and volatility.
This paper compares a number of stochastic volatility (SV) models for modeling and predicting the volatility of the four most capitalized cryptocurrencies (Bitcoin, Ethereum, Ripple, and Litecoin). The standard SV model, models with heavy-tails and moving average innovations, models with jumps, leverage effects and volatility in mean were considered. The Bayes factor for model fit was largely in favor of the heavy-tailed SV model. The forecasting performance of this model was also found superior than the other competing models. Overall, the findings of this study suggest using the heavy-tailed stochastic volatility model for modeling and forecasting the volatility of cryptocurrencies.
This project takes several common strategies for algorithmic stock trading and tests them on the cryptocurrency market. The three strategies used are moving average crossover, mean reversion, and pairs trading. Data was collected every five minutes for the top one hundred cryptocurrencies between October 5, 2017, and January 24, 2018. Due to the high volatility of the market, the data includes various market situations. Three noted situations are a rising market, falling market, and relatively stable market. The three strategies were modified to optimally follow each market situation. Modifications include adjusting parameters used in each strategy as well as mixing several strategies or dynamically changing between strategies. In each strategy and with each cryptocurrency, the benchmark against which the algorithm is tested is the market's performance, or what an investor would have after buying and holding. Returns are compared with the buying and holding strategy, and different scenarios are analyzed to determine the risk associated with buying and holding compared with an algorithmic strategy. Results will be taken with the market's actual trends and also with some alternate possible trends to test all market scenarios. A web interface will accompany the presentation, allowing users to test the strategies by entering their own parameters and instantly see the results.
In recent years cryptocurrency trading has captured the attention of practitioners and academics. The volume of the exchange with standard currencies has known a dramatic increasing of late. This paper addresses to the need of models describing a bitcoin-US dollar exchange dynamic and their use to evaluate European option having bitcoin as underlying asset.
This paper investigates the return-volatility asymmetry of Bitcoin. We find that the cross correlations between return and volatility (squared return) are mostly insignificant on a daily level. In the high-frequency region, we find thata power-law appears in negative cross correlation between returns and future volatilities, which suggests that the cross correlation is \revision{long ranged}. We also calculate a cross correlation between returns and the power of absolute returns, and we find that the strength of \revision{the cross correlations} depends on the value of the power.
Francisco López Herrera, División de Investigación, Facultad de Contaduría y Administración, Universidad Nacional Autónoma de México, Ciudad de México, México., Luis Guadalupe Macías-Trejo, Oscar V. De la Torre-Torres
Este artículo muestra los resultados de un análisis del desempeño de ocho de los criptoactivos más importantes entre la gran variedad que actualmente existe en el mercado. Se estudia su riesgo de mercado con base en métricas ampliamente utilizadas para activos financieros. El análisis se complementa con la evaluación de su desempeño dentro de portafolios formados con criterios convencionales. Se encuentra un comportamiento bastante heterogéneo entre los activos estudiados, sugiriendo que tal comportamiento obedece a las características específicas de cada uno de ellos, más que a las características comunes como una clase específica de activos.
Forecasting and assessing the risk of heat waves is a crucial public policy stake. Evaluate the probability of heat waves and their severity can be possible by knowing the temperature in continuous time. However, daily extremes (maxima and minima) might be the only available data. The Ornstein-Uhlenbeck process is commonly used to model temperature dynamic. An estimation of the process parameters using only daily observed suprema of temperatures is proposed here. This new approach is based on a least square minimization using the cumulative distribution function of the supremum. Risk measures related to heat waves are then obtained numerically. In order to calculate explicitly those risk measures, it can be useful to have the joint law of the Ornstein-Uhlenbeck process and its supremum. The study is _rst limited to the joint density / distribution of the endpoint and supremum of the Ornstein-Uhlenbeck process. This probability admits a density, solution of the Fokker-Planck equation and explicitly obtained as an expansion involving parabolic cylinder functions. The proof of the density expression relies on a decomposition on a Hilbert basis of the space via a spectral method. We also study the oscillating Ornstein-Uhlenbeck process, which drift parameter is piecewise constant depending on the sign of the process. The Laplace transform of this process hitting time is determined and we also calculate the probability for the process to be positive on a fixed time.
In this paper, we study forecasting problems of Bitcoin-realized volatility computed on data from the largest crypto exchange—Binance. Given the unique features of the crypto asset market, we find that conventional regression models exhibit strong model specification uncertainty. To circumvent this issue, we suggest using least squares model-averaging methods to model and forecast Bitcoin volatility. The empirical results demonstrate that least squares model-averaging methods in general outperform many other conventional regression models that ignore specification uncertainty.
Despite the current growing interest in Bitcoins-and cryptocurrencies in general-financial instruments, as well as studies related to them, are quite underdeveloped. Therefore, this article aims to provide a suitable pricing model for options written on this peculiar underlying. This is done through an artificial neural network approach, where classical pricing models-namely the trinomial tree, Monte Carlo simulation, and explicit finite difference method-are used as input layers. Results show that options written on Bitcoin turn out to be systematically overpriced when considering classical methods, whereas a noticeable improvement in price predictions is achieved by means of the proposed neural network model.
Julien Chevallier, Stéphane Goutte, Khaled Guesmi, Samir Saadi
This study contributes to the existing literature on the empirical characteristics of virtual currency allowing for a dynamic transition between different economic regimes and considering various crashes and rallies over the business cycle, that is captured by jumps. We combine Markov-switching models with Levy jump-diffusion offer a new model that captures the different sub-period of crises over the business cycle, that is captured by jumps. This method also enables to test the relevance of dynamic measures of regime switching concerning the independent pure-jump process, which are not frequently used in the literature. Bitcoin offers something different than a traditional currency; there is potential value of having a network that helps as a secure repository for the common knowledge of all transactions. Besides, the value of Bitcoin fluctuates so wildly that it may be too risky to serve as a credible store of value.
Recent studies have found that the log-volatility of asset returns exhibit roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using the multifractal detrended fluctuation analysis, we obtain the generalized Hurst exponent of the log-volatility increments and find that the generalized Hurst exponent is less than $1/2$, which indicates log-volatility increments that are rough. Furthermore, we find that the generalized Hurst exponent is not constant. This observation indicates that the log-volatility has multifractal property. Using shuffled time series of the log-volatility increments, we infer that the source of multifractality partly comes from the distributional property.
Dorje C. Brody, Lane P. Hughston, Bernhard K. Meister
A term structure model in which the short rate is zero is developed as a candidate for a theory of cryptocurrency interest rates. The price processes of crypto discount bonds are worked out, along with expressions for the instantaneous forward rates and the prices of interest-rate derivatives. The model admits functional degrees of freedom that can be calibrated to the initial yield curve and other market data. Our analysis suggests that strict local martingales can be used for modelling the pricing kernels associated with virtual currencies based on distributed ledger technologies.
Given that there are both continuous and discontinuous components in the movement of asset prices, existing asset pricing models that assume only continuous price movements should be revised. In this paper, we explore the features of jumps, which are discontinuous movements, by examining Bitcoin pricing. First, we identify jumps in the Bitcoin price on a daily basis, applying a non-parametric methodology and then break down the Bitcoin total rate of return into a jump rate of return and a continuous rate of return. In our empirical analysis, price jumps turn out to be independent of volatility. Moreover, the jumps in the Bitcoin price do not appear at regular intervals; rather, they tend to be concentrated in clusters during special periods, implying that once an economic crisis occurs, the crisis will last for a long time due to contagion effects and the economy will take a considerable amount of time to recover fully. Further, the contribution of the jump rate of return to the total rate of return of the Bitcoin price is lower than the contribution of the continuous return, implying that the pursuit of sustainable returns rather than large but temporary returns will improve the total rate of return over the long term. Finally, more jumps are observed when trading volume is lower, implying that market illiquidity drives discontinuous movement in asset prices. Overall, the features of jump risk are like two sides of the same coin and jump risks are expected to have a significant effect on asset pricing, suggesting that consideration of jumps is essential for risk management as well as asset pricing.
The goal of this paper is to explore the relationship between momentum effects and liquidity in cryptocurrency markets. Portfolios based on momentum-liquidity bivariate sorts are formed and rebalanced on a varying number of cryptocurrencies through time. We find a strong momentum effect in the most liquid cryptocurrencies, which supports the theories of investor herding behavior. Moreover, we propose two profitable long-only strategies: the illiquid losers and liquid winners, which exhibit improved risk adjusted performance over the market capitalization weighted portfolio.
Yu-Min Lian, Chi-Hung Cheng, Shih-Hsun Lin, Jui-Hsuan Lin
In this study, we make use of both the specific method of Monte Carlo simulation and the spot-futures parity with the cost of carry to establish a dynamic price model of Bitcoin futures and to conduct the appraisals and numerical analyses. More specifically, the electricity fees and equipment costs are taken into account and the proposed model is thereby built. Numerical results show that various cost factors have significant effects on the Bitcoin futures price. We employ Monte Carlo simulation to approximate the Bitcoin futures price and we use Python to program the computations.
The Holy Grail of a decentralised stablecoin is achieved on rigorous mathematical frameworks, obtaining multiple advantageous proofs: stability, convergence, truthfulness, faithfulness, and malicious-security. These properties could only be attained by the novel and interdisciplinary combination of previously unrelated fields: model predictive control, deep learning, alternating direction method of multipliers (consensus-ADMM), mechanism design, secure multi-party computation, and zero-knowledge proofs. For the first time, this paper proves: - the feasibility of decentralising the central bank while securely preserving its independence in a decentralised computation setting - the benefits for price stability of combining mechanism design, provable security, and control theory, unlike the heuristics of previous stablecoins - the implementation of complex monetary policies on a stablecoin, equivalent to the ones used by central banks and beyond the current fixed rules of cryptocurrencies that hinder their price stability - methods to circumvent the impossibilities of Guaranteed Output Delivery (G.O.D.) and fairness: standing on truthfulness and faithfulness, we reach G.O.D. and fairness under the assumption of rational parties As a corollary, a decentralised artificial intelligence is able to conduct the monetary policy of a stablecoin, minimising human intervention.