We study portfolio optimization of four major cryptocurrencies. Our time series model is a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals used to capture the non-Gaussian cryptocurrency return dynamics. Based on the time series model, we optimize the portfolio in terms of Foster-Hart risk. Those sophisticated techniques are not yet documented in the context of cryptocurrency. Statistical tests suggest that the MNTS distributed GARCH model fits better with cryptocurrency returns than the competing GARCH-type models. We find that Foster-Hart optimization yields a more profitable portfolio with better risk-return balance than the prevailing approach.
This paper aims to study the pricing of Bitcoin options with a view to incorporating both conditional heteroscedasticity and regime switching in Bitcoin returns. Specifically, a nonlinear time series model combining both the self-exciting threshold autoregressive (SETAR) model and the generalized autoregressive conditional heteroscedastic (GARCH) model is adopted for modeling Bitcoin return dynamics. Specifically, the SETAR model is used to model regime switching and the Heston-Nandi GARCH model is adopted to model conditional heteroscedasticity. Both the conditional Esscher transform and the variance-dependent pricing kernel are used to specify pricing kernels. Numerical studies on the Bitcoin option prices using real bitcoins data are presented.
Ai Jun Hou, Ning Wang, Cathy Y. H. Chen, Wolfgang Karl Härdle
Cryptocurrencies, especially Bitcoin (BTC), which comprise a new digital asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/BTC include a high level of speculation, extreme volatility and price discontinuity. We propose a pricing mechanism based on a stochastic volatility with a correlated jump (SVCJ) model and compare it to a flexible co-jump model by Bandi and Renò (2016). The estimation results of both models confirm the impact of jumps and co-jumps on options obtained via simulation and an analysis of the implied volatility curve. We show that a sizeable proportion of price jumps are significantly and contemporaneously anti-correlated with jumps in volatility. Our study comprises pioneering research on pricing BTC options. We show how the proposed pricing mechanism underlines the importance of jumps in cryptocurrency markets.
Alla Petukhina, Simon Trimborn, Wolfgang Karl Härdle, Hermann Elendner
Cryptocurrencies (CCs) have risen rapidly in market capitalization over the past years. Despite striking volatility, their high average returns and low correlations have established CCs as alternative investment assets for portfolio and risk management. We investigate the benefits of adding CCs to well-diversified portfolios of conventional financial assets for different types of investors, including risk-averse, return-maximizing and diversification-seeking investors who may trade at different frequencies, namely, daily, weekly or monthly. We calculate out-of-sample performance and diversification benefits for the most popular portfolio-construction rules, including mean-variance optimization, risk-parity, and maximum-diversification strategies, as well as combined strategies. Our results demonstrate that CCs can improve the risk-return profile of portfolios, but their benefit depends on investor objectives. In particular, diversification strategies (maximizing the portfolio diversification index or equating risk contributions) draw appreciably on CCs and show, in line with spanning tests, CCs to be non-redundant extensions of the investment universe. However, when we introduce liquidity constraints via the LIBRO method to account for illiquidity of many CCs, out-of-sample performance drops considerably, while the diversification benefits persist. We conclude that the utility of CC investments strongly depends on investor characteristics.
Decentralized Finance (DeFi) suffers from various financial risks nowadays. This paper presents MovER, a novel stablecoin system based on modern risk management, consisting of a diversified collateral framework with corresponding stabilizing/clearing mechanism. Moreover we build a powerful all-round risk evaluation framework on the basis of thought on the probability theory and mathematical statistics.
Financial institutions own balanced portfolios with many assets and hence a small risk. But they are not able to split them into smaller parts with comparable risk for resale due to regulators' restrictions caused by a lack of auditability. Blockchain and smart contracts allow overcoming this problem via tokenizing assets into a commodity. The paper seeks to answer the question: how to assemble as many as possible standardized packages from a given portfolio. The optimal algorithms for two special cases-discrete and continuous homogeneous-are provided.
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.
This paper offers the first-ever look at Bitcoin options by investigating the wedge between optimum Bitcoin option prices based on classical option valuation models (Black-Scholes-Merton and the Heston-Nandi GARCH (1, 1)) and actual premiums at which these options are trading. For this purpose, we use near-the-money call and put options traded on Deribit platform as on 27.01.2020, with the maturities ranging from January 31 to 25 September 2020. In addition, we analyse the risk inherent in Bitcoin options by calculating their Greeks and comparing them to those of traditional commodity options. Pricing results suggest slight overpricing and underpricing for Bitcoin call options with the strike $8, 000 maturing on 30.01.2020 and 28.02.2020, respectively. We also find that the Bitcoin options provide much stable deltas over time compared to the other commodity options. This result implies higher insulation from undue price rises with the passage of time for investors in Bitcoin options. Our results are useful to regulators, investors and market managers in better understanding the nuances of the Bitcoin options market in addition to making more informed investment choices.
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.