This paper addresses one of the main issues regarding numerical derivatives valuation, particularly the search for an alternative to the normality assumption of underlying asset returns, to obtain the price by using numerical techniques. There might be difficulties in making normality assumptions, which could produce over-valuated or sub-valuated prices of derivatives. Under this consideration, the Generalized Hyperbolic family has been proven to be a proper selection to model heavy tailed distribution behavior. The Normal Inverse Gaussian (NIG) distribution is a member flexible enough to model financial returns. NIG distribution can be used to model distribution returns under different states of nature. The indexes of the Brazil, Russia, India and China (BRIC) economies were studied at different time-periods using return data series from 2002 to 2005, 2006 to 2010 and 2011 to 2015, in such a manner to demonstrate with statistical criteria that NIG fits the empirical distribution in the three periods; even throughout economic downturn. This result may be used as an improvement in derivatives valuation with indexes as underlying assets.
This paper develops the ability of the normal inverse Gaussian distribution (NIG) to fit the returns of bitcoin (BTC). As the first cryptocurrency created, the behavior of this new asset is characterized by great volatility. The lack of a proper definition or classification under existing theory exacerbates this property in such a way that explosive periods followed by a rapid decline have been observed along the series, meaning bubble episodes. By detecting the periods in which a bubble rises and collapses, it is possible to study the statistical properties of such segments. In particular, adjusting a theoretical distribution may help to determine better strategies to hedge against these episodes. The NIG is an appropriate candidate not only because of its heavy-tailed property but also because it has been proven to be closed under convolution, a characteristic that can be implemented to measure multivariate value at risk. Using data on the price of BTC with respect to seven of the main global currencies, the NIG was able to fit every time segment despite the bubble behavior. In the out-of-sample tests, the NIG was proven to have an adjustment similar to that of a generalized hyperbolic (GH) distribution. This result could serve as a starting point for future studies regarding the statistical properties of cryptocurrencies as well as their multivariate distributions.
We estimated the stock market risk premium during the COVID-19 pandemic with a GARCH-in-Mean (GARCH-M)(1,1) model. The analysis then explored the presence of regime changes using a two-regime Markov-Switching GARCH (MS GARCH)(1,1) model. The sample we used included the stock market indexes of nine countries from three geographical regions, including: North America (Canada, USA, and Mexico), South America (Brazil and Argentina), and Asia (Japan, South Korea, Hong Kong, and Singapore), over two periods: (a) pre-COVID (from 1 January 2015 to 31 December 2019); and (b) COVID (from 1 January 2020 to 31 December 2021). Our GARCH-M(1,1) estimation results indicate that the more developed countries’ stock markets experienced an important increase in their risk premium during the COVID period, likely explained by the massive government anticyclical policies. By contrast, developing countries’ stock markets, particularly in Latin America, experienced a reduction, and in some cases, even a total loss of the risk premium effect. From the perspective of investors and portfolio risk managers, the identification of high and low volatility periods and their estimated probability of occurrence is useful for the characterization of stress scenarios and the design of emerging strategies. For governments and central bankers, the implementation of different policies should respond to the more likely scenarios but should also be prepared to respond to other less likely scenarios. Institutional preparedness to respond to as many different scenarios as may be identified with the use of MS GARCH models can make their interventions more successful. This work presents an objective example of how the use of MS GARCH models may be of use to practitioners in both the financial industry and government. We confirmed that the results of a two-regime MS GARCH model are superior to those obtained from a single-regime model.
This study presents a multivariate study regarding Bitcoin and its interactions with other financial assets of different classes. This is done by adjusting a multivariate semi heavy-tailed distribution to portfolios containing indexes, currencies, and commodities and one cryptocurrency. Later, a rolling window is deployed to obtain the dynamic parameters of the distribution in a weekly basis. With a Markowitz specification problem, the optimal portfolio weights are computed dynamically using the parameters of the multivariate NIG distribution as inputs. The results provide evidence that correlations of Bitcoin with other assets may provide certain degree of diversification to portfolios; nevertheless, the high volatility of this asset makes it unpractical to employ in significant weights. This paper is relevant for researchers and practitioners as it provides a new tool to manage portfolios with cryptocurrencies and more reliable weights to the asset allocation.
El objetivo de esta investigación es analizar la presencia de burbujas financieras o un comportamiento explosivo en cuatro criptomonedas: Ethereum, Ripple, Bitcoin Cash y EOS. La selección de los activos se basó en la capitalización de mercado. La metodología implementada fue una prueba simple y generalizada (SADF y GSADF) de una variación de la prueba aumentada de Dickey-Fuller propuesta por Phillips et al. (2011, 2015). Encontramos diez, siete, seis y siete comportamientos exuberantes en los activos mencionados, respectivamente. Esta metodología ha sido en gran parte inexplorada y podría emplearse de manera estándar en el sector financiero para cualquier otro activo. Esta es la primera investigación que detecta este tipo de comportamiento para un grupo de criptomonedas con frecuencia diaria. Con el presente trabajo y el artículo de Li et al. (2018), el 68,47% del mercado ha sido analizado bajo la metodología. En consecuencia, este comportamiento podría estar disperso en todo el sector.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.