Cryptocurrency price, especially Bitcoin (BTC), which has a new digital asset class, have attracted extraordinary attention around the world. Symptoms of CC / BTC include high level of ulation, extreme volatility and price breakdown. We propose a pricing mechanism based on random volatility with the correlated jump (SVCJ) model and compare it to the flexible cozump model by Bundy and Rene (2016). Estimated results from both models confirm the effect of jumps and cozumps on the options obtained by simulation and analyze the suggested instability curve. We show that a large part of price fluctuations are significant and contrasts with jumping into contemporaneity instability. Our study includes leading research on price BTC options. We will show how the proposed pricing policy emphasizes the importance of jumps in CC markets.
Cryptocurrency price (BTC), the network-based decentralized digital currency and payment system, has garnered worldwide attention and interest since it was first introduced in 2009. The rapidly growing research related to BTC shows a prominent role in this new digital asset class in contemporary financial markets.1 Several studies have suggested econometric methods to model the dynamics of BTC prices, including cross-sectional regression models involving the major traded cryptocurrencies (CCs) and also multivariate time series models.2Scaillet, Treccani, and Trevisan (2020) show that jumps are much more frequent in the BTC market than, for example, in the U.S. equity market (see, e.g., Eraker, 2004; Bajgrowicz, Scaillet, and Treccani, 2015; Bandi and Renò, 2016 among others). These earlier studies suggest that jumps should be considered when modeling BTC prices.
However, research on the BTC derivative markets is still limited despite the rapidly growing availability of BTC futures and options traded on an unregulated exchange platform (i.e., Deribit). Especially, the Chicago Mercantile Exchange (CME) Group, the world’s leading derivatives marketplace, launched BTC futures based on the CME CF BTC Reference Rate (BRR) on December 18, 2017. Limited research on the price and hedging of BTC derivatives has been somewhat attributed to the fact that the market for BTC derivatives (e.g., options) is unregulated, providing econometric challenges from the extraordinary occurrence of jumpers. Absence and most ula attendance is driven. This calls for a more flexible model for capturing abrupt jumps in return and variation processes.
stochastic and econometric properties
In this article cryptocurrency price, we contribute to the existing literature by exploring the stochastic and econometric properties of BTC. Dynamics and then pricing. The BTC options based on these properties. That is, the stochastic volatility with a correlated jump (SVCJ) model of Duffie, Pan, and Singleton (2000). And the SV with the possible nonlinearity structure of Bandi and Renò (2016)(BR hereafter). The employed SVCJ model incorporates jumps in both returns and the SV process. While the BR model captures the possible nonlinearity of return and variance processes and characterizes a nonaffine structure. We aim to provide a theoretical foundation for the future development of derivative markets on CCs.
Numerous empirical studies have applied the SVCJ model in different markets. For example, Eraker, Johannes, and Polson (2003) and Eraker (2004) use the SVCJ model to describe equity market returns and estimate equity option pricing. They find strong evidence of jumps in returns and volatility in the U.S. equity market. We further compare the SVCJ estimates to the simplified versions such as Bates (2000; SVJ hereafter) and the SV model.
For the purpose of robustness check, we compare our results with those from the BR model. Bandi and Renò (2016) propose a price and variance cojump model that generalizes the SVCJ model to capture. The possible nonlinearity in the parameters of the returns and variance processes. The BR model characterizes independent and correlated jumps. And allows for a nonparametric parameter structure, and estimates the parameters by using high-frequency data. We also apply this model to the dynamics of BTC.
SVCJ and BR models
First, as in the existing literature, the results from the SVCJ and BR models indicate that jumps are present in the returns. And variance processes and adding jumps to the returns and volatility improves the goodness of fit. Second, in contrast to existing studies that commonly report a negative leverage effect, we find that the correlation between the return and volatility is significantly positive in the SVCJ model. However, we cannot find significant negative relations between risk and return in the BR model. This implies that a rise of price is not associated with a decrease in volatility, which is consistent with the “inverse leverage effect” found in the commodity markets (Schwartz and Trolled, 2009).
Third, we find that the jump size in the return and variance of BTC is anticorrelated. The parameter estimates of the jump size (ρj) from both the SVCJ and BR models are negative (though the SVCJ estimate is insignificant). It is worth noting that the correlation between the price jump size and the volatility jump size turns out to be significant with a negative coefficient with high-frequency data, while tending to be insignificant for the SVCJ fitting using daily prices.
In Cryptocurrency price This finding is in line with existing studies of the stock market from Eraker (2004). Duffie, Pan, and Singleton (2000), and Bandi and Renò (2016), among others. For example, Bandi and Renò (2016) report an anticorrelation with the nonaffine structure. Aaker (2004) finds a negative correlation between jump size. When augmenting return data with opt data and a negative correlation between the size of the comp. Identified in latent instability (IV) memory. Using high-frequency frequency data, Jokod and Todorov (2009) and Todorov and Tuchen (2010) also report strong opposition to large jump size prices and volatility.
1 BTC Dynamic
We will briefly launch BTC. In 2009, BTC launched its first open-source distribution CC, nicknamed Satoshi Nakamoto by the developer in “Bitcoin: Peer-to-Peer Electronic Cash System”. It is a digital, decentralized, partly benami currency that is not supported by any government or other legal entity. The system has a pre-programmed supply of money that increases at a declining rate until it reaches a certain level. Since everything is based on open source, design and control are open to everyone.
Cryptocurrency price, our empirical analysis is based on daily end (SVCJ model) prices and five minute intraday (BR model) prices. Data will be from 1 August 2014 to 29 September 2017 and will be collected from Bloomberg. The dynamics of BTC daily prices (left panel) and BTC Returns (right panel) are described in Figure 1. This indicates that BTC returns are clearly jumping more often than stock returns or that scattered volatility is more volatile than bikes. BTC prices remained stable for most of 2015. In the first four months of 2016, the BTC price was in the range of 400-60 USD. It has risen dramatically since 2016 and rose to around 5000 USD by the end of our sample period in 2017. At the time of writing, BTC has a market capitalization of over $ 7 billion (Source: Coinmarketcap 2017).
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