Abstract
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 Ren\`o (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.
Highlights
Bitcoin (BTC), the network-based decentralized digital currency and payment system, has garnered worldwide attention and interest since it was first introduced in 2009
We propose a pricing mechanism based on a stochastic volatility with a correlated jump (SVCJ) model and compare it to a flexible cojump model by Bandi and Reno (2016)
We find that the standard set of stationary models, such as autoregressive integrated moving average(ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH), cannot fit the BTC returns well due to the presence of jumps
Summary
BTC was the first open-source distributed CC released in 2009, after it was introduced in a paper “Bitcoin: A Peer-to-Peer Electronic Cash System” by a developer under the pseudonym Satoshi Nakamoto. It is a digital, decentralized, partially anonymous currency, not backed by any government or other legal entity. At the time of the writing of this article, the BTC market capitalization is more than USD 7 billion (source: Coinmarketcap 2017) Both the BTC prices and returns react to big events in the BTC market. We find that the standard set of stationary models, such as autoregressive integrated moving average(ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH), cannot fit the BTC returns well due to the presence of jumps
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