Abstract
In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price. In addition, in our study of the Bitcoin option pricing, we find that the inclusion of jumps in returns and volatilities are significant in the historical time series of Bitcoin prices. The benefits of incorporating these jumps flow over into option pricing, as well as adequately capture the volatility smile in option prices. To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”. Crucially, using hedging options for the Bitcoin market, we also prove some important properties: Bitcoin options follow a convex, but not strictly convex function. This property provides adequate risk assessment for convex risk measure.
Highlights
In this paper, we conduct a fast calibration in the jump-diffusion model to capture the Bitcoin price dynamics, as well as the behavior of some components affecting the price itself, such as the risk of pitfalls and its ambiguous effect on the evolution of Bitcoin’s price
To the best of our knowledge, this is the first work to analyze the phenomenon of price jump risk and to interpret Bitcoin option valuation as “exceptionally ambiguous”
Bitcoin is notoriously volatile and has seen multiple booms and crashes. These peaks are in line with price bubbles, and the current Bitcoin market is comparable to the internet bubble of the late 1990s
Summary
Jump effect of Bitcoin price revaluation on Bitcoin/USD exchange rate, huge jump starting from Q3/2017. We focus on theoretical properties suggested model; choice thethe most suitable model parameters among thethe ones proposed in the literature is made in for most suitable model parameters among ones proposed in the literature is made view of market data considering historical volatility and jumps (e.g., Hilliard et al [20]). It is worth noting that a market for these contingent claims has recently appeared in the literature, such as Kapetanios, Neumann, and Skiadopoulos [21] and Qiao et al.Qiao [22].et al. Our study makes the following contributions: From a theoretical viewpoint, it con[22]. ElaboSecond, we conduct investigation of hedging strategies with jump-diffusion perfect replicarate on how Bitcoins an canin-depth be captured using a fast calibration in the Bates tion of a contingent claim.
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