Abstract
The objective of this study is, to show the importance of incorporating jumps in both returns and volatility dynamics for Bitcoin. For that purpose, we introduce the Double Exponential Jump-Diffusion model with Stochastic Volatility (DEJDSVJ) that contains asymmetric jumps. The use of the Markov Chain Monte Carlo methods for estimation has proved the meaningful presence of jumps in Bitcoin price and volatility. Moreover, based on the Bitcoin options market, a comparison between the underlying model, the Double Exponential Jump Diffusion model (DEJD) with Stochastic Volatility (no Jumps) and the Stochastic Volatility (SV) shows the goodness of the DEJDSVJ model’s calibration over others for pricing Bitcoin options.
Highlights
Bitcoin is a digital currency that satisfies the technical properties of money
Few studies are done about bitcoin options pricing, we find many relevant considerations in some articles. [9] proposed an option pricing model under double exponential jump diffusion with mean reverting stochastic volatility and stochastic interest rate
Some investors defend the importance of using Bitcoin, there are a lot of critics about it supported by governments and banks that do not trust the digital currency
Summary
Bitcoin is a digital currency that satisfies the technical properties of money. There is no central authority acting as a bank for Bitcoin. Its system is based on solving computational algorithms (cryptographic puzzles) known as mining process through a network called blockchain whose protocol was released by a pseudonymous Satoshi Nakamoto on 2009 [1]. Since it was generated, the price of bitcoin in USD dollar varies over time. The price of bitcoin in USD dollar varies over time This last decade, the fluctuations of Bitcoin’s price raised a lot of attention for investors.
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