Author(s)

Ndeye Fatou Sene¹, Mamadou Abdoulaye Konte², Jane Aduda³

¹Department of Mathematics, Pan African University Institute of Basic Sciences, Technology and Innovation, Nairobi, Kenya.
²Department of Economics, L.A.R.E.S, Gaston Berger University, Saint-Louis, Senegal.
³Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.

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.

Bitcoin, Double Exponential Jump-Diffusion, Stochastic Volatility, Markov Chain Monte Carlo

Sene, N. , Konte, M. and Aduda, J. (2021) Pricing Bitcoin under Double Exponential Jump-Diffusion Model with Asymmetric Jumps Stochastic Volatility. Journal of Mathematical Finance, 11, 313-330. doi: 10.4236/jmf.2021.112018.