Evaluation of bitcoin options with interest rate risk and systemic risk
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Bitcoin option, Co-Jump, Correlated bivariate jump-diffusion model, HJM model, Option pricing, Systematic jump risk.

How to Cite

Hsu, P.-P. ., & Wang, C.-H. . (2024). Evaluation of bitcoin options with interest rate risk and systemic risk. Journal of Asian Scientific Research, 14(3), 360–373. https://doi.org/10.55493/5003.v14i3.5090


This study introduces closed-form formulas for valuing European call options, assuming that Bitcoin follows a compound Poisson process. Additionally, instantaneous forward interest rates are considered in the Heath-Jarrow-Morton model, which includes a jump component. To address the impacts of systematic risk on Bitcoin price and interest rate, we model two stochastic processes using a correlated bivariate jump-diffusion model to capture individual jumps and systematic co-jumps. This study provides analytic formulas for pricing Bitcoin call options and zero-coupon bonds under the correlated jump-diffusion Heath-Jarrow-Morton model. Numerical analysis shows how co-jump intensity affects the prices of both zero-coupon bonds and Bitcoin call options. We specifically look at how these prices change in response to co-jump intensity across three different instantaneous forward rate term structures. The findings show that the prices of Bitcoin call options are contingent on the term structure types of zero-coupon bonds. In addition, the interaction of co-jump intensity and types of term structure also affects Bitcoin option prices. The practical significance of this study is to provide a comprehensive model to evaluate Bitcoin call options and enhance risk management strategies in the Bitcoin market when the Bitcoin market encounters changes in monetary policy or changes in macroeconomic conditions.

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