Evaluation of bitcoin options with interest rate risk and systemic risk

Pao-Peng Hsu () and Chiang-Hui Wang ()

Journal of Asian Scientific Research, 2024, vol. 14, issue 3, 360-373

Abstract: 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.

Keywords: Bitcoin option; Co-Jump; Correlated bivariate jump-diffusion model; HJM model; Option pricing; Systematic jump risk. (search for similar items in EconPapers)
Date: 2024
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