Valuation of bitcoin options

Abstract

We propose an equilibrium valuation model for bitcoin options by extending Cao. Bitcoin is interpreted as a foreign currency in a small open economy where money supply and aggregate dividend are exogenous. The equilibrium bitcoin prices increase with diffusive and jump risks of these two exogenous factors. Analytical option pricing formulas are obtained with Merton's model as a special case. Static analysis reveals that a bitcoin call (put) option value increases (decreases) with the money supply growth rate. Numerical analysis shows that all risks lead to a positive premium in option prices relative to the Black–Scholes model.

Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging

“…In addition, Dowd and Hutchinson [11] draw a very drastic conclusion: "Bitcoin will bite the dust". Furthermore, the preliminary findings of current works (e.g., Ardia et al [12], Fang et al [13], Bouri et al [14], Bouri and Gupta [15], and Cao and Celik [16]), argue that the heightened volatility of Bitcoin prices is likely to be driven by the uncertainty macroeconomics, e.g., the US-China trade war and the COVID-19 pandemic outbreak. Recently, a few studies have been devoted to combining the Bitcoin literature with that on option pricing to construct Bitcoin option pricing models with dynamic jumps.…”

“…whose price follows the process given in Equation (16). For the simulations, we used the following model parameters: cost-of-carry (b) = 5%, the riskless interest rate r = 0.02, option's time to maturity (τ) = 1, 3, or 6 months(M), and nonzero value of the mean jump size or expected jump size 𝑘 = −0.05.…”

Predicting the Price of Bitcoin, Dogecoin and Ethereum by Machine Learning

“…The two things indicated that the blockchain is just one step away. Finney improved Pow mechanism to full coverage of subsequent transport mechanisms [3]. At this time, all the theories and preparation for blockchain have done.…”

Crypto quanto and inverse options

“…(2020) propose the use of a stochastic volatility correlated jump (SVCJ) model to price bitcoin options. Cao and Celik (2021) suppose that the bitcoin price is a function of domestic money supply and S&P500 returns and value bitcoin options within this equilibrium model. Alexander et al.…”

“…Siu and Elliott (2021), Jalan et al (2021), and Chen and Huang (2021) all study the empirical application of various pricing models and Hou et al (2020) propose the use of a stochastic volatility correlated jump (SVCJ) model to price bitcoin options. Cao and Celik (2021) suppose that the bitcoin price is a function of domestic money supply and S&P500 returns and value bitcoin options within this equilibrium model. Alexander et al (2022) examine the behavior of implied volatility smiles of bitcoin options to infer whether demand pressures on market makers are motivated by directional or volatility traders.…”