Recovering risk aversion from Bitcoin option prices and realized returns

ABSTRACT

This study recovers the Bitcoin option-implied risk aversion by jointly estimating a cross-sectional dataset of option prices and time-series data of realized returns on underlying asset prices. The empirical analysis of Bitcoin options on Deribit shows that the risk aversion function exhibits a peak shape, with the level of implied risk aversion of Bitcoin options ranging from $-0.2$ to 0.05, which is significantly lower than that of the traditional options market; furthermore, maturity affects the level of option-implied risk aversion, with shorter maturity implying higher risk-aversion levels. Moreover, our research indicates that after halving of Bitcoin, investors’ risk aversion function becomes higher and steeper than before.

KEYWORDS:

• Bitcoin option
• risk aversion
• risk-neutral density
• subjective density

JEL CLASSIFICATION:

• G40
• G15
• G20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ SABR interpolation is a four-parameter stochastic volatility model that interpolates the implied volatility surface using the parameters $\mathit{\alpha },\mathit{\beta },\mathit{\rho },\mathit{\mu }$. SABR interpolation completes the interpolation of the available data in a two-step process. In the first step, the location parameters $\mathit{\mu }$ of the SABR model are calibrated by minimizing the difference between the market data and the SABR model. In the second step, the existing data are interpolated using the calibrated optimal parameters.

² Monte Carlo relies on repeated random sampling to obtain numerical results. The steps are: input variables, generate random input values, and perform deterministic calculations for each set of inputs. This process is repeated many times to produce numerous possible outcomes. The results are analysed statistically to obtain the paths of the probability density.

³ Maturities 4 to 10 are treated as 7 days, 11 to 17 as 14 days, 18 to 24 as 21 days, and 27 to 33 as 30 days.

Additional information

Funding

This work was supported by the Research Enhancement Program for Young Teachers of Northwest Normal University under Grant [NWNU-SKQN2023-29]; Gansu Provincial Philosophy and Social Science Planning Program under Grant [2023QN006].