Abstract
The recently developed Bitcoin futures and options contracts in cryptocurrency derivatives exchanges mark the beginning of a new era in Bitcoin price risk hedging. The need for these tools dates back to the market crash of 1987, when investors needed better ways to protect their portfolios through option insurance. These tools provide greater flexibility to trade and hedge volatile swings in Bitcoin prices effectively. The violation of constant volatility and the log-normality assumption of the Black–Scholes option pricing model led to the discovery of the volatility smile, smirk, or skew in options markets. These stylized facts; that is, the volatility smile and implied volatilities implied by the option prices, are well documented in the option literature for almost all financial markets. These are expected to be true for Bitcoin options as well. The data sets for the study are based on short-dated Bitcoin options (14-day maturity) of two time periods traded on Deribit Bitcoin Futures and Options Exchange, a Netherlands-based cryptocurrency derivative exchange. The estimated results are compared with benchmark Black–Scholes implied volatility values for accuracy and efficiency analysis. This study has two aims: (1) to provide insights into the volatility smile in Bitcoin options and (2) to estimate the implied volatility of Bitcoin options through numerical approximation techniques, specifically the Newton Raphson and Bisection methods. The experimental results show that Bitcoin options belong to the commodity class of assets based on the presence of a volatility forward skew in Bitcoin option data. Moreover, the Newton Raphson and Bisection methods are effective in estimating the implied volatility of Bitcoin options. However, the Newton Raphson forecasting technique converges faster than does the Bisection method.
Highlights
The emergence of Bitcoin futures and options contracts as cryptocurrencies develop received considerable attention recently
The results show that the newton Raphson and Bisection numerical estimation techniques are effective in estimating the implied volatility of Bitcoin options
The mean convergence count (MCC) is much lower for the Newton Raphson method estimation technique than for the Bisection estimation technique. These findings suggest that the Newton Raphson method is efficient for convergence to the desired solution compared to Bisection method for the two data sets studied here
Summary
The emergence of Bitcoin futures and options contracts as cryptocurrencies develop received considerable attention recently. The present study attempts to contribute to the growing literature on Bitcoin options, cryptocurrency derivatives, and options pricing by exploring the stylized facts of options pricing, considering the volatility smile in the emerging Bitcoin options, traded on Deribit Bitcoin Futures and Options Exchange. These methods require a large amount of training and validation data, which makes it effective only for spreadsheet and pedagogical applications In this backdrop, Chance et al (2016) proposed numerical root-finding iterative techniques to estimate implied volatility, which few studies in the finance literature apply to solve such problems. This study attempts to estimate the implied volatility of emerging Bitcoin options traded on the Deribit Bitcoin Futures and Options Exchange by using the Newton Raphson and Bisection numerical root-finding iterative techniques. This study applies the Newton Raphson and Bisection root-finding algorithms to numerically approximate the implied volatility of Bitcoin options from the pricing error equation c(σn) − cM = 0.
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