Estimation of Implied Volatility for Ethereum Options Using Numerical Approximation Methods

Abstract

This study demonstrates the use of numerical approximation techniques like Newton-Raphson Method, Bisection Method, Brent Method, and Secant Method to estimate the market implied volatility for short-dated Ethereum options with 21-day maturity, obtained from Deribit Crypto Options and Futures Exchange. The numerical approximation techniques are compared based on their convergence and time taken for execution. It is found that Newton-Raphson Method converges faster and performs computation in the least time in comparison to the other methods under consideration. This study further focuses on the determination of implied volatility structure for short maturity Ethereum options. The results show that the implied volatility assumes a deep smile far from the day of expiry and as we approach the expiry date, the volatility smile broadens. To the best of our knowledge, this is the first work to use approximation techniques to estimate the implied volatility for Ethereum options. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.