In this paper it is proved that the Black-Scholes implied volatility satisfies a second order non-linear partial … Black-Scholes implied volatility that improves on the existing numerical schemes from literature, both in speed and … parallelizability. We also show that the method is applicable to other problems, such as approximation of implied Bachelier volatility …

of a new era in Bitcoin price risk hedging. The need for these tools dates back to the market crash of 1987, when … 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 …

This paper describes a new parametric volatility surface that is arbitrage free, extremely rich and flexible, and has … Stochastic-Volatility Inspired (SVI) surface and demonstrate the advantages of the new methodology …