The Black-Scholes framework implies a constant volatility across term and strike, and a lognormal distribution for … and apply a model-independent, historically-consistent method for estimating the ‘fair' volatility surface of an asset … characteristics investors should be concerned with; (2) A review of historic SA index volatility skews and term structure, their …

volatility process spends longer time in regime 2 than it stays in regime 1. The predicted call option prices from both models …

We use machine learning methods to predict stock return volatility. Our out-of-sample prediction of realised volatility … realised volatility of 43.8% with an R2 being as high as double the ones reported in the literature. We further show that … machine learning methods can capture the stylized facts about volatility without relying on any assumption about the …