) index call and put options with different volatility forecasting approaches. Since the volatility is the key parameter in … pricing options, GARCH (Generalized Autoregressive Conditional Heteroskedasticity), implied volatility, historical volatility …, and implied volatility index (VBI) are used to determine the best volatility approach for pricing options according to …

The valuation of options and many other derivative instruments requires an estimation of exante or forward looking … volatility. This paper adopts a Bayesian approach to estimate stock price volatility. We find evidence that overall Bayesian … volatility estimates more closely approximate the implied volatility of stocks derived from traded call and put options prices …

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 …

We revisit the so-called Bergomi-Guyon expansion (Bergomi and Guyon, Stochastic volatility's orderly smiles, Risk, May … 2012). The expansion provides the smile of implied volatility at second order in the volatility of volatility for general … stochastic volatility models, including variance curve models. First, we present a new derivation of the price expansion which …