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 … compared to historical volatility estimates sourced from IVolatility.com (“IVolatility”). Our evidence suggests use of the …

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 …

three market regimes. A consistent parametric framework of stochastic volatility is used. All empirical market utility …

, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility … known as "volatility smile". They provide a discrete approximation to the continuous risk neutral process for the underlying … Barle and Cakici (BC). After the formation of IBT we can estimate the implied local volatility and the state price density …

We develop a discrete-time stochastic volatility option pricing model, which exploits the information contained in high …-frequency data. The Realized Volatility (RV) is used as a proxy of the unobservable log-returns volatility. We model its dynamics by … competing time-varying (i.e. GARCH-type) and stochastic volatility pricing models. The pricing improvement can be ascribed to …

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks … traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a …-form and structural models of stochastic volatility …

Many studies have documented that daily realized volatility estimates based on intraday returns provide volatility … that use daily returns as well as realized volatility. We derive convenient closed-form option valuation formulas and we … assess the option valuation properties using S&P500 return and option data. We find that realized volatility reduces the …