We consider calibration of log-normal stochastic volatility model and computation of option delta consistently with … statistical dynamics of the asset price and its implied volatility surface. We introduce the concept of volatility skew-beta which … any dynamics of implied volatility under the statistical measure and reproduce empirical option delta. The calibrated …

The interaction between the volatility and price dynamics is explored. We model stochastic asset prices using the asset … flow model with randomness arising directly from supply and demand. We show that the volatility is smallest at the extrema … system. The computations and analytical results presented here demonstrate that volatility increases when traders place …

volatility and its curve resembles a smile, meaning that the introduction of jumps is quantified via a smile according to implied … volatility. In order to derive such an implied volatility smile, an iterative search procedure referred to as the Newton …-Raphson algorithm is proposed. Numerical experiments of both the in-house pricing formula and its implied volatility recursive algorithm …

We introduce the beta stochastic volatility model and discuss empirical features of this model and its calibration … steeper forward skews, compared to traditional stochastic volatility models …

We employ a refined tree method to value employee stock options (ESOs) in the stochastic volatility model of Heston … valuation, personal market beliefs and stochastic volatility. We formulate theoretical results on ESO valuation independently of …

We first discuss the positive volatility skew observed in the implied volatilities of VIX options. To model this … volatility. Then we develop a robust method for unified pricing and hedging of different volatility products on the implied and …