underlying, their exposure to volatility risk, and their time decay. Our contribution to the literature is twofold: First, we … volatility according to Heston (1993). Within this setting, the portfolio returns are explained by the market and an additional … option factor, i.e., a portfolio of standard options exposed to volatility risk. We show that (i) any option factor is …

along with the specification of (a) the initial density, and (b) the volatility structure of the density. The volatility …

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 …

, and the corresponding implied volatility surfaces have been analyzed in some detail. In the non-asymptotic regimes, option … trivially expressed in terms of their implied volatility. Recently, attempts at calculating the asymptotic limits of the implied … volatility have yielded several expressions for the short-time, long-time, and wing asymptotics. In order to study the volatility …

We study here the large-time behavior of all continuous affine stochastic volatility models (in the sense of Keller …-Ressel) and deduce a closed-form formula for the large-maturity implied volatility smile. Based on refinements of the Gartner … condition assumed in Gatheral & Jacquier (GJ10) under which the Heston implied volatility converges to the SVI parameterization …

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate … the ever-increasing ow of option price information into the well-accepted local volatility model of Dupire. This leads to … considering both the local volatility surfaces and their corresponding prices as indexed by the observed underlying stock price as …

We introduce a closed form approximation for the implied volatility of ATM-forward options. The relative error of this …, having relative error less than 10−6 for all options with integrated volatility less than 1.9, such as options with maturity … less than three years and implied volatility less than 100%. Moreover, the approximate implied volatilities fall within the …

stochastic volatility model. This provides an efficient way of calculating the fair value of the strike for variance swaps. In …