We consider a tractable affine stochastic volatility model that generalizes the seminal Heston (1993) model by … variance, and we examine the impact of the distribution of jumps on the associated implied volatility smile. We provide … sufficient conditions for the asymptotic behavior of the implied volatility of variance for small and large strikes. In …

of stochastic volatility (Heston model) has been introduced in our publications “Complete Analytical Solution of the … model for Stochastic Volatility (SV). Our discovery of the probability density function of the European style Asian Options … constant volatility.All numerical evaluations based on our analytical results are practically instantaneous and absolutely …

volatility (Heston model), enabling complete analytical resolution of all problems associated with American Style Options … volatility (Heston model) is expressive enough to enable derivation for the first time ever of corollary closed-form analytical … constant or stochastic volatility, will be below or above any set of thresholds at termination. Such assessments are absolutely …

In this paper we investigate the asymptotics of forward-start options and the forward implied volatility smile in the …

We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility … smile in a large class of models, including the Heston stochastic volatility and time-changed exponential Levy models … particular) many results for the spot implied volatility smile.In passing we (i) show that the forward-start date has to be …

known announcements can produce significant distortions in option volatility surfaces. This presents a challenge, or …, frowns and W-shapes. Furthermore, we demonstrate the model's calibration to the observed volatility surface leading up to the … volatility interpolation. Finally, we discuss how the jump probabilities are becoming increasingly observable via alternative …

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 …

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 …