In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in … implied volatility function. The proof is based on saddlepoint methods and classical properties of holomorphic functions …

volatility model, by developing efficient transform based pricing methods. This non-affine model gives prices of options on … realized variance which allow upward sloping implied volatility of variance smiles. Heston's (1993) model, the benchmark affine … stochastic volatility model, leads to downward sloping volatility of variance smiles - in disagreement with variance markets in …

approximation including the case where the local volatility is (or is close to) Gaussian. Secondly, we construct a control variate …

In this paper, we solve the problem of solution of stochastic volatility models in which the volatility diffusion can … volatility variable along the PDE grid. Using this technique, we find the conditional expected values of moments of log of … volatility (or any other SDE) at any node on the PDE grid using just one dimensional PDE if we can describe its one step …

, 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 …

satisfied on Equity markets (because the correlation is generally negative), it does not hold for FX-related derivatives …

between stock returns and idiosyncratic return volatility at the firm level. By allowing for the volatility of the underlying … idiosyncratic choice variables to exhibit independent switches between a high and low volatility regime, we show that the options …' constant expected returns are composed of (i) a state dependent drift term that relates positively with the volatility regime …

We develop an asymptotic expansion technique for pricing timer options under general stochastic volatility models … around small volatility of variance. Closed-form approximation formulas have been obtained for the Heston model and the 3 …

We introduce a stochastic volatility model with self-exciting jump intensity to capture the change in pricing dynamic …