This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many … researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although … the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes …

to study the implied volatility smirk in Lévy markets. The dumping factor depends on a parameter beta, this results in a … volatility curves. Our main result shows a particular monotonicity behavior of the implied volatility of skewed models around the …

Chicago Board Options Exchange (CBOE) volatility index (VIX) options. Our methodology is analytically tractable and yet … modeling the stochastic co-volatility factor can significantly improve the in-sample fitting results due to the improved …

general local-stochastic volatility model with zero correlation. We do this using the Freidlin-Wentzell theory of large …-time asymptotic behaviour for call options using Holder's inequality, and the implied volatility. This avoids the use of possibly non …, which is analysed at length in Busca et al. We also derive a series expansion for the implied volatility in the small …

then apply a similar analysis to a time-dependent Heston stochastic volatility model, and we show to construct a time …-dependent mean reversion and volatility-of-variance function, so as to be consistent with the observed variance swap curve and a pre … second moments of the integrated variance, and derive an approximation for the price of a volatility swap under the time …

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 …

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 …

In this paper, European put option pricing with stochastic volatility forecasted by well known GARCH model is discussed …