In this paper, we deal with the pricing of power options when the dynamics of the risky underling asset follows the double stochastic volatility with double jump model. We prove efficiency of our considered model by fast Fourier transform method, Monte Carlo simulation and numerical results using power call options i.e. Monte Carlo simulation and numerical results show that the fast Fourier tra...

We consider European options pricing with double jumps and stochastic volatility. We derived closed-form solutions for European call options in a double exponential jump-diffusion model with stochastic volatility SVDEJD . We developed fast and accurate numerical solutions by using fast Fourier transform FFT technique. We compared the density of our model with those of other models, including th...

Extreme value theory for a class of stochastic volatility models, in which the logarithm of the conditional variance follows a Gaussian linear process, is developed. A result for the asymptotic tail behavior of the transformed stochastic volatility process is established and used to prove that the suitably normalized extremes converge in distribution to the double exponential (Gumbel) distribut...

This paper addresses alternative option pricing models and their estimation. The stock price dynamics is modeled by taking into account both stochastic volatility and jumps. Jumps are mimiced by the tempered stable process and stochastic volatility is introduced by time changing the stochastic process. We propose a characteristic function based iterative estimation method, which overcomes the p...

This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach. First, the paper derives an asymptotic expansion for generalized Wiener functionals. After it is appl...

This paper introduces a spatial framework for high-frequency returns and a faster double-conditional smoothing algorithm to carry out bivariate kernel estimation of the volatility surface. A spatial multiplicative component GARCH with random effects is proposed to deal with multiplicative random effects found from the data. It is shown that the probabilistic properties of the stochastic part an...

Imposing a symmetry condition on returns, Carr and Lee [2009] show that (double) barrier derivatives can be replicated by a portfolio of European options and can thus be priced using fast Fourier techniques (FFT). We show that prices of barrier derivatives in stochastic volatility models can alternatively be represented by rapidly converging series, putting forward an idea by Hieber and Scherer...

This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility of volatility can be defined both non–parametrically, where we link it to the quadratic variation of the sto...