We develop call option price approximations for both the market index and an individual asset using a singular perturbation of a continuous-time capital asset pricing model in a stochastic volatility environment. These approximations show the role played by the asset's beta parameter as a...

Multiscale stochastic volatility models have been developed as an efficient way to capture the principle effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book Fouque, Papanicolaou, Sircar and S{\o}lna (2011, CUP) analyzes models in which the...

The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the interconnectedness of the system entities and the corresponding...

In this paper, we present a new method for computing the first-order approximation of the price of derivatives on futures in the context of multiscale stochastic volatility studied in Fouque et al. (2011). It provides an alternative method to the singular perturbation technique presented in...

In this paper we propose to use Markov chain Monte Carlo methods to estimate the parameters of stochastic volatility models with several factors varying at different time scales. The originality of our approach, in contrast with classical factor models is the identification of two factors...

This paper addresses the impact of time fluctuations of a random medium on refocusing during a time-reversal experiment. Even in the presence of moderate time perturbations a coherent refocused pulse is observed. The theory predicts the level of recompression observed as well as the conditions...

Optional increasing paths passing through a given stopping point are studied. A characterization of the two extreme optional increasing paths is obtained. The past of a stopping point is defined, and a description of the largest stopping point smaller than two given stopping points is given. A...