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...

We propose a variance reduction method for Monte Carlo computation of option prices in the context of stochastic volatility. This method is based on importance sampling using an approximation of the option price obtained by a fast mean-reversion expansion introduced in Fouque et al (2000...

We present variance reduction methods for Monte Carlo simulations to evaluate European and Asian options in the context of multiscale stochastic volatility models. European option price approximations, obtained from singular and regular perturbation analysis [Fouque J P, Papanicolaou G, Sircar R...

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...

In this paper, we generalize the recently developed dimension reduction technique of Vecer for pricing arithmetic average Asian options. The assumption of constant volatility in Vecer's method will be relaxed to the case that volatility is randomly fluctuating and is driven by a mean-reverting...