Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of European and path-dependent options in a fast mean-reverting stochastic volatility setting. Our method is shown to be equivalent to those developed...

Using tools from spectral analysis, singular and regular perturbation theory, we develop a systematic method for analytically computing the approximate price of a derivative-asset. The payoff of the derivative-asset may be path-dependent. Additionally, the process underlying the derivative may...

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility models and, using spectral theory and singular perturbation techniques, we derive an approximation for the prices of European options in this setting. Three examples of random time-changes are provided and...

We introduce a class of local stochastic volatility models. Within our framework, we obtain an expression for both (i) the price of any European option and (ii) the induced implied volatility smile. To illustrate our method, we perform specific computations for a CEV-like model

We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential Lévy-type models.Both the volatility and jump-intensity of the Lévy process vary stochastically in time through a common driving factor. We provide an explicit formula for...

We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Lévy measure. Generalizing and extending the novel...