Building upon the ideas introduced in their previous book, Derivatives in Financial Markets
with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives …

If a GARCH model is estimated on a time series that contains parameter changes in the
conditional volatility process and these parameter changes are not accounted for, a distinct …

In this paper we propose to use a combination of regular and singular perturbations to
analyze parabolic PDEs that arise in the context of pricing options when the volatility is a …

In this paper we propose a flexible model to describe nonlinearities and long-range
dependence in time series dynamics. The new model is a multiple regime smooth transition …

We study the problem of parameter estimation for time-series possessing two, widely
separated, characteristic time scales. The aim is to understand situations where it is …

S&P 500 index data sampled at one-minute intervals over the course of 11.5 years (January
1989–May 2000) is analyzed, and in particular the Hurst parameter over segments of …

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 …

This paper studies the effect of introducing stochastic volatility in the first‐passage structural
approach to default risk. The impact of volatility time scales on the yield spread curve is …

This paper is a contribution to the valuation of derivative securities in a stochastic volatility
framework, which is a central problem in financial mathematics. The derivatives to be priced …

The skew effect in market implied volatility can be reproduced by option pricing theory based
on stochastic volatility models for the price of the underlying asset. Here we study the …