This article discusses the valuation and hedging of volatility swaps within the frame of a GARCH (1,1) stochastic volatility model. First we use a general and flexible partial differential equation (PDE) approach to determine the first two moments of the realized variance in a continuous or...

We derive a partial integro differential equation (PIDE) which relates the price of a calendar spread to the prices of butterfly spreads and the functions describing the evolution of the process. These evolution functions are the forward local variance rate and a new concept called the forward...

In this article we present an introduction to various Filtering algorithms and some of their applications to the world of Quantitative Finance. We shall first mention the fundamental case of Gaussian noises where we obtain the well-known Kalman Filter. Because of common nonlinearities, we will...

In this article we present an introduction to various Filtering algorithms and some of their applications to the world of Quantitative Finance. We shall first mention the fundamental case of Gaussian noises where we obtain the well-known Kalman Filter. Because of common nonlinearities, we will...

Cover -- Title Page -- Copyright -- Contents -- Foreword -- Acknowledgments (Second Edition) -- Acknowledgments (First Edition) -- Introduction (Second Edition) -- Introduction (First Edition) -- Summary -- Contributions and Further Research -- Data and Programs -- Chapter 1 The Volatility...