Numerous empirical proofs indicate the adequacy of the time discrete auto-regressive stochastic volatility models introduced by Taylor in the description of the log-returns of financial assets. The pricing and hedging of contingent products that use these models for their underlying assets is a...

We apply a quadratic hedging scheme developed by Foellmer, Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated...

We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan's (1995) delta...

The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of the VEC family, the number of parameters involved in the...

We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point...

We provide a general and flexible approach to LIBOR modeling based on the class of affine factor processes. Our approach respects the basic economic requirement that LIBOR rates are non-negative, and the basic requirement from mathematical finance that LIBOR rates are analytically tractable...

In mathematical Finance calculating the Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for finite-dimensional It\^{o}-diffusions. The existence of Malliavin weights relies on absolute continuity of laws of the projected diffusion process and a sufficiently...

Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as empirical aspects of the affine model class. Starting...

We present an arbitrage-free non-parametric yield curve prediction model which takes the full (discretized) yield curve as state variable. We believe that absence of arbitrage is an important model feature in case of highly correlated data, as it is the case for interest rates. Furthermore, the...

We introduce efficient numerical methods for generic HJM equations of interest rate theory by means of high-order weak approximation schemes. These schemes allow for QMC implementations due to the relatively low dimensional integration space. The complexity of the resulting algorithm is...