Filters

2007 - 20082

More filters

20192
Reset filters

Settings

Author: Kampen, Joerg × Type: Report ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Holomorphic transforms with application to affine processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Belomestny, Denis; Kampen, Joerg; Schoenmakers, John G.M.
    In a rather general setting of Itô-Lévy processes we study a class of transforms (Fourier for example) of the state variable of a process which are holomorphic in some disc around time zero in the complex plane. We show that such transforms are related to a system of analytic vectors for the generator of the process, and we state conditions which allow for holomorphic extension of these transforms into a strip which contains the positive real axis. Based on these extensions we develop a functional series expansion of these transforms in terms of the constituents of the generator. As application, we show that for multidimensional affine Itô-Lévy processes with state dependent jump part the Fourier transform is holomorphic in a time strip under some stationarity conditions, and give log-affine series representations for the transform.
  • Thumbnail Image
    Item
    Monte Carlo Greeks for financial products via approximative Greenian Kernels
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Kampen, Joerg; Kolodko, Anastasia; Schoenmakers, John G.M.
    In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. The results are applied in the context of a Libor market model.