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Author: Kolodko, Anastasia ×

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    Regression methods for stochastic control problems and their convergence analysis
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Belomestny, Denis; Kolodko, Anastasia; Schoenmakers, John G.M.
    In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particulary useful for problems with a high-dimensional state space and complex dependence structure of the underlying Markov process with respect to some control. The main idea behind the algorithms is to simulate a set of trajectories under some reference measure and to use the Bellman principle combined with fast methods for approximating conditional expectations and functional optimization. Theoretical properties of the presented algorithms are investigated and the convergence to the optimal solution is proved under mild assumptions. Finally, we present numerical results for the problem of pricing a high-dimensional Bermudan basket option under transaction costs in a financial market with a large investor.
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    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.
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    Pricing CMS spreads in the Libor market model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Belomestny, Denis; Kolodko, Anastasia; Schoenmakers, John
    We present two approximation methods for pricing of CMS spread options in Libor market models. Both approaches are based on approximating the underlying swap rates with lognormal processes under suitable measures. The first method is derived straightforwardly from the Libor market model. The second one uses a convexity adjustment technique under a linear swap model assumption. A numerical study demonstrates that both methods provide satisfactory approximations of spread option prices and can be used for calibration of a Libor market model to the CMS spread option market.