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DDC: 510 × Subject: Monte Carlo method ×

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    Regression methods in pricing American and Bermudan options using consumption processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Belomestny, Denis; Milstein, Grigor N.; Spokoiny, Vladimir
    Here we develop methods for efficient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying sample space with payoffs at the optimal stopping times, we propose sequential estimates for continuation values, values of the consumption process, and stopping times on the sample paths. The approach admits constructing both low and upper bounds for the price by Monte Carlo simulations. The methods are illustrated by pricing Bermudan swaptions and snowballs in the Libor market model.
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    Deviational particle Monte Carlo for the Boltzmann equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Wagner, Wolfgang
    The paper describes the deviational particle Monte Carlo method for the Boltzmann equation. The approach is an application of the general ``control variates'' variance reduction technique to the problem of solving a nonlinear equation. The deviation of the solution from a reference Maxwellian is approximated by a system of positive and negative particles. Previous results from the literature are modified and extended. New algorithms are proposed that cover the nonlinear Boltzmann equation (instead of a linearized version) with a general interaction model (instead of hard spheres). The algorithms are obtained as procedures for generating trajectories of Markov jump processes. This provides the framework for deriving the limiting equations, when the number of particles tends to infinity. These equations reflect the influence of various numerical approximation parameters. Detailed simulation schemes are provided for the variable hard sphere interaction model.