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End date: 2009 × Start date: 2000 × Has files: Yes × Type: Text × Subject: American options ×

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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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    Fixed domain transformations and split-step finite difference schemes for nonlinear black-scholes equations for American options
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Ankudinova, Julia; Ehrhardt, Matthias
    Due to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical Black-Scholes model become unrealistic and the model results in strongly or fully nonlinear, possibly degenerate, parabolic diffusion-convection equations, where the stock price, volatility, trend and option price may depend on the time, the stock price or the option price itself. In this chapter we will be concerned with several models from the most relevant class of nonlinear Black-Scholes equations for American options with a volatility depending on different factors, such as the stock price, the time, the option price and its derivatives. We will analytically approach the option price by following the ideas proposed by evcovic and transforming the free boundary problem into a fully nonlinear nonlocal parabolic equation defined on a fixed, but unbounded domain. Finally, we will present the results of a split-step finite difference schemes for various volatility models including the Leland model, the Barles and Soner model and the Risk adjusted pricing methodology model.