M. A. H. Dempster and J. P. Hutton, Fast numerical valuation of American, exotic and complex options, Applied Mathematical Finance, 4 (1997), pp. 1--20.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... methods up to into essentially two categories: direct methods, such as pivoting techniques [7] and iterative methods, such as Newton iteration [25] and interior point algorithms [22] Some of these methods which have been applied specifically to American option pricing include linear programming [9], pivoting methods, 14] and interior point methods [15] As pointed out in [15] pivoting methods (such as Lemke s algorithm [7] and LP approaches are not well equipped to handle sparse systems, especially in more than one dimension (multifactor options) Complementarity problems (both linear ....

M.A.H. Dempster and J.P. Hutton. Fast numerical valuation of American, exotic and complex options. Appl. Math. Fin., 4:1--20, 1997.

....of poor quality. Placing nodes according to features of the problem appears to be more important than obtaining positive coe#cients. Note that implicit finite di#erence methods have occasionally been used for multidimensional problems in finance (Brennan and Schwartz, 1980; Wilmott et al. 1993; Dempster and Hutton, 1997), but it has recently been demonstrated in Zvan et al. 2000) that the FVM has several advantages over finite di#erence schemes in this context. 3 Readers unfamiliar with this terminology should think of the convective term involving first order derivatives and the di#usive term involving second ....

Dempster, M. A. H. and J. P. Hutton (1997). Fast numerical valuation of American, exotic and complex options. Applied Mathematical Finance 4, 1--20.

....option pricing PDE is O # #t (#S) 2 # . Let N be the number of timesteps. If we assume that #S = O(#t) 1 N , then the number of iterations required per timestep would be O(N 1 2 ) To overcome the problems with relaxation techniques, methods based on linear programming have been suggested [7, 11]. However, the computational complexity of this approach increases rapidly for problems having more than one space like dimension. A multigrid method has been suggested in [4] to accelerate convergence of the basic relaxation method. Although this is a promising technique, multigrid methods are ....

M.A.H. Dempster and J.P. Hutton. Fast numerical valuation of American, exotic and complex options. Appl. Math. Fin., 4:1--20, 1997.

....schemes do differ from typical finite difference element methods due to the fact that they restrict node placement. The analysis is done in the context of the finite volume method (FVM) A more common approach in the finance literature for multidimensional problems is to use finite differences [7, 27, 9], but it has recently been demonstrated in [31] that the FVM has several advantages over finite difference schemes in this context. The outline of the paper is as follows. Section 2 describes the discretization and Section 3 contains a discussion of when and how one can ensure that the ....

M. A. H. Dempster and J. P. Hutton. Fast Numerical Valuation of American, Exotic and Complex Options. Applied Mathematical Finance, 4:1--20, 1997.

....and non early exercise parts of the computational domain. It is therefore a daunting task, at the present time, to produce black box option pricing software based on multigrid techniques which can be used in day to day financial applications. An alternative method based on linear programming [9] has recently been proposed. However, if the underlying PDE is more than one dimensional, then the linear programming method used in [9] may become computationally infeasible. The objective of this article is to develop a general method for handling the American early exercise feature. We simply ....

....option pricing software based on multigrid techniques which can be used in day to day financial applications. An alternative method based on linear programming [9] has recently been proposed. However, if the underlying PDE is more than one dimensional, then the linear programming method used in [9] may become computationally infeasible. The objective of this article is to develop a general method for handling the American early exercise feature. We simply view the problem as a nonlinear differential algebraic system (DAE) where the (in general) nonlinear constraint can be imposed using a ....

M.A.H. Dempster and J.P. Hutton. Fast numerical valuation of American, exotic and complex options. Appl. Math. Finance, 4:1--20, 1997.

....put option is by Brennan and Schwartz [2] In spite of the pioneering e orts of these authors This work was based on research supported by the National Science Research Foundation under grant CCR9624018. 1 and others, including Jaillet, Lamberton, and Lapeyre [18] and Dempster and Hutton [10, 11], it is our belief that the linear complementarity approach to pricing American options is very much at its infancy and its full potential has yet to be realized. This paper aims to further explore the linear complementarity problem (LCP) and its extensions as a powerful mathematical tool for the ....

.... highly structured and has very desirable theoretical properties that render the problem solvable by most well known methods, such as the those described in [5] For the detailed numerical treatment of the vanilla American option by linear complementarity and linear programming methods, we refer to [26, 10, 11] and the references therein. We begin our discussion with a variant of the basic Black Scholes model. 2.1 Cox s model of constant elasticity of variance In 1975, John Cox proposed an option pricing model that generalized the Black Scholes model, by postulating a certain non stationarity of the ....

M.A.H. Dempster and J.P. Hutton, \Fast numerical valuation of American, exotic and complex options", Applied Mathematical Finance 4 (1997) 1-20.

.... is used [15] In addition, linear complementarity problems with non tridiagonal coefficient matrices can arise in different asset pricing models, e.g. a jump diffusion model [21] Computational investigation of American option pricing using the discretized linear complementarity has been made in [11, 10, 12, 15]. In [20] the projected SOR approach has been considered. In [11] the discretized linear complementarity problems from the standard finite difference approximation are solved as linear programming 1 problems by the simplex method. More sophisticated methods such as Lemke s algorithm and ....

M. A. H. DEMPSTER AND J. P. HUTTON, Fast numerical valuation of American, exotic and complex options, Applied Mathematical Finance, 4 (1997), pp. 1--20.

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M. A. H. Dempster and J. P. Hutton, Fast numerical valuation of American, exotic and complex options, Applied Mathematical Finance, 4 (1997), pp. 1--20.

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