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Analysis of the SSAP Method for the Numerical Valuation of High-Dimensional Multivariate American Securities (1999)

Coyle, L. N. ; Yang, J. J.

Springer

Algorithmica 25 (1999), S. 75-98

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ISSN: 1432-0541

Keywords: Key words. American options, American pricing, Monte Carlo simulation, Optimal control, Finite-difference, Itô process.

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract. We consider a new numerical method developed by Barraquand and Martineau for the pricing of American securities where the payoff depends on several sources of uncertainty. This method utilizes Monte Carlo simulation and is referred to as Stratified State Aggregation along the Payoff (SSAP). Since there are no other methods that so effectively reduce the dimensionality of high-dimensional problems, the SSAP method has generated significant interest. Numerical results are presented showing that, if a sufficiently large number of time steps are used, in the cases of the two-dimensional maximum and minimum options, SSAP typically prices to within 6 cents of the true price. However, we show that if the security depends on two or more sources of uncertainty, then the price obtained by the SSAP method will not, in general, converge to the correct theoretical price, due in large part to incorrect exercise decisions being made. We analyze the exercise regions in the cases of the two-dimensional maximum and minimum options and show how SSAP makes incorrect exercise decisions. Suggestions for improving SSAP pricing accuracy by choosing a partition other than the payoff are discussed.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/PL00009284

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Fluorine atom abstraction by Si(100). I. Experimental (1999)

Tate, M. R. ; Gosalvez-Blanco, D. ; Pullman, D. P. ; [et al.]

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 111 (1999), S. 3679-3695

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ISSN: 1089-7690

Source: AIP Digital Archive

Topics: Physics , Chemistry and Pharmacology

Notes: In the interaction of low energy F2 with Si(100) at 250 K, a dissociative chemisorption mechanism called atom abstraction is identified in which only one of the F atoms is adsorbed while the other F atom is scattered into the gas phase. The dynamics of atom abstraction are characterized via time-of-flight measurements of the scattered F atoms. The F atoms are translationally hyperthermal but only carry a small fraction (∼3%) of the tremendous exothermicity of the reaction. The angular distribution of F atoms is unusually broad for the product of an exothermic reaction. These results suggest an "attractive" interaction potential between F2 and the Si dangling bond with a transition state that is not constrained geometrically. These results are in disagreement with the results of theoretical investigations implying that the available potential energy surfaces are inadequate to describe the dynamics of this gas–surface interaction. In addition to single atom abstraction, two atom adsorption, a mechanism analogous to classic dissociative chemisorption in which both F atoms are adsorbed onto the surface, is also observed. The absolute probability of the three scattering channels (single atom abstraction, two atom adsorption, and unreactive scattering) for an incident F2 are determined as a function of F2 exposure. The fluorine coverage is determined by integrating the reaction probabilities over F2 exposure, and the reaction probabilities are recast as a function of fluorine coverage. Two atom adsorption is the dominant channel [P2=0.83±0.03(95%, N=9)] in the limit of zero coverage and decays monotonically to zero. Single atom abstraction is the minor channel (P1=0.13±0.03) at low coverage but increases to a maximum (P1=0.35±0.08) at about 0.5 monolayer (ML) coverage before decaying to zero. The reaction ceases at 0.94±0.11(95%, N=9) ML. Thermal desorption and helium diffraction confirm that the dangling bonds are the abstraction and adsorption sites. No Si lattice bonds are broken, in contrast to speculation by other investigators that the reaction exothermicity causes lattice disorder. © 1999 American Institute of Physics.