Parallel execution of an integral approach of the passage to the security derivative that it fixes the price Ltd world of supercomputers of the quádrico we we use an integral approach of the passage
- From: "therealistexists@xxxxxxxxxxx" <therealistexists@xxxxxxxxxxx>
- Date: 27 Apr 2006 16:26:40 -0700
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Parallel execution of an integral approach of the passage to the
security derivative that it fixes the price Ltd world of supercomputers
of the quádrico we we use an integral approach of the passage deciding
the underlying random equations shape financier to fix the price
derivative of the security. The integral methodology of the passage is
known well in the field of mechanics of quantum and defines values of
the expectation as integral exceeding functionaries or histories of the
additions (passages) of quantum or the random dynamic system. Such
integrals are a limit of the sequence of the finite-dimensional
multiple integrals gotten discretizing the interval of the time under
the consideration, that corresponds to the time to the expiration in
the box of derivatives financial. Essentially, a continuous random
process is specified by its density of the functional probability
better that for its law of the evolution (a random distinguishing
equation, SDE). The formula of Feynman-Kac guarantees the equivalence
of the two formulations. Known mount numerical Carlo well (MC) and
methods quasi of Monte Carlo (QMC) for the calculation of conditional
values of the expectation in random processes is seen as devices
normally generating appropriate random passages of the excess of the
averages. In the structure of the integral approach of the passage
discretized of the density of the probability is needed to generate
appropriate functions multivariate. When MC and QMC will be
essentially the only existing numerical methods for the raised
dimensional problems (that they correspond to derivatives with many
seguranças underlying), suffer from the slow properties of the
convergence. In the example of low dimensional problems many
techniques are available, based in integrating for differencies finite
partial the distinguishing equation (PDE) that it corresponds to the
SDE in the hand or a simplified dràstica assumption in the
probabilities of the transistion (that is methods binomial). We use an
alternative method for the numerical computation of formulation
integral of the passage of the random financial problem that is
elegant, easy to extend for options passage-dependents and Americans,
amenable to a parallel execution and with good properties of the
convergence and the stability. The numerical method deterministic of
the green function (GFDNM) trusts approaching the probabilities of the
transistion for the stages discretized of the time, and computing the
integrals for the numerical quadrature standard on a grating
discretized. In the fact, the probability of the transistion
represents the green function of the PDE that corresponds to the
underlying SDE the evolution of the financial security. The
conditional values of the expectation are simply products of the vector
of payoff for one determined number of matrices of the transistion.
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