14,746 research outputs found
Review of modern numerical methods for a simple vanilla option pricing problem
Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better
Regression Driven F--Transform and Application to Smoothing of Financial Time Series
In this paper we propose to extend the definition of fuzzy transform in order
to consider an interpolation of models that are richer than the standard fuzzy
transform. We focus on polynomial models, linear in particular, although the
approach can be easily applied to other classes of models. As an example of
application, we consider the smoothing of time series in finance. A comparison
with moving averages is performed using NIFTY 50 stock market index.
Experimental results show that a regression driven fuzzy transform (RDFT)
provides a smoothing approximation of time series, similar to moving average,
but with a smaller delay. This is an important feature for finance and other
application, where time plays a key role.Comment: IFSA-SCIS 2017, 5 pages, 6 figures, 1 tabl
On the interpretation and identification of dynamic Takagi-Sugenofuzzy models
Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Distribution functions of linear combinations of lattice polynomials from the uniform distribution
We give the distribution functions, the expected values, and the moments of
linear combinations of lattice polynomials from the uniform distribution.
Linear combinations of lattice polynomials, which include weighted sums, linear
combinations of order statistics, and lattice polynomials, are actually those
continuous functions that reduce to linear functions on each simplex of the
standard triangulation of the unit cube. They are mainly used in aggregation
theory, combinatorial optimization, and game theory, where they are known as
discrete Choquet integrals and Lovasz extensions.Comment: 11 page
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