194 research outputs found
Accelerated American option pricing with deep neural networks
Given the competitiveness of a market-making environment, the ability to speedily quote option prices consistent with an ever-changing market environment is essential. Thus, the smallest acceleration or improvement over traditional pricing methods is crucial to avoid arbitrage. We propose a method for accelerating the pricing of American options to near-instantaneous using a feed-forward neural network. This neural network is trained over the chosen (e.g., Heston) stochastic volatility specification. Such an approach facilitates parameter interpretability, as generally required by the regulators, and establishes our method in the area of eXplainable Artificial Intelligence (XAI) for finance. We show that the proposed deep explainable pricer induces a speed-accuracy trade-off compared to the typical Monte Carlo or Partial Differential Equation-based pricing methods. Moreover, the proposed approach allows for pricing derivatives with path-dependent and more complex payoffs and is, given the sufficient accuracy of computation and its tractable nature, applicable in a market-making environment
Comment on 'Second-Order Statistical Structure of Geomagnetic Field Reversals' by P. S. Naidu
In a recent paper, Naidu [1975] has proposed that the reversal intervals of the geomagnetic field for the period 0-76 m.y. are not independent. In fact, the author has fitted a first order autoregressive moving average model to the data published by Heirtzler et al. [1968]. This conclusion, if true, is of importance because it suggests that the mechanism governing the reversals of the geomagnetic dynamo possesses a memory
Correlations and the relativistic structure of the nucleon self-energy
A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter
is to decompose the self energy of the nucleons into Lorentz scalar and vector
components. A new method is introduced for this decomposition. It is based on
the dependence of the single-particle energy on the small component in the
Dirac spinors used to calculate the matrix elements of the underlying NN
interaction. The resulting Dirac components of the self-energy depend on the
momentum of the nucleons. At densities around and below the nuclear matter
saturation density this momentum dependence is dominated by the non-locality of
the Brueckner G matrix. At higher densities these correlation effects are
suppressed and the momentum dependence due to the Fock exchange terms is
getting more important. Differences between symmetric nuclear matter and
neutron matter are discussed. Various versions of the Bonn potential are
considered.Comment: 18 pages LaTeX, including 6 figure
Relativistic Structure of the Nucleon Self-Energy in Asymmetric Nuclei
The Dirac structure of the nucleon self-energy in asymmetric nuclear matter
cannot reliably be deduced from the momentum dependence of the single-particle
energies. It is demonstrated that such attempts yield an isospin dependence
with even a wrong sign. Relativistic studies of finite nuclei have been based
on such studies of asymmetric nuclear matter. The effects of these isospin
components on the results for finite nuclei are investigated.Comment: 9 pages, Latex 4 figures include
Long-Term Variations in the Growth and Decay Rates of Sunspot Groups
Using the combined Greenwich (1874-1976) and Solar Optical Observatories
Network (1977-2009) data on sunspot groups, we study the long-term variations
in the mean daily rates of growth and decay of sunspot groups. We find that the
minimum and the maximum values of the annually averaged daily mean growth rates
are ~52% per day and ~183% per day, respectively, whereas the corresponding
values of the annually averaged daily mean decay rates are ~21% per day and
~44% per day, respectively. The average value (over the period 1874-2009) of
the growth rate is about 70% more than that of the decay rate. The growth and
the decay rates vary by about 35% and 13%, respectively, on a 60-year
time-scale. From the beginning of Cycle 23 the growth rate is substantially
decreased and near the end (2007-2008) the growth rate is lowest in the past
about 100 years.Comment: 1 table, 13 figures, accepted by Solar Physic
Effective DBHF Method for Asymmetric Nuclear Matter and Finite Nuclei
A new decomposition of the Dirac structure of nucleon self-energies in the
Dirac Brueckner-Hartree-Fock (DBHF) approach is adopted to investigate the
equation of state for asymmetric nuclear matter. The effective coupling
constants of , , and mesons with a density
dependence in the relativistic mean field approach are deduced by reproducing
the nucleon self-energy resulting from the DBHF at each density for symmetric
and asymmetric nuclear matter. With these couplings the properties of finite
nuclei are investigated. The agreement of charge radii and binding energies of
finite nuclei with the experimental data are improved simultaneously in
comparison with the projection method. It seems that the properties of finite
nuclei are sensitive to the scheme used for the DBHF self-energy extraction. We
may conclude that the properties of the asymmetric nuclear matter and finite
nuclei could be well described by the new decomposition approach of the G
matrix.Comment: 16 pages, 5 figure
Search for Short-Term Periodicities in the Sun's Surface Rotation: A Revisit
The power spectral analyses of the Sun's surface equatorial rotation rate
determined from the Mt. Wilson daily Doppler velocity measurements during the
period 3 December 1985 to 5 March 2007 suggests the existence of 7.6 year, 2.8
year, 1.47 year, 245 day, 182 day and 158 day periodicities in the surface
equatorial rotation rate during the period before 1996.
However, there is no variation of any kind in the more accurately measured
data during the period after 1995. That is, the aforementioned periodicities in
the data during the period before the year 1996 may be artifacts of the
uncertainties of those data due to the frequent changes in the instrumentation
of the Mt. Wilson spectrograph. On the other hand, the temporal behavior of
most of the activity phenomena during cycles 22 (1986-1996) and 23 (after 1997)
is considerably different. Therefore, the presence of the aforementioned
short-term periodicities during the last cycle and absence of them in the
current cycle may, in principle, be real temporal behavior of the solar
rotation during these cycles.Comment: 11 pages, 6 figures, accepted for publication in Solar Physic
Scalar and vector decomposition of the nucleon self-energy in the relativistic Brueckner approach
We investigate the momentum dependence of the nucleon self-energy in nuclear
matter. We apply the relativistic Brueckner-Hartree-Fock approach and adopt the
Bonn A potential. A strong momentum dependence of the scalar and vector
self-energy components can be observed when a commonly used pseudo-vector
choice for the covariant representation of the T-matrix is applied. This
momentum dependence is dominated by the pion exchange. We discuss the problems
of this choice and its relations to on-shell ambiguities of the T-matrix
representation. Starting from a complete pseudo-vector representation of the
T-matrix, which reproduces correctly the pseudo-vector pion-exchange
contributions at the Hartree-Fock level, we observe a much weaker momentum
dependence of the self-energy. This fixes the range of the inherent uncertainty
in the determination of the scalar and vector self-energy components. Comparing
to other work, we find that extracting the self-energy components by a fit to
the single particle potential leads to even more ambiguous results.Comment: 35 pages RevTex, 7 PS figures, replaced by a revised and extended
versio
Relativistic Brueckner-Hartree-Fock calculations with explicit intermediate negative energy states
In a relativistic Brueckner-Hartree-Fock calculation we include explicit
negative-energy states in the two-body propagator. This is achieved by using
the Gross spectator-equation, modified by medium effects. Qualitatively our
results compare well with other RBHF calculations. In some details significant
differences occur, e.g, our equation of state is stiffer and the momentum
dependence of the self-energy components is stronger than found in a reference
calculation without intermediate negative energy states.Comment: 13 pages Revtex, 5 figures included seperatel
Higher spin quaternion waves in the Klein-Gordon theory
Electromagnetic interactions are discussed in the context of the Klein-Gordon
fermion equation. The Mott scattering amplitude is derived in leading order
perturbation theory and the result of the Dirac theory is reproduced except for
an overall factor of sixteen. The discrepancy is not resolved as the study
points into another direction. The vertex structures involved in the scattering
calculations indicate the relevance of a modified Klein-Gordon equation, which
takes into account the number of polarization states of the considered quantum
field. In this equation the d'Alembertian is acting on quaternion-like plane
waves, which can be generalized to representations of arbitrary spin. The
method provides the same relation between mass and spin that has been found
previously by Majorana, Gelfand, and Yaglom in infinite spin theories
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