871 research outputs found
A Closed-Form Approximation of Likelihood Functions for Discretely Sampled Diffusions: the Exponent Expansion
In this paper we discuss a closed-form approximation of the likelihood
functions of an arbitrary diffusion process. The approximation is based on an
exponential ansatz of the transition probability for a finite time step , and a series expansion of the deviation of its logarithm from that of a
Gaussian distribution. Through this procedure, dubbed {\em exponent expansion},
the transition probability is obtained as a power series in . This
becomes asymptotically exact if an increasing number of terms is included, and
provides remarkably accurate results even when truncated to the first few (say
3) terms. The coefficients of such expansion can be determined
straightforwardly through a recursion, and involve simple one-dimensional
integrals.
We present several examples of financial interest, and we compare our results
with the state-of-the-art approximation of discretely sampled diffusions
[A\"it-Sahalia, {\it Journal of Finance} {\bf 54}, 1361 (1999)]. We find that
the exponent expansion provides a similar accuracy in most of the cases, but a
better behavior in the low-volatility regime. Furthermore the implementation of
the present approach turns out to be simpler.
Within the functional integration framework the exponent expansion allows one
to obtain remarkably good approximations of the pricing kernels of financial
derivatives. This is illustrated with the application to simple path-dependent
interest rate derivatives. Finally we discuss how these results can also be
used to increase the efficiency of numerical (both deterministic and
stochastic) approaches to derivative pricing.Comment: 28 pages, 7 figure
Finite-size spin-wave theory of a collinear antiferromagnet
The ground-state and low-energy properties of the two-dimensional
Heisenberg model in the collinear phase are investigated using finite-size
spin-wave theory [Q. F. Zhong and S. Sorella, {\em Europhys. Lett.} {\bf 21},
629 (1993)], and Lanczos exact diagonalizations. For spin one-half -- where the
effects of quantization are the strongest -- the spin-wave expansion turns out
to be quantitatively accurate for . In this regime, both
the magnetic structure factor and the spin susceptibility are very close to the
spin-wave predictions. The spin-wave estimate of the order parameter in the
collinear phase, , is in remarkable agreement with recent
neutron scattering measurements on .Comment: 10 pages, 3 figure
Algorithmic differentiation and the calculation of forces by quantum Monte Carlo
We describe an efficient algorithm to compute forces in quantum Monte Carlo
using adjoint algorithmic differentiation. This allows us to apply the space
warp coordinate transformation in differential form, and compute all the 3M
force components of a system with M atoms with a computational effort
comparable with the one to obtain the total energy. Few examples illustrating
the method for an electronic system containing several water molecules are
presented. With the present technique, the calculation of finite-temperature
thermodynamic properties of materials with quantum Monte Carlo will be feasible
in the near future.Comment: 32 pages, 4 figure, to appear in The Journal of Chemical Physic
Quantum Phase Transition in Coupled Spin Ladders
The ground state of an array of coupled, spin-half, antiferromagnetic ladders
is studied using spin-wave theory, exact diagonalization (up to 36 sites) and
quantum Monte Carlo techniques (up to 256 sites). Our results clearly indicate
the occurrence of a zero-temperature phase transition between a N\'eel ordered
and a non-magnetic phase at a finite value of the inter-ladder coupling
(). This transition is marked by remarkable changes in the
structure of the excitation spectrum.Comment: 4 pages, 6 postscript figures, to appear in Physical Review
Ising transition in the two-dimensional quantum Heisenberg model
We study the thermodynamics of the spin- two-dimensional quantum
Heisenberg antiferromagnet on the square lattice with nearest () and
next-nearest () neighbor couplings in its collinear phase (),
using the pure-quantum self-consistent harmonic approximation. Our results show
the persistence of a finite-temperature Ising phase transition for every value
of the spin, provided that the ratio is greater than a critical value
corresponding to the onset of collinear long-range order at zero temperature.
We also calculate the spin- and temperature-dependence of the collinear
susceptibility and correlation length, and we discuss our results in light of
the experiments on LiVOSiO and related compounds.Comment: 4 page, 4 figure
Finite size Spin Wave theory of the triangular Heisenberg model
We present a finite size spin wave calculation on the Heisenberg
antiferromagnet on the triangular lattice focusing in particular on the
low-energy part of the excitation spectrum. For s=1/2 the good agreement with
the exact diagonalization and quantum Monte Carlo results supports the
reliability of the spin wave expansion to describe the low-energy spin
excitations of the Heisenberg model even in presence of frustration. This
indicates that the spin susceptibility of the triangular antiferromagnet is
very close to the linear spin wave result.Comment: 6 pages (LateX), 2 ps-figure
The Mott Metal-Insulator transition in the half-filled Hubbard model on the Triangular Lattice
We investigate the metal-insulator transition in the half-filled Hubbard
model on a two-dimensional triangular lattice using both the
Kotliar-Ruckenstein slave-boson technique, and exact numerical diagonalization
of finite clusters. Contrary to the case of the square lattice, where the
perfect nesting of the Fermi surface leads to a metal-insulator transition at
arbitrarily small values of U, always accompanied by antiferromagnetic
ordering, on the triangular lattice, due to the lack of perfect nesting, the
transition takes place at a finite value of U, and frustration induces a
non-trivial competition among different magnetic phases. Indeed, within the
mean-field approximation in the slave-boson approach, as the interaction grows
the paramagnetic metal turns into a metallic phase with incommensurate spiral
ordering. Increasing further the interaction, a linear spin-density-wave is
stabilized, and finally for strong coupling the latter phase undergoes a
first-order transition towards an antiferromagnetic insulator. No trace of the
intermediate phases is instead seen in the exact diagonalization results,
indicating a transition between a paramagnetic metal and an antiferromagnetic
insulator.Comment: 5 pages, 4 figure
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