1,341 research outputs found
Multivariate option pricing with time varying volatility and correlations
In recent years multivariate models for asset returns have received much attention, in particular this is the case for models with time varying volatility. In this paper we consider models of this class and examine their potential when it comes to option pricing. Specifically, we derive the risk neutral dynamics for a general class of multivariate heteroskedastic models, and we provide a feasible way to price options in this framework. Our framework can be used irrespective of the assumed underlying distribution and dynamics, and it nests several important special cases. We provide an application to options on the minimum of two indices. Our results show that not only is correlation important for these options but so is allowing this correlation to be dynamic. Moreover, we show that for the general model exposure to correlation risk carries an important premium, and when this is neglected option prices are estimated with errors. Finally, we show that when neglecting the non-Gaussian features of the data, option prices are also estimated with large errors.multivariate risk premia, option pricing, GARCH models
Bosons Confined in Optical Lattices: the Numerical Renormalization Group revisited
A Bose-Hubbard model, describing bosons in a harmonic trap with a
superimposed optical lattice, is studied using a fast and accurate variational
technique (MF+NRG): the Gutzwiller mean-field (MF) ansatz is combined with a
Numerical Renormalization Group (NRG) procedure in order to improve on both.
Results are presented for one, two and three dimensions, with particular
attention to the experimentally accessible momentum distribution and possible
satellite peaks in this distribution. In one dimension, a comparison is made
with exact results obtained using Stochastich Series Expansion.Comment: 10 pages, 15 figure
Integrable two-channel p_x+ip_y-wave superfluid model
We present a new two-channel integrable model describing a system of spinless
fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC
crossover of the s-wave case, the p-wave model has a third order quantum phase
transition. The critical point coincides with the deconfinement of a single
molecule within a BEC of bound dipolar molecules. The exact many-body
wavefunction provides a unique perspective of the quantum critical region
suggesting that the size of the condensate wavefunction, that diverges
logarithmically with the chemical potential, could be used as an experimental
indicator of the phase transition.Comment: 4 pages, 4 figure
A solvable model of a one-dimensional quantum gas with pair interaction
We propose a solvable model of a one-dimensional harmonic oscillator quantum
gas of two sorts of particles, fermions or bosons, which allows to describe the
formation of pairs due to a suitable pair interaction. These pairs we call
"pseudo-bosons" since the system can be approximated by an ideal bose gas for
low temperatures. We illustrate this fact by considering the specific heat and
the entropy function for N=8 pairs. The model can also be evaluated in the
thermodynamic limit if the harmonic oscillator potential is suitable scaled
Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime
Recent experiments on ultracold atomic alkali gases in a one-dimensional
optical lattice have demonstrated the transition from a gas of soft-core bosons
to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons
behave like fermions in many respects. We have studied the underlying many-body
physics through numerical simulations which accommodate both the soft-core and
hard-core limits in one single framework. We find that the Tonks-Girardeau gas
is reached only at the strongest optical lattice potentials. Results for
slightly higher densities, where the gas develops a Mott-like phase already at
weaker optical lattice potentials, show that these Mott-like short range
correlations do not enhance the convergence to the hard-core limit.Comment: 4 pages, 3 figures, replaced with published versio
Integrable models for asymmetric Fermi superfluids: Emergence of a new exotic pairing phase
We introduce an exactly-solvable model to study the competition between the
Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) and breached-pair superfluid in
strongly interacting ultracold asymmetric Fermi gases. One can thus investigate
homogeneous and inhomogeneous states on an equal footing and establish the
quantum phase diagram. For certain values of the filling and the interaction
strength, the model exhibits a new stable exotic pairing phase which combines
an inhomogeneous state with an interior gap to pair-excitations. It is proven
that this phase is the exact ground state in the strong coupling limit, while
numerical examples demonstrate that also at finite interaction strength it can
have lower energy than the breached-pair or LOFF states.Comment: Revised version accepted for publicatio
Maximum occupation number for composite boson states
One of the major differences between fermions and bosons is that fermionic
states have a maximum occupation number of one, whereas the occupation number
for bosonic states is in principle unlimited. For bosons that are made up of
fermions, one could ask the question to what extent the Pauli principle for the
constituent fermions would limit the boson occupation number. Intuitively one
can expect the maximum occupation number to be proportional to the available
volume for the bosons divided by the volume occupied by the fermions inside one
boson, though a rigorous derivation of this result has not been given before.
In this letter we show how the maximum occupation number can be calculated from
the ground-state energy of a fermionic generalized pairing problem. A very
accurate analytical estimate of this eigenvalue is derived. From that a general
expression is obtained for the maximum occupation number of a composite boson
state, based solely on the intrinsic fermionic structure of the bosons. The
consequences for Bose-Einstein condensates of excitons in semiconductors and
ultra cold trapped atoms are discussed.Comment: 4 pages, Revte
Ghosts, Strong Coupling and Accidental Symmetries in Massive Gravity
We show that the strong self-interaction of the scalar polarization of a
massive graviton can be understood in terms of the propagation of an extra
ghost-like degree of freedom, thus relating strong coupling to the sixth degree
of freedom discussed by Boulware and Deser in their Hamiltonian analysis of
massive gravity. This enables one to understand the Vainshtein recovery of
solutions of massless gravity as being due to the effect of the exchange of
this ghost which gets frozen at distances larger than the Vainshtein radius.
Inside this region, we can trust the two-field Lagrangian perturbatively, while
at larger distances one can use the higher derivative formulation. We also
compare massive gravity with other models, namely deconstructed theories of
gravity, as well as DGP model. In the latter case we argue that the Vainshtein
recovery process is of different nature, not involving a ghost degree of
freedom.Comment: 21 page
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