Optimal Mortgage Refinancing with Inattention

Despite the enormous volume of refinancing activity in conventional residential mortgages, reaching record levels during recent years of historically low interest rates, the solution to the problem of how to time refinancing decisions optimally has remained elusive. It is recognized that the decision should depend, among other factors, on the ‘call’ options of the outstanding and the new mortgage. Determining the value of these options is a challenge in the absence of an observable optionless mortgage yield curve. We solve this by calibrating a benchmark interest rate process to the value of the new mortgage and then apply the notion of refinancing efficiency to the timing decision. In particular, risk-averse decision makers can use refinancing efficiency to measure how close to optimal a refinancing is. We analyse the sensitivity of the decision to interest rate volatility and also show how to incorporate homeowner-specific considerations, namely borrowing horizon and income taxes. While calibration and ...

The electronic structure and geometry optimization of cobaltocene and nickelocene molecules are calculated using DFT/B3LYP with the basis set of 6-31G (d).The Eigen values, Eigen vector and population analysis of the molecules show that the first 12 molecular orbitals in cobaltocene and 14 in nickelocene have contribution from 2pz orbitals of carbon of (C5H5)- and 4s, 4p and 3d orbitals of cobalt and nickel respectively. We found that the extent of involvement of metal orbitals in the two cases is different. In cobaltocene the maximum involvement out of 4s and 4p orbital is in the order 4s>4pz>4py>4px and in 3d orbitals the order is 3dyz>3dxy>3dxz>3d2z>3dx2-y2. The involvement of corresponding orbital in nickelocene with respect to the 4s and 4p orbitals is in the order of 4py>4px>4s>4pz and in 3d orbitals the order is 3dyz>3dx2-y2>3dxy>3dxz>3dz2 molecules. The total involvement of 3d, 4s and 4p orbitals of metal and 2pz orbitals of the ten carbon atoms of both ligands of (C5H5)- in cobaltocene and nickelocene respectively are 40.2388 and 38.3776 hence we can conclude that cobaltocene is more stable than nickelocene. Similar results are found from calculation of parameters like dipole moment, HOMO-LUMO gap and Mullikan charge distribution. The population analysis shows that only 2pz orbitals of carbon of (C5H5)- and 3d orbitals of metal provide electrons to MOs of cobaltocene and nickelocene.

A model-free method, based on optical invariants, of analyzing the reflectivity of thin adsorbed dielectric films is extended to dielectric waveguide techniques such as optical waveguide lightmode spectroscopy (OWLS). The reliability of film parameters determined from three general types of techniques (OWLS, scanning angle reflectometry, and scanning angle ellipsometry) is compared in the context of uniaxially anisotropic adsorbed films, with major axis perpendicular to the film. Expressions for the invariants for stratified anisotropic films in terms of simple moments of the layer optical distribution are presented. These general methods hold out the promise of more extended analysis of the optical response of thin films adsorbing on dielectric waveguides, while avoiding the pitfalls of specific optical models.

With the advent of surveys generating multi-epoch photometry and the discovery of large numbers of variable stars, the classification of these stars has to be automatic. We have developed such a classification procedure for about 1700 stars from the variable star catalogue of the All-Sky Automated Survey 1–2 (ASAS 1–2) by selecting the periodic stars and by applying an unsupervised Bayesian classifier using parameters obtained through a Fourier decomposition of the light curve. For irregular light curves we used the period and moments of the magnitude distribution for the classification. In the case of ASAS 1–2, 83 per cent of variable objects are red giants. A general relation between the period and amplitude is found for a large fraction of those stars. The selection led to 302 periodic and 1429 semiperiodic stars, which are classified in six major groups: eclipsing binaries, ‘sinusoidal curves’, Cepheids, small amplitude red variables, SR and Mira stars. The type classification error level is estimated to be about 7 per cent.

The Market Price of Aggregate Risk and the Wealth Distribution

The mechanisms, distribution, and total moment of earthquakes within the bending oceanic plate seaward of trenches constrain possible mechanical models of the lithosphere. The average annual horizontal slip in normal fault earthquakes, as estimated from the cumulative seismic moment, exceeds the total extension predicted by an elastic plate model. Thus bending is not predominantly an elastic process but must include a large amount of permanent deformation. Normal‐faulting earthquakes are associated with every major trench system in the Pacific and Indian oceans, but events indicating horizontal compression are rare. The predominance of normal faults over thrust faults, normal events as deep as 25 km within the lithosphere (well constrained by pP), and the existence of large (Ms > 7.5) normal fault earthquakes suggest that the average oceanic lithosphere is not under regional horizontal compressive stress which is a large fraction of the bending stresses. The location of thrust fault events as deep as 40–50 km within the bending plate requires the lithosphere to have significant strength at least as deep as 50 km. A two‐layer plate model with elastic‐perfectly plastic rheology can satisfy these seismological constraints and fit the observed shape of the trench and outer rise. Large regional stresses are not required, and variations in thickness and strength are not needed to fit individual profiles. In our preferred average model the mechanical plate is 50 km thick, with a weak (1‐kbar yield strength) upper layer and a strong (6 kbar) lower layer. The mechanism for plastic strain at yield is assumed to be slip accompanying earthquakes. Normal fault earthquakes are consistent with Coulomb criterion failure, but some other failure mechanism must be invoked for the thrust fault earthquakes. The bottom of the plate is thought to be defined by a transition to steady state creep, induced either by increasing temperature with depth or by a change from dry to wet rheology. Variations in regional stresses should produce corresponding changes in the shapes of the topographic profiles. An examination of the tectonic settings of a number of profiles suggests that increasing horizontal compression should decrease the curvature of the profile in the vicinity of the zero‐crossing point on the seaward wall of the trench.

Using a penalized maximum likelihood, we estimate, for the first time, the velocity distribution of white dwarfs in the solar neighbourhood. Our sample consists of 129 675 white dwarfs within 500 pc in Gaia Early Data Release 3. The white dwarf velocity distributions reveal a similar structure to the rest of the solar neighbourhood stars, reflecting that white dwarfs are subject to the same dynamical processes. In the velocity distribution for three magnitude-binned subsamples, we, however, find a novel structure at (U, V) = (7, −19) km s−1 in fainter samples, potentially related to the Coma Berenices stream. We also see a double-peaked feature in U − W at U ≈ −30 km s−1 and in V − W at V ≈ −20 km s−1 for fainter samples. We determine the velocity distribution and velocity moments as a function of absolute magnitude for two samples based on the bifurcation identified in Gaia Data Release 2 in the colour–magnitude diagram. The brighter, redder sequence has a larger velocity dispersion than the fainter, bluer sequence across all magnitudes. It is hard to reconcile this kinematic difference with a bifurcation caused purely by atmospheric composition, while it fits neatly with a significant age difference between the two sequences. Our results provide novel insights into the kinematic properties of white dwarfs and demonstrate the power of analytical techniques that work for the large fraction of stars that do not have measured radial velocities in the current era of large-scale astrometric surveys.

This study presents a novel approach to analyzing the present value of total profit for fixed and indexed mortgage products in order to determine the optimal mortgage interest rate that would maximize the bank’s expected total profit based on applying the approach used in operations research to the field of finance. The study considers the impact of lending rate, demand, prepayment, and defaults on bank profits and emphasizes the trade-offs between potential gains and losses when setting the lending rate. As such, we not only used a fixed-rate mortgage model or an index mortgage model with the interest rate as the decision variable, but also employed mathematical analysis methods to find out the loan rate that maximizes the present value of the bank’s expected total profit. The findings revealed that an increase in interest rate, loan amount, and demand positively impacted the bank profits, while prepayment had an adverse effect. The study highlights the importance of carefully evaluating various factors that influence revenue in order to arrive at the most appropriate lending rate that will optimize profits. The results provide valuable insights into the optimal mortgage interest rate and the factors that determine the revenue and profits of a bank, with implications for cost–benefit analysis, fixed-rate mortgage, indexed mortgage, lending rate, defaults, and maximum profit. This study contributes to the existing literature on mortgage products. It provides practical implications for banks in managing their mortgage products efficiently in order to enhance their financial performance and recommends optimizing mortgage interest rates for maximum bank profits by taking the lending rate, demand, and prepayment effects into account.

The statistical possibilities of studying intrasystem processes in multielement systems are determined by solving the problem of the moments of distributions specified in mathematical and physical formulations. The characteristic properties of the distributions can be revealed by analyzing the simple and product moments (integer, fractional, and functional) and the relationships between them. The proposed method of complex analysis of experimental data and theoretical calculations is illustrated using the examples of the Maxwellian velocity distribution of molecules, the Planck radiation spectral power distribution, and the size distribution of microscopic particles in a disperse-hardened alloy.

Taxing Capital in the Presence of Trickle Down Effects: A Sufficient Statistics Approach

Thirty-one plugs of alkaline volcanic rocks of Cenozoic age (37 Ma in mean) occur in the Upper Benue valley, northern Cameroon (Central Africa). The complete alkaline series (alkaline basalts, hawaiites, mugearites, phonolites, trachytes and rhyolites) is represented. Basalts contain phenocrysts of olivine, Al-Ti-rich diopside, and Ti-magnetite, and hawaiites-abundant microphenocrysts of plagioclase. Mugearites have a trachytic texture and contain xenocrysts of K-feldspar, apatite, quartz and unstable biotite. Phonolites are peralkaline. Trachytes (peralkaline and non-peralkaline) and rhyolites are characterised by their sodic mineralogy with aegirine-augite, richterite, and arfvedsonite phenocrysts. There is a large compositional gap between basaltic and felsic lavas, except the mugearites. Despite this gap, major- and trace-element distributions are in favour of a co-magmatic origin for the basaltic and felsic lavas. The Upper Benue valley basalts are similar in their chemical and isotopic features to other basalts from both the continental and oceanic sectors of the Cameroon Line. The Upper Benue valley basaltic magmas (87Sr/86Sr≈0.7035; e Nd=+3.9) originate from an infra-lithospheric reservoir. The Sr–Nd isotopic composition and high Sr contents of the mugearites suggest that they are related to mantle-derived magmas and that they result from the mixing, at shallow crustal levels, of a large fraction of trachytic magma with a minor amount of basaltic magma. Major-element modelling of the basalt–trachyte evolution (through hawaiite and mugearite compositions) does not support an evolution through fractional crystallization alone. The fluids have played a significant role in the felsic lavas genesis, as attested by the occurrence of F-rich minerals, calcite and analcite. An origin of the Upper Benue valley rhyolitic magmas by fractional crystallization of mantle-derived primitive magmas of basaltic composition, promoted or accompanied by volatile, halogen-rich fluid phases, may be the best hypothesis for the genesis of these lavas. These fluids also interact with the continental crust, resulting in the high Sr-isotope initial ratios (0.710) in the rhyolites, whereas the Nd isotopic composition has been less affected (e Nd=+0.4).