141 resultados para Black-Scholes Equation

em Indian Institute of Science - Bangalore - Índia


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We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.

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Motivated by the viscosity bound in gauge/gravity duality, we consider the ratio of shear viscosity (eta) to entropy density (s) in black hole accretion flows. We use both an ideal gas equation of state and the QCD equation of state obtained from lattice for the fluid accreting onto a Kerr black hole. The QCD equation of state is considered since the temperature of accreting matter is expected to approach 10(12) K in certain hot flows. We find that in both the cases eta/s is small only for primordial black holes and several orders of magnitude larger than any known fluid for stellar and supermassive black holes. We show that a lower bound on the mass of primordial black holes leads to a lower bound on eta/s and vice versa. Finally we speculate that the Shakura-Sunyaev viscosity parameter should decrease with increasing density and/or temperatures. (C) 2012 Elsevier B.V. All rights reserved.

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Aerosol black carbon (BC) mass concentrations ([BC]), measured continuously during a multi-platform field experiment, Integrated Campaign for Aerosols gases and Radiation Budget (ICARB, March-May 2006), from a network of eight observatories spread over geographically distinct environments of India, (which included five mainland stations, one highland station, and two island stations (one each ill Arabian Sea and Bay of Bengal)) are examined for their spatio-temporal characteristics. During the period of study, [BC] showed large variations across the country, with values ranging from 27 mu g m(3) over industrial/urban locations to as low as 0.065 mu g m(-3) over the Arabian Sea. For all mainland stations, [BC] remained high compared to highland as well as island stations. Among the island stations, Port Blair (PBR) had higher concentration of BC, compared to Minicoy (MCY), implying more absorbing nature of Bay of Bengal aerosols than Arabian Sea. The highland station Nainital (NTL), in the central Himalayas, showed low values of [BC], comparable or even lower than that of the island station PBR, indicating the prevalence of cleaner environment over there. An examination of the changes in the mean temporal features, as the season advances from winter (December-February) to pre-monsoon (March-May), revealed that: (a) Diurnal variations were pronounced over all the mainland stations, with all afternoon low and a nighttime high: (b) At the islands, the diurnal variations, though resembled those over the mainlands, were less pronounced; and (c) In contrast to this, highland station showed an opposite pattern with an afternoon high and a late night or early morning low. The diurnal variations at all stations are mainly caused by the dynamics of local Atmospheric Boundary Layer (ABL), At the entire mainland as well as island stations (except HYD and DEL), [BC] showed a decreasing trend from January to May, This is attributed to the increased convective mixing and to the resulting enhanced vertical dispersal of species in the ABL. In addition, large short-period modulations were observed at DEL and HYD, which appeared to be episodic, An examination of this in the light of the MODIS-derived fire count data over India along with the back-trajectory analysis revealed that advection of BC from extensive forest fires and biomass-burning regions upwind were largely responsible for this episodic enhancement in BC at HYD and DEL.

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We propose a unified model to explain Quasi-Periodic Oscillation (QPO), particularly of high frequency, observed from black hole and neutron star systems globally. We consider accreting systems to be damped harmonic oscillators exhibiting epicyclic oscillations with higher-order nonlinear resonance to explain QPO. The resonance is expected to be driven by the disturbance from the compact object at its spin frequency. The model explains various properties parallelly for both types of the compact object. It describes QPOs successfully for ten different compact sources. Based on this, we predict the spin frequency of the neutron star Sco X-1 and specific angular momentum of black holes GRO J1655–40, XTE J1550–564, H1743–322, and GRS 1915+105.

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Recently, it has been shown that the inclusion of higher signal harmonics in the inspiral signals of binary supermassive black holes (SMBH) leads to dramatic improvements in the parameter estimation with Laser Interferometer Space Antenna (LISA). In particular, the angular resolution becomes good enough to identify the host galaxy or galaxy cluster, in which case the redshift can be determined by electromagnetic means. The gravitational wave signal also provides the luminosity distance with high accuracy, and the relationship between this and the redshift depends sensitively on the cosmological parameters, such as the equation-of-state parameter w = p(DE)/rho(DE) of dark energy. Using binary SMBH events at z < 1 with appropriate masses and orientations, one would be able to constrain w to within a few per cent. We show that, if the measured sky location is folded into the error analysis, the uncertainty on w goes down by an additional factor of 2-3, leaving weak lensing as the only limiting factor in using LISA as a dark energy probe.

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The LISA Parameter Estimation Taskforce was formed in September 2007 to provide the LISA Project with vetted codes, source distribution models and results related to parameter estimation. The Taskforce's goal is to be able to quickly calculate the impact of any mission design changes on LISA's science capabilities, based on reasonable estimates of the distribution of astrophysical sources in the universe. This paper describes our Taskforce's work on massive black-hole binaries (MBHBs). Given present uncertainties in the formation history of MBHBs, we adopt four different population models, based on (i) whether the initial black-hole seeds are small or large and (ii) whether accretion is efficient or inefficient at spinning up the holes. We compare four largely independent codes for calculating LISA's parameter-estimation capabilities. All codes are based on the Fisher-matrix approximation, but in the past they used somewhat different signal models, source parametrizations and noise curves. We show that once these differences are removed, the four codes give results in extremely close agreement with each other. Using a code that includes both spin precession and higher harmonics in the gravitational-wave signal, we carry out Monte Carlo simulations and determine the number of events that can be detected and accurately localized in our four population models.

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The distribution of black leaf nodes at each level of a linear quadtree is of significant interest in the context of estimation of time and space complexities of linear quadtree based algorithms. The maximum number of black nodes of a given level that can be fitted in a square grid of size 2n × 2n can readily be estimated from the ratio of areas. We show that the actual value of the maximum number of nodes of a level is much less than the maximum obtained from the ratio of the areas. This is due to the fact that the number of nodes possible at a level k, 0≤k≤n − 1, should consider the sum of areas occupied by the actual number of nodes present at levels k + 1, k + 2, …, n − 1.

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We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

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We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

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It has been shown that it is possible to extend the validity of the Townsend breakdown criterion for evaluating the breakdown voltages in the complete pd range in which Paschen curves are available. Evaluation of the breakdown voltages for air (pd=0.0133 to 1400 kPa · cm), N2(pd=0.0313 to 1400 kPa · cm) and SF6 (pd=0.3000 to 1200 kPa · cm) has been done and in most cases the computed values are accurate to ±3% of the measured values. The computations show that it is also possible to estimate the secondary ionization coefficient ¿ in the pd ranges mentioned above.

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Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

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It is shown that in the finite-element formulation of the general quasi-harmonic equation using tetrahedral elements, for every member of the element family there exists just one numerical universal matrix indpendent of the size, shape and material properties of the element. Thus the element matrix is conveniently constructed by manipulating this single matrix along with a set of reverse sequence codes at the same time accounting for the size, shape and material properties in a simple manner.

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Conceptual advances in the field of membrane transport have, in the main, utilized artificial membranes, both planar and vesicular. Systems of biological interest,viz., cells and organelles, resemble vesicles in size and geometry. Methods are, therefore, required to extend the results obtained with planar membranes to liposome systems. In this report we present an analysis of a fluorescence technique, using the divalent cation probe chlortetracycline, in small, unilamellar vesicles, for the study of divalent cation fluxes. An ion carrier (X537 A) and a pore former (alamethicin) have been studied. The rate of rise of fluorescence signal and the transmembrane ion gradient have been related to transmembrane current and potential, respectively. A second power dependence of ion conduction-including the electrically silent portion thereof — on X537 A concentration, has been observed. An exponential dependence of ldquocurrentrdquo on ldquotransmembrane potentialrdquo in the case of alamethicin is also confirmed. Possible errors in the technique are discussed.

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Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.