Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Growth accounting in items of turbulence and death: efficiency, technology, capital accumulation and human capital 1929-1950

We employ a non-parametrical approach to growth accounting (Data Envelopment Analysis,DEA) to disentangle the proximate sources of labour productivity growth in 41 nationsbetween 1929 and 1950 by decomposing productivity growth into four components:technological change; efficiency catch-up (movements towards the production frontier),capital accumulation and human capital accumulation. We show that efficiency catch-upgenerally explains productivity growth, whereas technological change and factoraccumulation were limited and distorted by the effects of war. War clearly hamperedefficiency. Moreover, an unbalanced ratio of human capital to physical capital (a gap to thetechnological leader) was crucial for efficiency catching-up.

Death and resurrection of the human IRGM gene

Immunity-related GTPases (IRG) play an important role in defense against intracellular pathogens. One member of this gene family in humans, IRGM, has been recently implicated as a risk factor for Crohn's disease. We analyzed the detailed structure of this gene family among primates and showed that most of the IRG gene cluster was deleted early in primate evolution, after the divergence of the anthropoids from prosimians ( about 50 million years ago). Comparative sequence analysis of New World and Old World monkey species shows that the single-copy IRGM gene became pseudogenized as a result of an Alu retrotransposition event in the anthropoid common ancestor that disrupted the open reading frame (ORF). We find that the ORF was reestablished as a part of a polymorphic stop codon in the common ancestor of humans and great apes. Expression analysis suggests that this change occurred in conjunction with the insertion of an endogenous retrovirus, which altered the transcription initiation, splicing, and expression profile of IRGM. These data argue that the gene became pseudogenized and was then resurrected through a series of complex structural events and suggest remarkable functional plasticity where alleles experience diverse evolutionary pressures over time. Such dynamism in structure and evolution may be critical for a gene family locked in an arms race with an ever-changing repertoire of intracellular parasites.

Neuroprotective role of PrPC against kainate-induced epileptic seizures and cell death depends on the modulation of JNK3 activation by GluR6/7-PSD-95 binding

Cellular prion protein (PrPC) is a glycosyl-phosphatidylinositol¿anchored glycoprotein. When mutated or misfolded, the pathogenic form (PrPSC) induces transmissible spongiform encephalopathies. In contrast, PrPC has a number of physiological functions in several neural processes. Several lines of evidence implicate PrPC in synaptic transmission and neuroprotection since its absence results in an increase in neuronal excitability and enhanced excitotoxicity in vitro and in vivo. Furthermore, PrPC has been implicated in the inhibition of N-methyl-D-aspartic acid (NMDA)¿mediated neurotransmission, and prion protein gene (Prnp) knockout mice show enhanced neuronal death in response to NMDA and kainate (KA). In this study, we demonstrate that neurotoxicity induced by KA in Prnp knockout mice depends on the c-Jun N-terminal kinase 3 (JNK3) pathway since Prnpo/oJnk3o/o mice were not affected by KA. Pharmacological blockage of JNK3 activity impaired PrPC-dependent neurotoxicity. Furthermore, our results indicate that JNK3 activation depends on the interaction of PrPC with postsynaptic density 95 protein (PSD-95) and glutamate receptor 6/7 (GluR6/7). Indeed, GluR6¿PSD-95 interaction after KA injections was favored by the absence of PrPC. Finally, neurotoxicity in Prnp knockout mice was reversed by an AMPA/KA inhibitor (6,7-dinitroquinoxaline-2,3-dione) and the GluR6 antagonist NS-102. We conclude that the protection afforded by PrPC against KA is due to its ability to modulate GluR6/7-mediated neurotransmission and hence JNK3 activation.

Neuroprotective role of PrPC against kainate-induced epileptic seizures and cell death depends on the modulation of JNK3 activation by GluR6/7-PSD-95 binding

Cellular prion protein (PrPC) is a glycosyl-phosphatidylinositol¿anchored glycoprotein. When mutated or misfolded, the pathogenic form (PrPSC) induces transmissible spongiform encephalopathies. In contrast, PrPC has a number of physiological functions in several neural processes. Several lines of evidence implicate PrPC in synaptic transmission and neuroprotection since its absence results in an increase in neuronal excitability and enhanced excitotoxicity in vitro and in vivo. Furthermore, PrPC has been implicated in the inhibition of N-methyl-D-aspartic acid (NMDA)¿mediated neurotransmission, and prion protein gene (Prnp) knockout mice show enhanced neuronal death in response to NMDA and kainate (KA). In this study, we demonstrate that neurotoxicity induced by KA in Prnp knockout mice depends on the c-Jun N-terminal kinase 3 (JNK3) pathway since Prnpo/oJnk3o/o mice were not affected by KA. Pharmacological blockage of JNK3 activity impaired PrPC-dependent neurotoxicity. Furthermore, our results indicate that JNK3 activation depends on the interaction of PrPC with postsynaptic density 95 protein (PSD-95) and glutamate receptor 6/7 (GluR6/7). Indeed, GluR6¿PSD-95 interaction after KA injections was favored by the absence of PrPC. Finally, neurotoxicity in Prnp knockout mice was reversed by an AMPA/KA inhibitor (6,7-dinitroquinoxaline-2,3-dione) and the GluR6 antagonist NS-102. We conclude that the protection afforded by PrPC against KA is due to its ability to modulate GluR6/7-mediated neurotransmission and hence JNK3 activation.

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Thomas Mann's Death in Venice or Plutarch's way towards Eros

In Death in Venice Thomas Mann refers explicitly to Plato's Symposium and Phaedrus in order to explain the relationship between Gustav von Aschenbach and Tadzio but he hides that his novel also depends on Plutarch's Eroticus. Why? The aim of this article is precisely to reveal the different reasons for such an attitude. Indeed, Plutarch speaks highly of conjugal love in his Eroticus and this way is not followed by Mann in Death in Venice but, at the same, the German writer finds in this Plutarch's philosophical dialogue all the necessary elements to build his story of masculine love and decides not to manage without it.

Nonequilibrium thermodynamic fluctuations of black holes

With the aid of the Landau-Lifshitz theory for thermodynamic fluctuations we estimate and comment on the fluctuations in the rates of mass, angular momentum, and other relevant quantities of massive Schwarzschild and Kerr black holes.

Black holes from nucleating strings

We evaluate the probability that a loop of string that has spontaneously nucleated during inflation will form a black hole upon collapse, after the end of inflation. We then use the observational bounds on the density of primordial black holes to put constraints on the parameters of the model. Combining these constraints with current upper limits on the expansion rate during inflation, we conclude that the density of black holes formed from nucleating strings is too low to be observed. Also, constraints on domain wall nucleation and monopole pair production during inflation are briefly discussed.

Brane-world creation and black holes

An inflating brane world can be created from ``nothing'' together with its anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial sections bounded by the brane. During inflation, the continuum of KK modes is separated from the massless zero mode by the gap m=(3/2)H, where H is the Hubble rate. We consider the analogue of the Nariai solution and argue that it describes the pair production of ``black cigars'' attached to the inflating brane. In the case when the size of the instantons is much larger than the AdS radius, the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and 4D gravitational entropies are the same in this limit. We also consider thermal instantons with an AdS black hole in the bulk. These may be interpreted as describing the creation of a hot universe from nothing or the production of AdS black holes in the vicinity of a pre-existing inflating brane world. The Lorentzian evolution of the brane world after creation is briefly discussed. An additional ``integration constant'' in the Friedmann equation-accompanying a term which dilutes like radiation-describes the tidal force in the fifth direction and arises from the mass of a spherical object inside the bulk. In general, this could be a 5-dimensional black hole or a ``parallel'' brane world of negative tension concentrical with our brane-world. In the case of thermal solutions, and in the spirit of the AdS/CFT correspondence, one may attribute the additional term to thermal radiation in the boundary theory. Then, for temperatures well below the AdS scale, the entropy of this radiation agrees with the entropy of the black hole in the AdS bulk.

Quantum black hole entropy and newton constant renormalization

ty that low-energy effective field theory could be sufficient to understand the microscopic degrees of freedom underlying black hole entropy. We propose a qualitative physical picture in which black hole entropy refers to a space of quasicoherent states of infalling matter, together with its gravitational field. We stress that this scenario might provide a low-energy explanation of both the black hole entropy and the information puzzle.

Correlations between black holes formed in cosmic string breaking

An analysis of cosmic string breaking with the formation of black holes attached to the ends reveals a remarkable feature: the black holes can be correlated or uncorrelated. We find that, as a consequence, the number-of-states enhancement factor in the action governing the formation of uncorrelated black holes is twice the one for a correlated pair. We argue that when an uncorrelated pair forms at the ends of the string, the physics involved is more analogous to thermal nucleation than to particle-antiparticle creation. Also, we analyze the process of intercommuting strings induced by black hole annihilation and merging. Finally, we discuss the consequences for grand unified strings. The process whereby uncorrelated black holes are formed yields a rate which significantly improves over those previously considered, but still not enough to modify string cosmology. 1995 The American Physical Society.

Black holes as fundamental strings: Comparing the absorption of scalars

The recently proposed correspondence principle of Horowitz and Polchinski provides a concrete means to relate (among others) black holes with electric Neveu-SchwarzNeveu-Schwarz charges to fundamental strings and correctly match their entropies. We further test this correspondence by examining the greybody factors in the absorption rates of neutral, minimally coupled scalars by a near extremal black hole. Perhaps surprisingly, the results disagree in general with the absorption by weakly coupled strings. Though this does not disprove the correspondence, it indicates that it might not be simple in this region of the black hole parameter space.

Can extreme black Holes have (long) Abelian Higgs hair?

It has been argued that a black hole horizon can support the long-range fields of a Nielsen-Olesen string and that one can think of such a vortex as black hole "hair." In this paper, we examine the properties of an Abelian Higgs vortex in the presence of a charged black hole as we allow the hole to approach extremality. Using both analytical and numerical techniques, we show that the magnetic field lines (as well as the scalar field) of the vortex are completely expelled from the black hole in the extreme limit. This was to be expected, since extreme black holes in Einstein-Maxwell theory are known to exhibit such a "Meissner effect" in general. This would seem to imply that a vortex does not want to be attached to an extreme black hole. We calculate the total energy of the vortex fields in the presence of an extreme black hole. When the hole is small relative to the size of the vortex, it is energetically favored for the hole to remain inside the vortex region, contrary to the intuition that the hole should be expelled. However, as we allow the extreme horizon radius to become very large compared to the radius of the vortex, we do find evidence of an instability. This proves that it is energetically unfavorable for a thin vortex to interact with a large extreme black hole. This would seem to dispel the notion that a black hole can support "long" Abelian Higgs hair in the extreme limit. We show that these considerations do not go through in the near-extreme limit. Finally, we discuss the implications for strings that end at black holes, as in the processes where a string snaps by nucleating black holes.