At the peak of the tech bubble, only 0.57% of market valuation comes from dividends in the next year. Taking the ratio of total market value to the value of one-year dividends, we obtain a valuation-based duration of 175 years. In contrast, at the height of the global financial crisis, more than 2.2% of market value is from dividends in the next year, implying a duration of 46 years. What drives valuation duration? We find that market participants have limited information about cash flow beyond one year. Therefore, an increase in valuation duration is due to a decrease in the discount rate rather than good news about long-term growth. Accordingly, valuation duration negatively predicts annual market return with an out-of-sample R2 of 15%, robustly outperforming other predictors in the literature. While the price-dividend ratio reflects the overall valuation level, our valuation-based measure of duration captures the slope of the valuation term structure. We show that valuation duration, as a discount rate proxy, is a critical state variable that augments the price-dividend ratio in spanning the (latent) state space for stock-market dynamics.
Traditional art pricing models often lack fine measurements of painting content. This paper proposes a new content measurement: the Shannon information quantity measured by the singular value decomposition (SVD) entropy of the painting image. Using a large sample of artworks' auction records and images, we show that the SVD entropy positively affects the sales price at 1% significance level. Compared to the other commonly adopted content variables, the SVD entropy has advantages in variable significance, sample robustness as well as model fit. Considering the convenient availability of digital painting images and the straightforward calculation algorithm of this measurement, we expect its wide application in future research.
Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this paper, we use the large deviations theory for the analysis of short-maturity Asian options. We present a local volatility model for the underlying market that incorporates a jump term in addition to the drift and diffusion terms. We estimate the asymptotics for the out-of-the-money, in-the-money, and at-the-money short-maturity Asian call and put options. Under appropriate assumptions, we show that the asymptotics for out-of-the-money Asian call and put options are governed by rare events. For the at-the-money Asian options, the result is more involved and in that case, we find the upper and lower bounds of the asymptotics of the Asian option price.
In this paper, we extend the market price of risk for delivery periods (MPDP) of electricity swap contracts by introducing a dimension for jump risk. As introduced by Kemper et al. (2022), the MPDP arises through the use of geometric averaging while pricing electricity swaps in a geometric framework. We adjust the work by Kemper et al. (2022) in two directions: First, we examine a Merton type model taking jumps into account. Second, we transfer the model to the physical measure by implementing mean-reverting behavior. We compare swap prices resulting from the classical arithmetic (approximated) average to the geometric weighted average. Under the physical measure, we discover a decomposition of the swap's market price of risk into the classical one and the MPDP.
During the last four decades, digital technologies have disrupted many industries. Car control systems have gone from mechanical to digital. Telephones have changed from sound boxes to portable computers. But have the firms that digitized their products and services become more valuable than firms that didn’t? Here we introduce the construct of digital proximity, which considers the interdependent activities of firms linked in an economic network. We then explore how the digitization of products and services affects a company’s Tobin’s q—the ratio of market value over assets—a measure of the intangible value of a firm. Our panel regression methods and robustness tests suggest the positive influence of a firm’s digital proximity on its Tobin’s q. This implies that firms able to come closer to the digital sector have increased their intangible value compared to those that have failed to do so. These findings contribute a new way of measuring digitization and its impact on firm performance that is complementary to traditional measures of information technology (IT) intensity.
D. Vernooy, Vladimir S. Ilchenko, H. Mabuchi
et al.
Measurements of the quality factor Q approximately 8x10(9) are reported for the whispering-gallery modes (WGM's) of quartz microspheres for the wavelengths 670, 780, and 850 nm; these results correspond to finesse f approximately 2.2x10(6) . The observed independence of Q from wavelength indicates that losses for the WGM's are dominated by a mechanism other than bulk absorption in fused silica in the near infrared. Data obtained by atomic force microscopy combined with a simple model for surface scattering suggest that Q can be limited by residual surface inhomogeneities. Absorption by absorbed water can also explain why the material limit is not reached at longer wavelengths in the near infrared.
In clinical practice, physicians make a series of treatment decisions over the course of a patient's disease based on his/her baseline and evolving characteristics. A dynamic treatment regime is a set of sequential decision rules that operationalizes this process. Each rule corresponds to a decision point and dictates the next treatment action based on the accrued information. Using existing data, a key goal is estimating the optimal regime, that, if followed by the patient population, would yield the most favorable outcome on average. Q- and A-learning are two main approaches for this purpose. We provide a detailed account of these methods, study their performance, and illustrate them using data from a depression study.
For H. Exton's q-analogue of the Bessel function (going back to W. Hahn in a special case, but different from F. H. Jackson's q-Bessel functions) we derive Hansen-Lommel type orthogonality relations, which, by a symmetry, turn out to be equivalent to orthogonality relations which are q-analogues of the Hankel integral transform pair. These results are implicit, in the context of quantum groups, in a paper by Vaksman and Korogodskii. As a specialization we get q-cosines and q-sines which admit q-analogues of the Fourier-cosine and Fourier-sine transforms
In this paper we study the theory Q. We prove a basic result that says that, in a sense explained in the paper, Q can be split into two parts. We prove some consequences of this result. (i) Q is not a poly-pair theory. This means that, in a strong sense, pairing cannot be defined in Q. (ii) Q does not have the Pudlák Property. This means that there two interpretations of $$\mathsf{S}^1_2$$S21 in Q which do not have a definably isomorphic cut. (iii) Q is not sententially equivalent with $$\mathsf{PA}^-$$PA-. This tells us that we cannot do much better than mutual faithful interpretability as a measure of sameness of Q and $$\mathsf{PA}^-$$PA-. We briefly consider the idea of characterizing Q as the minimal-in-some-sense theory of some kind modulo some equivalence relation. We show that at least one possible road towards this aim is closed.
Optical microresonators hold great potential for many fields of research and technology. However, due to their small dimensions typical microresonators exhibit a large frequency spacing between resonances and a limited tunability. This impedes their use in a large class of applications which either require a resonance of the microcavity to coincide with a predetermined frequency, e.g., an optical transition in atoms, or a tailored frequency spacing between resonances, e.g., for the generation of optical frequency combs. Here, we present a fully tunable ultra-high-Q whispering-gallery-mode “bottle microresonator”, fabricated from standard optical glass fibres. Due to its highly prolate shape, the bottle microresonator gives rise to a class of whispering-gallery-modes (WGMs) with advantageous properties, see Fig. 1. In addition to the radial confinement by continuous total internal reflection at the resonator surface, the light in these “bottle modes” oscillates back and forth along the resonator axis between two turning-points which are defined by an angular momentum barrier [1]. The resulting axial standing wave structure can be compared to the one observed in Fabry-Pérot microresonators.