We survey recent results on the behavior of the Black-Scholes implied volatility at extreme strikes. There are simple and universal formulae that give quantitative links between tail behavior and moment explosions of the underlying on one hand, and growth of the famous volatility smile on the other hand. Some original results are included as well.

Due to the impressive amount of new data provided by the RXTE satellite in the past decade, our knowledge of the phenomenology of accretion onto black holes has increased considerably. In particular, it has been possible to schematize the outburst evolution of transient systems on the basis of their spectral and timing properties, and link them to the ejection of relativistic jets as observed i...

This article studies the behavior of an index It which is assumed to be a tradable security, to satisfy the BSM model dIt/It = μdt + σdWt, and to be efficient in the following sense: we do not expect a prespecified trading strategy whose value is almost surely always nonnegative to outperform the index greatly. The efficiency of the index imposes severe restrictions on its appreciation rate; in...

Given that the options market is now very large and significant part of the trade of financial instruments, the evaluation of pricing of these derivatives becomes very important for regulators as well as market participants. The value of an option can be estimated by using a variety of quantitative techniques based on the concept of risk neutral pricing. In the famous Black-Scholes pricing form...

We study the conditions for 2-dimensional dilaton gravity models to have dynamical formation of black holes and construct all such models. Furthermore we present a parametric representation of the general solutions of the black holes.

In this paper we study the pricing and hedging of arithmetic Asian basket spread options of the European type and present the main results of Deelstra et al. (2008). Asian basket spread options are written on a multivariate underlying. Thus we fi rst need to specify a fi nancial market model containing multiple stocks. We choose to use the famous Black and Scholes model. by: Griselda Deelstra, ...

MANY CLAIM that the mergers, leveraged buyouts, and restructurings in the U.S. corporate sector during the 1980s had a detrimental effect on industrial spending for research and development. Critics of this recent activity point to the stagnation in real R&D expenditures by the private sector during the 1980s and suggest that these restructurings were a major cause of the decline. I Others view...

Previous authors have calculated the mass function of primordial black holes only on scales which are well outside the horizon at the end of inflation. Here we extend the calculation to sub-horizon scales, on which the density perturbation never becomes classical. Regarding the formation of black holes as a ‘measurement’ of the (high peaks) of the density perturbation, we estimate a mass functi...

A modified narrow-width approximation that allows for O(Γ/M)-accurate predictions for resonant particle decay with similar intermediate masses is proposed and applied to MSSM processes to demonstrate its importance for searches for particle physics beyond the Standard Model.