Volatility and dividend risk in perpetual American options

American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and dividend policy-- of the underlaying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because some of the most relevant facts that may potentially affect a firm will entail sharp predictable effects. We will analyse the consequences of this potential risk on perpetual American derivatives, a topic connected with a wide class of recurrent problems in physics: holders of American options must look for the fair price and the optimal exercise strategy at once, a typical question of free absorbing boundaries. We present explicit solutions to the most common contract specifications and derive analytical expressions concerning the mean and higher moments of the exercise time.Comment: 21 pages, 5 figures, iopart, submitted for publication; deep revision, two new appendice

On low-sampling-rate Kramers-Moyal coefficients

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.Comment: 9 pages, 4 figure

Collective behavior of stock price movements in an emerging market

To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack of distinct sector identity in emerging markets is explicitly shown by reconstructing the network of mutually interacting stocks. Spectral analysis of C for NSE reveals that, the few largest eigenvalues deviate from the bulk of the spectrum predicted by random matrix theory, but they are far fewer in number compared to, e.g., NYSE. We show this to be due to the relative weakness of intra-sector interactions between stocks, compared to the market mode, by modeling stock price dynamics with a two-factor model. Our results suggest that the emergence of an internal structure comprising multiple groups of strongly coupled components is a signature of market development.Comment: 10 pages, 10 figure

Promoted Ignition and Burning Tests of Stainless Steel in Flowing and Nonflowing Oxygen

The Industry-Sponsored Metals Combustion Test Program 96-1 was coordinated through Wendell Hull & Associates, Inc. on behalf of several contributing companies, and all design and testing was performed at the NASA White Sands Test Facility. Phase I of this test program studied the threshold pressure for self-sustained burning of various types and sizes of stain less steel rods in nonflowing oxygen, as observed in Standard Test Method for Determining the Combustion Behavior of Metallic Materials in Oxygen-Enriched Atmospheres (ASTM G 124-95). Phase II studied the ignition and propagation of burning of 316L stainless steel rods and pipe in flowing gaseous oxygen. The test sample configurations were chosen to replicate previous promoted ignition and burning tests as well as to represent geometries and cross-sectional thicknesses common in industrial piping applications. The gas pressw'es and velocities for the test matrix were selected to generally compare with CGA G-4.4 guidelines for the use of stain less steel in oxygen service. This paper summarizes the results from the Phase I nonflowing oxygen tests and presents in detail the results of the Phase II flowing oxygen tests. The maximum sample burn-length is shown as a function of test pressure in Phase 1 and also as a function of gas velocity in Phase IT. These results indicate that flowing oxygen, under the given test conditions, significantly affects maximum sample burn length as compared to nonflowing oxygen. Supplementary flowing oxygen test data on stainless steel rods from a follow-up test program are consistent with these results and are presented herein

Coupled continuous time random walks in finance

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between transactions. These two random variables (log-return and waiting time) are typically not independent. For these coupled CTRW models, we can now compute the limiting stochastic process (just like Brownian motion is the limit of a simple random walk), even in the case of heavy tailed (power-law) price jumps and/or waiting times. The probability density functions for this limit process solve fractional partial differential equations. In some cases, these equations can be explicitly solved to yield descriptions of long-term price changes, based on a high-resolution model of individual trades that includes the statistical dependence between waiting times and the subsequent log-returns. In the heavy tailed case, this involves operator stable space-time random vectors that generalize the familiar stable models. In this paper, we will review the fundamental theory and present two applications with tick-by-tick stock and futures data.Comment: 7 pages, 2 figures. Paper presented at the Econophysics Colloquium, Canberra, Australia, November 200

Wigner and Kondo physics in quantum point contacts revealed by scanning gate microscopy

Quantum point contacts exhibit mysterious conductance anomalies in addition to well known conductance plateaus at multiples of 2e^2/h. These 0.7 and zero-bias anomalies have been intensively studied, but their microscopic origin in terms of many-body effects is still highly debated. Here we use the charged tip of a scanning gate microscope to tune in situ the electrostatic potential of the point contact. While sweeping the tip distance, we observe repetitive splittings of the zero-bias anomaly, correlated with simultaneous appearances of the 0.7 anomaly. We interpret this behaviour in terms of alternating equilibrium and non-equilibrium Kondo screenings of different spin states localized in the channel. These alternating Kondo effects point towards the presence of a Wigner crystal containing several charges with different parities. Indeed, simulations show that the electron density in the channel is low enough to reach one-dimensional Wigner crystallization over a size controlled by the tip position

Amnestically induced persistence in random walks

We study how the Hurst exponent $\alpha$ depends on the fraction $f$ of the total time $t$ remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker's position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer's disease and other dementias.Comment: 4 pages, 3 figs, subm. to Phys. Rev. Let

Reaction ⁶Li(p, Δ⁺⁺)⁶He At 1.04 GeV And The Δ−N Interaction

The reaction ⁶Li(p, Δ⁺⁺)⁶He has been studied at 1.04 GeV for transferred momenta ranging from 0.11 to 0.35 (GeV/c)2. An exponential decrease of the cross section is observed. A Glauber-type calculation is presented. The possibility of extracting information on σ(ΔN) and α(ΔN) is discussed

Landau levels and magnetopolaron effect in dilute GaAs:N

The magnetic-field dependence of the energy spectrum of GaAs doped with nitrogen impurities is investigated. Our theoretical model is based on the phenomenological Band Anticrossing Model (BAC) which we extended in order to include magnetic field and electron - phonon interaction. Due to the highly localized nature of the nitrogen state, we find that the energy levels are very different from those of pure GaAs. The polaron correction results in a lower cyclotron resonance energy as compared to pure GaAs. The magneto-absorption spectrum exhibits series of asymmetric peaks close to the cyclotron energy

Spurious trend switching phenomena in financial markets

The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection of price peaks that imposes a condition on the statistics of price change and of trade volumes that skew their distributions. For the intertrade times, the extrema and power laws results from the format of transaction data