A Comparative Study of American Option Valuation and Computation

For many practitioners and market participants, the valuation of financial derivatives is considered of very high importance as its uses range from a risk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods for valuing financial derivatives such as American options. A closed form analytical solution for American options has been very difficult to obtain due to the different boundary conditions imposed on the valuation problem. Following the method of solving the American option as a free boundary problem in the spirit of the "no-arbitrage" pricing framework of Black-Scholes, the option price and hedging parameters can be represented as an integral equation consisting of the European option value and an early exercise value dependent upon the optimal free boundary. Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accurate but inefficient, or accuracy has been compensated for computational speed. A new numerical approach to the valuation of American options by cubic splines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made to the behaviour of the American option's early exercise boundary with other pricing models

Comparing symptoms and emotion recognition in African American and White samples with schizophrenia

Racial status has an important role in schizophrenia, with African American samples being rated lower than White participants on a range of constructs. In many studies, however, demographic factors are not accounted for. In the present study, African American (n = 106) and White participants (n = 81) were compared on symptom severity and emotion recognition scales while controlling for other demographic factors. Contrary to our hypothesis, there were no differences in symptoms between racial groups. However, White participants performed better on an emotion recognition measure than African Americans. These differences were most prominent in response to negatively-valenced stimuli. This study replicated previous findings of racial differences in emotion recognition but not symptom severity. Future research should assess the role of racial identity on symptom severity. In addition, further research is needed to assess if utilising multi-ethnic stimuli improves performance by racial minorities on emotion recognition measures

Avalanches in Breakdown and Fracture Processes

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.Comment: 15 pages, 12 figures, submitted to Phys. Rev. E, corrected typo in authors name, no changes to the pape

Development of extinction imagers for the determination of atmospheric optical extinction: final report

The primary goals of this project for JTO and ONR (Grant N00014-07-1-1060) were to further develop Extinction Imagers for use in the ocean environment, and to extend the capabilities into the Short Wave IR (SWIR). Extinction Imaging is a method for determining the effective extinction coefficient over an extended path using a sensor at one end of the path. It uses calibrated imagers to acquire the relative radiance of a dark target near the other the end of the path and the horizon sky in the direction of the dark target. It is completely passive and thus covert, and the hardware is robust and relatively inexpensive. It uses rigorous equations, which determine the extinction coefficient from the measured apparent contrast of the radiance of the dark target with respect to the horizon sky. The project was very successful. We found that the ocean surface could readily be used as a dark target in red and SWIR wavelengths. Both the red and the SWIR measurement results were excellent for daytime. Comparisons with standard instruments, as well as uncertainty analysis, indicated that extinction imagers provide better measurements of the atmospheric extinction losses over extended paths than other methods of which we are aware. Our secondary goals were to address the night regime, and to address slanted paths above the horizontal. Regarding night, we found that the visible sensor acquired excellent data, but the ocean surface was not a good dark target in our wavelengths. Recommendations on the handling of night are given in the report. Regarding the lines of sight above the horizon, we developed a slant path algorithm that determines beam transmittance. It performed very well. Recommendations are made regarding integration of these techniques for military applications.Joint Technology Office via Office of Naval ResearchGrant N00014-07-1-106

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state

Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach

Using a liquid-state approach based on Ornstein-Zernike equations, we study the behavior of a fluid inside a porous disordered matrix near the liquid-gas critical point.The results obtained within various standard approximation schemes such as lowest-order $\gamma$-ordering and the mean-spherical approximation suggest that the critical behavior is closely related to that of the random-field Ising model (RFIM).Comment: 10 pages, revtex, to appear in Physical Review Letter

Positron Emission Tomography/Computed Tomography with Gallium-68-labeled Prostate-specific Membrane Antigen Detects Relapse After Vascular-targeted Photodynamic Therapy in a Prostate Cancer Model

BACKGROUND: Evaluating the efficacy of focal therapy for prostate cancer is limited by current approaches and may be improved with biological imaging techniques. OBJECTIVE: We assessed whether positron emission tomography/computed tomography with gallium-68-labeled prostate-specific membrane antigen (Ga-PSMA PET/CT) can be used to predict relapse after vascular-targeted photodynamic therapy (VTP). DESIGN, SETTING, AND PARTICIPANTS: A total of 1×10 LNCaP cells were grafted subcutaneously in the flanks of 6-8-wk-old SCID mice. Of 24 mice with measurable tumors 6 wk after tumor implantation, 20 were treated with VTP (150mW/cm) to ablate the tumors. Blood prostate-specific antigen (PSA) levels were assessed, and ⁶⁸Ga-PSMA PET/CT images were performed 1 d before VTP and 1 and 4 wk after. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: Local tumor relapse was evaluated by histology, and tumors were analyzed by prostate-specific membrane antigen (PSMA) and PSA immunohistochemistry. T tests and Kruskal-Wallis tests were used to determine significance. RESULTS AND LIMITATIONS: Four weeks after VTP, 11 (65%) mice had complete responses and six (35%) had tumor relapses confirmed by histology (hematoxylin and eosin, and PSMA immunohistochemistry). All mice with local relapse had positive Ga-PSMA PET/CT findings 4 wk after VTP; all complete responders did not. One week after VTP, the relapse detection sensitivity of Ga-PSMA PET/CT was 75%, whereas the sensitivity of PSA was only 33%. Compared with controls, relapsed tumors had a three-fold reduction in the number of cells with strong PSA staining by immunohistochemistry (1.5% vs 4.5%; p=0.01). CONCLUSIONS: In a preclinical prostate cancer model, we show that Ga-PSMA PET/CT can identify and predict relapse earlier than blood PSA level. These findings support further testing in clinical trials. PATIENT SUMMARY: Positron emission tomography/computed tomography with gallium-68-labeled prostate-specific membrane antigen may be used to follow and evaluate treatment outcomes in men who receive focal therapy for prostate cancer

Weather Avoidance Guidelines for NASA Global Hawk High-Altitude Unmanned Aircraft Systems (UAS)

The current Global Hawk flight rules would probably not have been effective in the single event of greatest concern (the Emily encounter). The cloud top had not reached 50,000 ft until minutes before the encounter. The TOT and lightning data would not have been available until near the overflight time since this was a rapidly growing cell. This case would have required a lastminute diversion when lightning became frequent. Avoiding such a cell probably requires continual monitoring of the forward camera and storm scope, whether or not cloud tops have been exceeding specific limits. However, the current overflight rules as strictly interpreted would have prohibited significant fractions of the successful Global Hawk overpasses of Karl and Matthew that proved not to be hazardous. Many other high altitude aircraft (ER2 and Global Hawk) flights in NASA tropical cyclone field programs have successfully overflown deep convective clouds without incident.The convective cell that caused serious concern about the safety of the ER2 in Emily was especially strong for a tropical cyclone environment, probably as strong or stronger than any that was overflown by the ER2 in 20 previous flights over tropical cyclones. Specifically, what made that cell a safety concern was the magnitude of the vertical velocity of the updraft, at least 20 m/s (4000 ft/minute) at the time the ER2 overflew it. Such a strong updraft can generate strong gravity waves at and above the tropopause, posing a potential danger to aircraft far above the maximum altitude of the updraft itself or its associated cloud top. Indeed, the ER2 was probably at least 9000 ft above that cloud top. Cloudtop height, by itself, is not an especially good indicator of the intensity of convection and the likelihood of turbulence. Nor is overflying high cloud tops (i.e. > 50,000 ft) of particular concern unless there is other evidence of very strong convective updrafts beneath those tops in the path of the aircraft. center dot Lightning, especially lightning with a high flash rate, is well correlated with convective intensity. Lightning with a minimal flash rate (say 13 flashes per minute) is indicative of updraft speeds of about 10 m/s in the mixed phase region where charge is being separated, generally at altitudes about 2025 kft in a hurricane. That is still stronger than typical updrafts (more like 5 m/s). An unresolved issue is whether there is a high and instantaneous correlation between vertical velocity in the middle troposphere (necessary for lightning generation) and near cloud top (more direct concern for overflights)

Clusters and Fluctuations at Mean-Field Critical Points and Spinodals

We show that the structure of the fluctuations close to spinodals and mean-field critical points is qualitatively different than the structure close to non-mean-field critical points. This difference has important implications for many areas including the formation of glasses in supercooled liquids. In particular, the divergence of the measured static structure function in near-mean-field systems close to the glass transition is suppressed relative to the mean-field prediction in systems for which a spatial symmetry is broken.Comment: 5 pages, 1 figur