Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities

We present new numerical schemes for pricing perpetual Bermudan and American options as well as α-quantile options. This includes a new direct calculation of the optimal exercise boundary for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener–Hopf method. Our direct calculation of the price of α-quantile options combines for the first time the Dassios–Port–Wendel identity and the Spitzer identities for the extrema of processes. Our results show that the new pricing methods provide excellent error convergence with respect to computational time when implemented with a range of Lévy processes

Hilbert transform, spectral filters and option pricing

We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maximum or the minimum of a random path, or the joint distribution at maturity with the extrema staying below or above barriers. We use as examples the methods by Feng and Linetsky (Math Finance 18(3):337–384, 2008) and Fusai et al. (Eur J Oper Res 251(4):124–134, 2016) to price discretely monitored barrier options where the underlying asset price is modelled by an exponential Lévy process. Both methods show exponential convergence with respect to the number of grid points in most cases, but are limited to polynomial convergence under certain conditions. We relate these rates of convergence to the Gibbs phenomenon for Fourier transforms and achieve improved results with spectral filtering

Fluctuation identities with continuous monitoring and their application to the pricing of barrier options

We present a numerical scheme to calculate fluctuation identities for exponential Lévy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential Lévy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener–Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-z domain) as the monitoring time step approaches zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme

Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS2_2 using multiphoton microscopy

We report second- and third-harmonic generation in monolayer MoS$_\mathrm{2}$ as a tool for imaging and accurately characterizing the material's nonlinear optical properties under 1560 nm excitation. Using a surface nonlinear optics treatment, we derive expressions relating experimental measurements to second- and third-order nonlinear sheet susceptibility magnitudes, obtaining values of $|\chi_s^{(2)}|=2.0\times10^{-20}$ m$^2$ V$^{-1}$ and for the first time for monolayer MoS$_\mathrm{2}$, $|\chi_s^{(3)}|=1.7\times10^{-28}$ m$^3$ V$^{-2}$. These sheet susceptibilities correspond to effective bulk nonlinear susceptibility values of $|\chi_{b}^{(2)}|=2.9\times10^{-11}$ m V$^{-1}$ and $|\chi_{b}^{(3)}|=2.4\times10^{-19}$ m$^2$ V$^{-2}$, accounting for the sheet thickness. Experimental comparisons between MoS$_\mathrm{2}$ and graphene are also performed, demonstrating $\sim$3.4 times stronger third-order sheet nonlinearity in monolayer MoS$_\mathrm{2}$, highlighting the material's potential for nonlinear photonics in the telecommunications C band.Comment: Accepted by 2D Materials, 28th Oct 201

Self-Pulsating Semiconductor Lasers: Theory and Experiment

We report detailed measurements of the pump-current dependency of the self-pulsating frequency of semiconductor CD lasers. A distinct kink in this dependence is found and explained using rate-equation model. The kink denotes a transition between a region where the self-pulsations are weakly sustained relaxation oscillations and a region where Q-switching takes place. Simulations show that spontaneous emission noise plays a crucial role for the cross-over.Comment: Revtex, 16 pages, 7 figure

Effective thermal conductivity of a thin composite material

The thermal conductivity of a randomly oriented composite material is modeled using a probabilistic approach in order to determine if a size effect exists for the thermal conductivity at small composite thickness. The numerical scheme employs a random number generator to position the filler elements, which have a relatively high thermal conductivity, within a matrix having a relatively low thermal conductivity. Results indicate that, below some threshold thickness, the composite thermal conductivity increases with decreasing thickness, while above the threshold the thermal conductivity is independent of thickness. The threshold thickness increases for increasing filler fraction and increasing k{sub f}/k{sub m}, the ratio between filler and matrix thermal conductivities

New county records of three Baptisia species in Arkansas, with an updated distribution map

New county records of three Baptisia species are reported in Arkansas, together with an updated distribution map

Applicability of Nanofluids in High Flux Solar Collectors

Concentrated solar energy has become the input for an increasing number of experimental and commercial thermal systems over the past 10-15 years [M. Thirugnanasambandam et al., Renewable Sustainable Energy Rev. 14 (2010)]. Recent papers have indicated that the addition of nanoparticles to conventional working fluids (i.e., nanofluids) can improve heat transfer and solar collection [H. Tyagi et al., J. Sol. Energy Eng. 131, 4 (2009); P. E. Phelan et al., Annu. Rev. Heat Transfer 14 (2005)]. This work indicates that power tower solar collectors could benefit from the potential efficiency improvements that arise from using a nanofluid working fluid. A notional design of this type of nanofluid receiver is presented. Using this design, we show a theoretical nanofluid enhancement in efficiency of up to 10% as compared to surface-based collectors when solar concentration ratios are in the range of 100-1000. Furthermore, our analysis shows that graphite nanofluids with volume fractions on the order of 0.001% or less are suitable for 10-100 MW(e) power plants. Experiments on a laboratory-scale nanofluid dish receiver suggest that up to 10% increase in efficiency is possible (relative to a conventional fluid)-if operating conditions are chosen carefully. Lastly, we use these findings to compare the energy and revenue generated in a conventional solar thermal plant to a nanofluid-based one. It is found that a 100 MW(e) capacity solar thermal power tower operating in a solar resource similar to Tucson, AZ, could generate similar to$ 3.5 million more per year by incorporating a nanofluid receiver. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3571565