Spectral Energy Distributions of Passive T Tauri Disks: Inclination

We compute spectral energy distributions (SEDs) for passive T Tauri disks viewed at arbitrary inclinations. Semi-analytic models of disks in radiative and hydrostatic equilibrium are employed. Over viewing angles for which the flared disk does not occult the central star, the SED varies negligibly with inclination. For such aspects, the SED shortward of ~80 microns is particularly insensitive to orientation, since short wavelength disk emission is dominated by superheated surface layers which are optically thin. The SED of a nearly edge-on disk is that of a class I source. The outer disk occults inner disk regions, and emission shortward of ~30 microns is dramatically extinguished. Spectral features from dust grains may appear in absorption. However, millimeter wavelength fluxes decrease by at most a factor of 2 from face-on to edge-on orientations. We present illustrative applications of our SED models. The class I source 04108+2803B is considered a T Tauri star hidden from view by an inclined circumstellar disk. Fits to its observed SED yield model-dependent values for the disk mass of ~0.015 solar masses and a disk inclination of ~65 degrees relative to face-on. The class II source GM Aur represents a T Tauri star unobscured by its circumstellar disk. Fitted parameters include a disk mass of \~0.050 solar masses and an inclination of ~60 degrees.Comment: Accepted to ApJ, 20 pages, 7 figures, aaspp4.st

Radiative interactions in laminar duct flows

Analyses and numerical procedures are presented for infrared radiative energy transfer in gases when other modes of energy transfer occur simultaneously. Two types of geometries are considered, a parallel plate duct and a circular duct. Fully developed laminar incompressible flows of absorbing-emitting species in black surfaced ducts are considered under the conditions of uniform wall heat flux. The participating species considered are OH, CO, CO2, and H2O. Nongray as well as gray formulations are developed for both geometries. Appropriate limiting solutions of the governing equations are obtained and conduction-radiation interaction parameters are evaluated. Tien and Lowder's wide band model correlation was used in nongray formulation. Numerical procedures are presented to solve the integro-differential equations for both geometries. The range of physical variables considered are 300 to 2000 K for temperature, 0.1 to 100.0 atm for pressure, and 0.1 to 100 cm spacings between plates/radius of the tube. An extensive parametric study based on nongray formulation is presented. Results obtained for different flow conditions indicate that the radiative interactions can be quite significant in fully developed incompressible flows

On the valuation of fader and discrete barrier options in Heston's Stochastic Volatility Model

We focus on closed-form option pricing in Hestons stochastic volatility model, in which closed-form formulas exist only for few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times. --exotic options,Heston Model,Characteristic Function,Multidimensional Fast Fourier Transforms

Efficient Numerical Methods for Pricing American Options under Lévy Models

Two new numerical methods for the valuation of American and Bermudan options are proposed, which admit a large class of asset price models for the underlying. In particular, the methods can be applied with Lévy models that admit jumps in the asset price. These models provide a more realistic description of market prices and lead to better calibration results than the well-known Black-Scholes model. The proposed methods are not based on the indirect approach via partial differential equations, but directly compute option prices as risk-neutral expectation values. The expectation values are approximated by numerical quadrature methods. While this approach is initially limited to European options, the proposed combination with interpolation methods also allows for pricing of Bermudan and American options. Two different interpolation methods are used. These are cubic splines on the one hand and a mesh-free interpolation by radial basis functions on the other hand. The resulting valuation methods allow for an adaptive space discretization and error control. Their numerical properties are analyzed and, finally, the methods are validated and tested against various single-asset and multi-asset options under different market models

The sparse grid combination technique for quantities of interest

The curse of dimensionality is a major problem for large scale simulations. One way to tackle this problem is the sparse grid combination technique. While a full grid requires O{h_n^{-d}} grid points the sparse grid combination technique needs significantly less points. In contrast to the traditional combination technique, which combines solution functions themselves, this work puts its focus on the combination technique with quantities of interest and their surpluses. After introducing the concept of surpluses that describe how much the solution changes if the grids are refined, we defined the combination technique as a sum of these surpluses. We show how the concept of surpluses can be utilized to deduce error bounds for the quantity of interest and helps to adapt the combination technique to problems with different error models. To improve the error bound we introduce a new extrapolated version of the combination technique and see how the surpluses are affected. To evaluate our theoretical results we perform numerical experiments where we consider integration problems and the gyrokinetic plasma turbulence simulation GENE. The experimental results for the integration problems nicely confirm our derived theoretical results