Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.     

Asymmetric total synthesis of the indole alkaloid cyclopiazonic acid and first structure-activity data

The indole alkaloid α-cyclopiazonic acid (CPA) is one of the few known inhibitors of sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) besides the terpenoids thapsigargin and artemisinin. We report here the first asymmetric total synthesis of cyclopiazonic acid by a modification of the Knight synthesis, currently the most efficient route to CPA. First structure-activity data of CPA derivatives and stereoisomers are presented and will be discussed in connection with the published crystal structures of CPA-SERCA complexes.     

Synthesis and characterisation of the SrxBa1−xFeO3−y-system and the fluorinated phases SrxBa1−xFeO2F

Compounds in the system Sr_xBa_1?xFeO_3?y have been prepared under different partial pressures of oxygen. In this system, different perovskite-type structures are found depending highly on the values of x and y. Fluorination using polyvinylidenedifluoride (PVDF) gives oxyfluoride materials of composition Sr_xBa_1?xFeO₂F, which normally crystallize in the cubic perovskite structure. Rietveld refinement results provide information about the packing density for oxide and oxyfluoride samples and allow a general comparison between these two different types of materials. Furthermore, the determination of the average iron oxidation state also showed that the oxygen deficiency, y, depends significantly on the value of x and the structure determined by the Sr/Ba ratio.     

Lexicographic products with high reconstruction numbers

The reconstruction number of a graph is the smallest number of vertex-deleted subgraphs needed to uniquely determine the graph up to isomorphism. Bollobás showed that almost all graphs have reconstruction number equal to three. McMullen and Radziszowski published a catalogue of all graphs on at most ten vertices with reconstruction number greater than three. We introduce constructions that generalize the examples identified in their work. In particular, we use lexicographic products of vertex transitive graphs with certain starter graphs from the work of Myrvold and from the work of Harary and Plantholt to generate new infinite families of graphs with high reconstruction numbers. In the process, we settle a question of McMullen and Radziszowski.     

Variational dimension of random sequences and its application

A concept of variational dimension is introduced for a random sequence with stationary increments. In the Gaussian case, the variational dimension in the limit coincides with the Hausdorff dimension of a proper random process. Applications of the concept are illustrated by examples of neurological data and network traffic analysis.     

Vase‐Kite Equilibrium of Resorcin[4]arene Cavitands Investigated Using Molecular Dynamics Simulations with Ball‐and‐Stick Local Elevation Umbrella Sampling

A key feature of resorcin[4]arene cavitands is their ability to switch between a closed/contracted (Vase ) and an open/expanded (Kite ) conformation. The mechanism and dynamics of this interconversion remains, however, elusive. In the present study, the Vase ‐Kite transitions of a quinoxaline‐based and of a dinitrobenzene‐based resorcin[4]arene are investigated using molecular dynamics (MD) simulations in three environments (vacuum, chloroform, and toluene) and at three temperatures (198.15, 248.15, and 298.15 K). The challenge of sampling the Vase ‐Kite transition, which occurs experimentally on the millisecond time scale, is overcome by calculating relative free energies using ball‐and stick local elevation umbrella sampling (B&S‐LEUS) to enhance the statistics on the relevant states and to promote interconversion transitions. Associated unbiased MD simulations also evidence for the first time a complete Vase ‐to‐Kite transition, as well as transitions between degenerate Kite 1 and Kite 2 forms and solvent‐exchange events. The calculated Vase ‐to‐Kite free‐energy changes ΔG are in qualitative agreement with the experimental magnitudes and trends. The level of quantitative agreement is, however, limited by the force‐field accuracy and, in particular, by the approximate treatment of intramolecular interactions at the classical level. The results are in line with a less stable Vase state for the dinitrobenzene compared to the quinoxaline compound, and a negative entropy change ΔS for the Vase ‐to‐Kite transition of the latter compound. Relative free energies calculated for intermediates also suggest that the Vase ‐Kite transition does not follow a concerted mechanism, but an asynchronous one with sequential opening of the flaps. In particular, the conformation involving two adjacent flaps open in a parallel direction (cis‐p) represents a likely intermediate, which has not been observed experimentally to date.