Lookback option pricing using the Fourier transform B-spline method

We derive a new, efficient closed-form formula approximating the price of discrete lookback options, whose underlying asset price is driven by an exponential semimartingale process, which includes (jump) diffusions, Lévy models, affine processes and other models. The derivation of our pricing formula is based on inverting the Fourier transform using B-spline approximation theory. We give an error bound for our formula and establish its fast rate of convergence to the true price. Our method provides lookback option prices across the quantum of strike prices with greater efficiency than for a single strike price under existing methods. We provide an alternative proof to the Spitzer formula for the characteristic function of the maximum of a discretely observed stochastic process, which yields a numerically efficient algorithm based on convolutions. This is an important result which could have a wide range of applications in which the Spitzer formula is utilized. We illustrate the numerical efficiency of our algorithm by applying it in pricing fixed and floating discrete lookback options under Brownian motion, jump diffusion models, and the variance gamma process

Improving simultaneous saccharification and co-fermentation of pretreated wheat straw using both enzyme and substrate feeding

<p>Abstract</p> <p>Background</p> <p>Simultaneous saccharification and co-fermentation (SSCF) has been recognized as a feasible option for ethanol production from xylose-rich lignocellulosic materials. To reach high ethanol concentration in the broth, a high content of water-insoluble solids (WIS) is needed, which creates mixing problems and, furthermore, may decrease xylose uptake. Feeding of substrate has already been proven to give a higher xylose conversion than a batch SSCF. In the current work, enzyme feeding, in addition to substrate feeding, was investigated as a means of enabling a higher WIS content with a high xylose conversion in SSCF of a xylose-rich material. A recombinant xylose-fermenting strain of <it>Saccharomyces cerevisiae </it>(TMB3400) was used for this purpose in fed-batch SSCF experiments of steam-pretreated wheat straw.</p> <p>Results</p> <p>By using both enzyme and substrate feeding, the xylose conversion in SSCF could be increased from 40% to 50% in comparison to substrate feeding only. In addition, by this design of the feeding strategy, it was possible to process a WIS content corresponding to 11% in SSCF and obtain an ethanol yield on fermentable sugars of 0.35 g g^-1.</p> <p>Conclusion</p> <p>A combination of enzyme and substrate feeding was shown to enhance xylose uptake by yeast and increase overall ethanol yield in SSCF. This is conceptually important for the design of novel SSCF processes aiming at high-ethanol titers. Substrate feeding prevents viscosity from becoming too high and thereby allows a higher total amount of WIS to be added in the process. The enzyme feeding, furthermore, enables keeping the glucose concentration low, which kinetically favors xylose uptake and results in a higher xylose conversion.</p

A novel hybrid organosolv: steam explosion method for the efficient fractionation and pretreatment of birch biomass

Background: The main role of pretreatment is to reduce the natural biomass recalcitrance and thus enhance sac- charification yield. A further prerequisite for efficient utilization of all biomass components is their efficient fractiona- tion into well-defined process streams. Currently available pretreatment methods only partially fulfill these criteria. Steam explosion, for example, excels as a pretreatment method but has limited potential for fractionation, whereas organosolv is excellent for delignification but offers poor biomass deconstruction. Results: In this article, a hybrid method combining the cooking and fractionation of conventional organosolv pre - treatment with the implementation of an explosive discharge of the cooking mixture at the end of pretreatment was developed. The effects of various pretreatment parameters (ethanol content, duration, and addition of sulfuric acid) were evaluated. Pretreatment of birch at 200 °C with 60% v/v ethanol and 1% w/w biomass H 2 SO 4 was proven to be the most efficient pretreatment condition yielding pretreated solids with 77.9% w/w cellulose, 8.9% w/w hemicellulose, and 7.0 w/w lignin content. Under these conditions, high delignification of 86.2% was demonstrated. The recovered lignin was of high purity, with cellulose and hemicellulose contents not exceeding 0.31 and 3.25% w/w, respectively, and ash to be < 0.17% w/w in all cases, making it suitable for various applications. The pretreated solids presented high saccharification yields, reaching 68% at low enzyme load (6 FPU/g) and complete saccharification at high enzyme load (22.5 FPU/g). Finally, simultaneous saccharification and fermentation (SSF) at 20% w/w solids yielded an ethanol titer of 80 g/L after 192 h, corresponding to 90% of the theoretical maximum. Conclusions: The novel hybrid method developed in this study allowed for the efficient fractionation of birch biomass and production of pretreated solids with high cellulose and low lignin contents. Moreover, the explosive dis- charge at the end of pretreatment had a positive effect on enzymatic saccharification, resulting in high hydrolyzability of the pretreated solids and elevated ethanol titers in the following high-gravity SSF. To the best of our knowledge, the ethanol concentration obtained with this method is the highest so far for birch biomass

Ecodesign and the Circular Economy: Conflicting Policies in Europe

The number of policies that address the various life cycle environmental impacts of products are increasing, especially in Europe. With the rise of the Circular Economy (CE) concept, the traditional product policies have been supported by new ones that pursue new policy objectives such as increasing product lifetimes and encourage more repairs. In this contribution we discuss principles for improving synergies and reduce conflicts among different product policies. We then outline some of the recent conflicts between policies that have emerged in the context of the CE. We conclude that often the conflicts can be mitigated, or that it is possible to reach a compromise. However, we need to accept that in many cases there is no solution that will satisfy all involved stakeholders