Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing

Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately and in real-time. Among the growing literature addressing this problem, Gass et al. [Finance Stoch., 22 (2018), pp. 701--731] propose a complexity reduction technique for parametric option pricing based on Chebyshev interpolation. As the number of parameters increases, however, this method is affected by the curse of dimensionality. In this article, we extend this approach to treat high-dimensional problems: Additionally, exploiting low-rank structures allows us to consider parameter spaces of high dimensions. The core of our method is to express the tensorized interpolation in the tensor train format and to develop an efficient way, based on tensor completion, to approximate the interpolation coefficients. We apply the new method to two model problems: American option pricing in the Heston model and European basket option pricing in the multidimensional Black--Scholes model. In these examples, we treat parameter spaces of dimensions up to 25. The numerical results confirm the low-rank structure of these problems and the effectiveness of our method compared to advanced techniques

Phytochemical and biological characterization of dry outer scales extract from Tropea red onion (Allium cepa L. var. Tropea)–A promising inhibitor of pancreatic lipase

Background: Allium cepa L. var. Tropea is typically cultivated in Calabria (Italy) and it is certified as “Cipolla Rossa di Tropea Calabria-PGI” (Tropea red onion). The use of clinically available anti-obesity drugs such as Orlistat is being gradually dismissed due to their side-effects and this has encouraged the search for alternative inhibitors of intestinal lipases such as phytochemicals showing less side-effects. In this study we aimed to evaluate for the first time the anti-obesity potential of the hydroalcoholic extract from the dry outer scales of Tropea red onion by the assesment of its capacity to inhibit pancreatic lipase. Its possible mechanism of action was also studied with planar lipid membranes (PLMs) surrogate of intestinal membranes. Methods: Specialized metabolites in the extract were determined by GC–MS, HPLC-DAD, HPLC-UV-DAD and HPLC-HRMS analyses. Inhibition of pancreatic lipase was studied in vitro against crude lipase Type II from porcine pancreas. PLMs used in the electrophysiology measurements were made up of DOPS:DOPE:POPC. Results: The extract contained quercetin-4′-O-glucoside, quercetin and quercetin-3,4′-O-diglucoside as the most abundant phenolics. Among apolar constituents, γ-sitosterol, linoleic and stearic acids were dominant. The lipase inhibitory effect of the extract had an IC50 value equal to 0.77±0.03 mg/mL (positive control, IC50 = 0.018 mg/mL). The electrophysiological study demonstrated that the extract is able to incorporate into PLMs and to form transient channel-like events Conclusions: Taken altogether, the results allow us to suggest that the hydroalcoholic extract from the dry outer scales of Tropea red onion could prevent lipid ester hydrolysis and it has a protective effect against phospholipase as found for interfacially active compounds

Chemical Composition of and Inhibition of Angiotensin-Converting Enzyme by Senecio samnitum huet

Abstract Extracts of Senecio samnitum Huet and derived methyl ester of chlorogenic acid have been shown to inhibit angiotensin-converting enzyme (ACE) by using an in vitro bioassay based on the enzymatic cleavage of the chromophore-fluorophore labeled substrate dansyltriglycine into dansylglycine, which is quantitatively measured by high-performance liquid chromatography (HPLC). GC=MS and NMR identified compounds present within the studied S. samnitum extracts. The most effective fraction was obtained in ethyl acetate, which gave 52.56 AE 0.23% (SD) inhibition at 300 mg=ml. The major constituent of this fraction, the methyl ester of chlorogenic acid, showed significant ACE inhibition of 56.78 AE 0.25% at a concentration of 82.5 mg=ml

Influence of the environmental factors on chemical composition and biological activity of bergamot (Citrus bergamia Risso)

Oil of bergamot is receiving renewed popularity in aromatherapy. The biovariability of Citrus bergamia grown wild in Calabria (Italy) was investigated as far as chemical markers (linalool, linalyl acetate and bergapten) content and antioxidant and antifungal activities of the methanolic extracts. The average content in the markers presents slight variations with the altitude and more evident changes with the latitude of the areas of plant collection

In vitro antioxidant effect and inhibition of alpha-amylase of two varieties of Amaranthus caudatus seeds

This study reports on the biological properties, antioxidant and antidiabetic, of two varieties of Amaranthus caudatus seeds, Oscar blanco and Victor red. Oil, squalene and phenolic contents were also determined. Seeds of both investigated varieties were found to possess very different levels of squalene (2.2% in Oscar blanco variety and 7.5% in Victor red variety). Although the antioxidant activity of A. caudatus var. Oscar blanco and A. caudatus var. Victor red statistically did not differ significantly from each other (IC50 values of ethyl acetate extracts were 0.50 mg/ml and 0.62 mg/ml, respectively), significant differences were noticed in relation to antidiabetic activity (inhibition of a-amylase, EC 3.2.1.1) of methanolic extracts that showed 50.5% for A. caudatus var. Oscar blanco and 28% for A. caudatus var. Victor red at concentration of 25m g/ml

Hypericum perforatum: Influences of the habitat on chemical composition, photo-induced cytotoxicity, and antiradical activity

Context: Hypericin, isolated from Hypericum perforatum L. and about another 300 Hypericum species (Guttiferae), is one of the most powerful photosensitizers found in nature. Objective: The aim of this study was to assess the variability of chemical composition and biological activities of four H. perforatum samples, collected at different altitudes in the South Apennine of Italy. Materials and methods: MTT assay was used to evaluate the antiproliferative activity of different samples concentrations (0.6–100 µg/mL) after irradiation at 365 nm. The inhibition of nitric oxide production was evaluated after 24 h of incubation using the macrophage cell line RAW 264.7 and sample solutions ranging from 12.5 to 1000 µg/mL. Antioxidant activities were evaluated using 2,2-diphenyl-1-picrylhydrazyl (DPPH) assay and β-carotene bleaching test (ranges were 12.5–1000 and 1–400 µg/mL, respectively). Chemical composition was evaluated through HPTLC, and different contents of hypericin and rutin have been observed. Results: The most phototoxic sample was collected from Zumpano (no. 1 at 370 m), with IC50 values of 24.61 ± 0.02 μg/mL. Sample no. 1 showed also the best radical scavenging activity (IC50 value of 9.18 ± 0.03 μg/mL) and the best antioxidant activity (IC50 value of 10.04 ± 0.03 μg/mL after 30 min of incubation). Best activity of extract no. 1 was well in accordance with chemical data, including the phenolic total content and particular metabolome profile. Discussion and conclusion: This paper confirms the usefulness in maintaining the exploration of H. perforatum activities, in order to confirm its potentiality as a multipurpose plant