Hierarchical adaptive sparse grids and quasi Monte Carlo for option pricing under the rough Bergomi model

The rough Bergomi (rBergomi) model, introduced recently in [4], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet exhibits remarkable fit to empirical implied volatility surfaces. In the absence of analytical European option pricing methods for the model, and due to the non-Markovian nature of the fractional driver, the prevalent option is to use the Monte Carlo (MC) simulation for pricing. Despite recent advances in the MC method in this context, pricing under the rBergomi model is still a timeconsuming task. To overcome this issue, we design a novel, hierarchical approach, based on i) adaptive sparse grids quadrature (ASGQ), and ii) quasi Monte Carlo (QMC). Both techniques are coupled with Brownian bridge construction and Richardson extrapolation. By uncovering the available regularity, our hierarchical methods demonstrate substantial computational gains with respect to the standard MC method, when reaching a sufficiently small relative error tolerance in the price estimates across different parameter constellations, even for very small values of the Hurst parameter. Our work opens a new research direction in this field, i.e., to investigate the performance of methods other than Monte Carlo for pricing and calibrating under the rBergomi model

Hierarchical adaptive sparse grids and quasi Monte Carlo for option pricing under the rough Bergomi model

The rough Bergomi (rBergomi) model, introduced recently in [4], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet exhibits remarkable fit to empirical implied volatility surfaces. In the absence of analytical European option pricing methods for the model, and due to the non-Markovian nature of the fractional driver, the prevalent option is to use the Monte Carlo (MC) simulation for pricing. Despite recent advances in the MC method in this context, pricing under the rBergomi model is still a timeconsuming task. To overcome this issue, we design a novel, hierarchical approach, based on i) adaptive sparse grids quadrature (ASGQ), and ii) quasi Monte Carlo (QMC). Both techniques are coupled with Brownian bridge construction and Richardson extrapolation. By uncovering the available regularity, our hierarchical methods demonstrate substantial computational gains with respect to the standard MC method, when reaching a sufficiently small relative error tolerance in the price estimates across different parameter constellations, even for very small values of the Hurst parameter. Our work opens a new research direction in this field, i.e., to investigate the performance of methods other than Monte Carlo for pricing and calibrating under the rBergomi model

Numerical smoothing with hierarchical adaptive sparse grids and quasi-Monte Carlo methods for efficient option pricing

When approximating the expectation of a functional of a stochastic process, the efficiency and performance of deterministic quadrature methods, such as sparse grid quadrature and quasi-Monte Carlo (QMC) methods, may critically depend on the regularity of the integrand. To overcome this issue and reveal the available regularity, we consider cases in which analytic smoothing cannot be performed, and introduce a novel numerical smoothing approach by combining a root finding algorithm with one-dimensional integration with respect to a single well-selected variable. We prove that under appropriate conditions, the resulting function of the remaining variables is a highly smooth function, potentially affording the improved efficiency of adaptive sparse grid quadrature (ASGQ) and QMC methods, particularly when combined with hierarchical transformations (i.e., Brownian bridge and Richardson extrapolation on the weak error). This approach facilitates the effective treatment of high dimensionality. Our study is motivated by option pricing problems, and our focus is on dynamics where the discretization of the asset price is necessary. Based on our analysis and numerical experiments, we show the advantages of combining numerical smoothing with the ASGQ and QMC methods over ASGQ and QMC methods without smoothing and the Monte Carlo approach

Dynamics of Diblock Copolymers in Dilute Solutions

We consider the dynamics of freely translating and rotating diblock (A-B), Gaussian copolymers, in dilute solutions. Using the multiple scattering technique, we have computed the diffusion and the friction coefficients D_AB and Zeta_AB, and the change Eta_AB in the viscosity of the solution as functions of x = N_A/N and t = l_B/l_A, where N_A, N are the number of segments of the A block and of the whole copolymer, respectively, and l_A, l_B are the Kuhn lengths of the A and B blocks. Specific regimes that maximize the efficiency of separation of copolymers with distinct "t" values, have been identified.Comment: 20 pages Revtex, 7 eps figures, needs epsf.tex and amssymb.sty, submitted to Macromolecule

Effect of Different Growth Conditions on Certain Biochemical Parameters of Different Cyanobacterial Strains

Aims: Variation in the traditional growth medium conditions to enhance the production of lipids, carbohydrates, protein and the free amino acids content of three cyanobacterial species. Methodology and Results: Three species of cyanobacteria (Anabaena laxa, Anabaena fertilissima and Nostoc muscorum) were collected from the culture collection of Soils, Water and Environment Research Institute, Agriculture Research Center, Giza, Egypt, to investigate their biochemical composition under different growth conditions, using BG110 (nitrogen free) as growth medium. These conditions were represented by control medium, static glucose medium with (1%, w/v), aerated medium (aerated by bubbling technique depending on CO2 normally existed in air with a concentration of 0.03%), molasses medium (0.7%, v/v) and aerated medium enriched with glucose (1%, w/v). Lipid content, total carbohydrates, soluble proteins and free amino acids were determined at the previous conditions. Glucose at 0.7% (w/v) was the most favorable for lipid production in A. laxa, where it exhibited the highest lipid content (427 μg/g fresh wt.). Increasing molasses concentration up to 0.7% (v/v) produced an increase in lipid contents of the tested cyanobacterial strains. The highest lipid content of both N. muscorum (366.2 μg/g fresh wt.) and A. laxa (357.4 μg/g fresh wt.) were recorded at molasses concentrations of 0.1 and 0.7% (v/v), respectively. A. laxa expressed high significant values for both proteins (31.6 μg/mL) and free amino acids (40.5 mg/g dry wt.) after 6 days of incubation period under aerated enriched glucose condition (1%, w/v). Also, at the same growth conditions, A. fertilissima exhibited high significant values for carbohydrates at 4th day (876.8 mg/g dry wt.). Conclusion, significance and impact of study: Aerated enriched glucose medium (1%, w/v) was the best growth medium condition used in the present study

Relationship between biomarkers of muscle damage and redox status in response to a weightlifting training session: effect of time-of-day

The aims of the present study were to: (1) investigate the effect of a weightlifting training session and time-of-day (TOD) upon biological parameters (i.e., oral temperature, hematological, C-reactive protein (CRP), and oxidative stress) and (2) assess their possible link with muscle damage responses. Nine weightlifters (21 ± 0.5 years) performed, in a randomized order, three Olympic-Weightlifting sessions (i.e., at 08:00, 14:00, and 18:00). Blood samples were collected at rest, 3 min and 48 h after each training session. Between pre- and post-training session, ANOVA showed significant increases in oxidative stress markers at the three TODs (p < 0.01) and significant increases for creatine kinase (CK) and lactate dehydrogenase (LDH) only at 08:00 and 18:00 (p < 0.05). At rest, the results showed a significant diurnal variation for the majority of the selected parameters except for malondialdehyde (MDA), total bilirubin, and CRP with higher values observed at 18:00 (p < 0.05). After the training session, given the higher rate of increase during the morning session, these diurnal variations persisted for temperature and WBC (p < 0.01) and were suppressed for CK, LDH, uric acid (UA), catalase, and glutathione peroxidase. The main significant correlations (p < 0.001) were observed between: (1) CK and MDA (r = 0.6) and CK and UA (r = 0.66 and r = 0.82) during the morning and evening training sessions; (2) CK and CRP only during the morning session (r = 0.5); and (3) CRP and WBC during the three training sessions (r = 0.8). In conclusion, the present findings: (1) confirm that the muscle damage responses could be induced by a high level of oxidative stress and (2) suggest to avoid scheduling training sessions in the morning given the higher muscle damage, inflammatory, and oxidative responses at this TOD

An ABS control logic based on wheel force measurement

The paper presents an anti-lock braking system (ABS) control logic based on the measurement of the longitudinal forces at the hub bearings. The availability of force information allows to design a logic that does not rely on the estimation of the tyre-road friction coefficient, since it continuously tries to exploit the maximum longitudinal tyre force. The logic is designed by means of computer simulation and then tested on a specific hardware in the loop test bench: the experimental results confirm that measured wheel force can lead to a significant improvement of the ABS performances in terms of stopping distance also in the presence of road with variable friction coefficien