Sequential Monte Carlo pricing of American-style options under stochastic volatility models

We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be expressed as functions of conditional distributions of volatility, given observed data. By constructing statistics summarizing information about these conditional distributions, one can obtain high quality approximate solutions. Although the required conditional distributions are in general intractable, they can be arbitrarily precisely approximated using sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes, is potentially heavy computational demand. We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz [The Review of Financial Studies 14 (2001) 113-147], and the other solving the same problem using a "brute force" gridding approach. We estimate an illustrative SV model using Markov chain Monte Carlo (MCMC) methods for three equities. We also demonstrate the use of our algorithm by estimating the posterior distribution of the market price of volatility risk for each of the three equities.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS286 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Reframing return-to-sport postpartum: the 6 Rs framework

Editorial

Gating of TonB-dependent transporters by substrate-specific forced remodelling

Membrane proteins play vital roles in inside-out and outside-in signal transduction by responding to inputs that include mechanical stimuli. Mechanical gating may be mediated by the membrane or by protein(s) but evidence for the latter is scarce. Here we use force spectroscopy, protein engineering and bacterial growth assays to investigate the effects of force on TonB-TonB dependent transporter (TBDT) complexes of Gram-negative bacteria. We confirm the feasibility of protein-only mediated mechanical gating by demonstrating that the interaction between TonB and BtuB (a TBDT) is sufficiently strong under force to create a channel through the TBDT. In addition, by comparing the dimensions of the force-induced channel in BtuB and a second TBDT (FhuA) we show that the mechanical properties of the interaction are perfectly tuned to their function by inducing formation of a channel whose dimensions are tailored to the ligand

Gating of TonB-dependent transporters by substrate-specific forced remodelling

Membrane proteins play vital roles in inside-out and outside-in signal transduction by responding to inputs that include mechanical stimuli. Mechanical gating may be mediated by the membrane or by protein(s) but evidence for the latter is scarce. Here we use force spectroscopy, protein engineering and bacterial growth assays to investigate the effects of force on complexes formed between TonB and TonB-dependent transporters (TBDT) from Gram-negative bacteria. We confirm the feasibility of protein-only mediated mechanical gating by demonstrating that the interaction between TonB and BtuB (a TBDT) is sufficiently strong under force to create a channel through the TBDT. In addition, by comparing the dimensions of the force-induced channel in BtuB and a second TBDT (FhuA), we show that the mechanical properties of the interaction are perfectly tuned to their function by inducing formation of a channel whose dimensions are tailored to the ligand

Unfolding dynamics of proteins under applied force

Understanding the mechanisms of protein folding is a major challenge that is being addressed effectively by collaboration between researchers in the physical and life sciences. Recently, it has become possible to mechanically unfold proteins by pulling on their two termini using local force probes such as the atomic force microscope. Here, we present data from experiments in which synthetic protein polymers designed to mimic naturally occurring polyproteins have been mechanically unfolded. For many years protein folding dynamics have been studied using chemical denaturation, and we therefore firstly discuss our mechanical unfolding data in the context of such experiments and show that the two unfolding mechanisms are not the same, at least for the proteins studied here. We also report unexpected observations that indicate a history effect in the observed unfolding forces of polymeric proteins and explain this in terms of the changing number of domains remaining to unfold and the increasing compliance of the lengthening unstructured polypeptide chain produced each time a domain unfolds

Pregnancy in the female athlete - Part 1: antenatal

As female participation in sport and exercise continues to increase, there is a strong likelihood that a strength and conditioning (S&C) coach will work with a pregnant athlete. High profile athletes such as Serena Williams and Dame Jessica Ennis-Hill have shown recently that it is not uncommon for female athletes to become mothers during their careers, rather than after they have retired. However, historically pregnancy was perceived as time spent away from sport and being active was wrongly associated with a high, unreasonable risk to the unborn foetus. The challenge for the S&C coach working with pregnant athletes is navigating the wide range of global recommendations that are often aimed at active or inactive individuals, but not at elite athletes. It is fundamental that any coach working with pregnant athletes is knowledgeable about the physiological and anatomical changes that occur throughout the trimesters, the nutritional demands of pregnancy, and its effect on weight management in order to appropriately facilitate athlete and foetal health during the antenatal period. Therefore, the aim of this initial review is to summarise current literature and provide key insights that promote best practice for practitioners working with pregnant athletes. The use of ‘women’ throughout this paper will refer to the general population and ‘sportswomen’ to the athletic population. ‘Antenatal’ refers to a pregnant woman before childbirth and the term ‘postnatal’ means after childbirth, something which will be covered in part 2 of this review series

Tuning protein mechanics through an ionic cluster graft from an extremophilic protein.

Proteins from extremophilic organisms provide excellent model systems to determine the role of non-covalent interactions in defining protein stability and dynamics as well as being attractive targets for the development of robust biomaterials. Hyperthermophilic proteins have a prevalence of salt bridges, relative to their mesophilic homologues, which are thought to be important for enhanced thermal stability. However, the impact of salt bridges on the mechanical properties of proteins is far from understood. Here, a combination of protein engineering, biophysical characterisation, single molecule force spectroscopy (SMFS) and molecular dynamics (MD) simulations directly investigates the role of salt bridges in the mechanical stability of two cold shock proteins; BsCSP from the mesophilic organism Bacillus subtilis and TmCSP from the hyperthermophilic organism Thermotoga maritima. Single molecule force spectroscopy shows that at ambient temperatures TmCSP is mechanically stronger yet, counter-intuitively, its native state can withstand greater deformation before unfolding (i.e. it is mechanically soft) compared with BsCSP. MD simulations were used to identify the location and quantify the population of salt bridges, and reveal that TmCSP contains a larger number of highly occupied salt bridges than BsCSP. To test the hypothesis that salt-bridges endow these mechanical properties on the hyperthermophilic CSP, a charged triple mutant (CTM) variant of BsCSP was generated by grafting an ionic cluster from TmCSP into the BsCSP scaffold. As expected CTM is thermodynamically more stable and mechanically softer than BsCSP. We show that a grafted ionic cluster can increase the mechanical softness of a protein and speculate that it could provide a mechanical recovery mechanism and that it may be a design feature applicable to other proteins

Emission-aware Energy Storage Scheduling for a Greener Grid

Reducing our reliance on carbon-intensive energy sources is vital for reducing the carbon footprint of the electric grid. Although the grid is seeing increasing deployments of clean, renewable sources of energy, a significant portion of the grid demand is still met using traditional carbon-intensive energy sources. In this paper, we study the problem of using energy storage deployed in the grid to reduce the grid's carbon emissions. While energy storage has previously been used for grid optimizations such as peak shaving and smoothing intermittent sources, our insight is to use distributed storage to enable utilities to reduce their reliance on their less efficient and most carbon-intensive power plants and thereby reduce their overall emission footprint. We formulate the problem of emission-aware scheduling of distributed energy storage as an optimization problem, and use a robust optimization approach that is well-suited for handling the uncertainty in load predictions, especially in the presence of intermittent renewables such as solar and wind. We evaluate our approach using a state of the art neural network load forecasting technique and real load traces from a distribution grid with 1,341 homes. Our results show a reduction of >0.5 million kg in annual carbon emissions -- equivalent to a drop of 23.3% in our electric grid emissions.Comment: 11 pages, 7 figure, This paper will appear in the Proceedings of the ACM International Conference on Future Energy Systems (e-Energy 20) June 2020, Australi

Collagen-like motifs of SasG: a novel fold for protein mechanical strength

The Staphylococcus aureus surface protein G (SasG) is associated with host colonisation and biofilm formation. As colonisation occurs at the liquid-substrate interface bacteria are subject to a myriad of external forces and, presumably as a consequence, SasG displays extreme mechanical strength. This mechanical phenotype arises from the B-domain; a repetitive region composed of alternating E and G5 subdomains. These subdomains have an unusual structure comprising collagen-like regions capped by triple-stranded β-sheets. To identify the determinants of SasG mechanical strength, we characterised the mechanical phenotype and thermodynamic stability of 18 single substitution variants of a pseudo-wildtype protein. Visualising the mechanically-induced transition state at a residue-level by Φ-value analysis reveals that the main force-bearing regions are the N- and C-terminal ‘Mechanical Clamps’ and their side-chain interactions. This is tailored by contacts at the pseudo-hydrophobic core interface. We also describe a novel mechanical motif - the collagen-like region and show that glycine to alanine substitutions, analogous to those found in Osteogenesis Imperfecta (brittle bone disease), result in a significantly reduced mechanical strength

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit