On parameter estimation of stochastic volatility models from stock data using particle filter - Application to AEX index -

We consider the problem of estimating stochastic volatility from stock data. The estimation of the volatility process of the Heston model is not in the usual framework of the filtering theory. Discretizing the continuous Heston model to the discrete-time one, we can derive the exact volatility filter and realize this filter with the aid of particle filter algorithm. In this paper, we derive the optimal importance function and construct the particle filter algorithm for the discrete-time Heston model. The parameters contained in system model are also estimated by constructing the augmented states for the system and parameters. The developed method is applied to the real data (AEX index)

Topics in particle filtering and smoothing

Particle filtering/smoothing is a relatively new promising class of algorithms\ud to deal with the estimation problems in nonlinear and/or non-\ud Gaussian systems. Currently, this is a very active area of research and\ud there are many issues that are not either properly addressed or are still\ud open.\ud One of the key issues in particle filtering is a suitable choice of the\ud importance function. The optimal importance function which includes the\ud information from the most recent observation, is difficult to obtain in most\ud practical situations. In this thesis, we present a new Gaussian approximation\ud to this optimal importance function using the moment matching\ud method and compare it with some other recently proposed importance\ud functions.\ud In particle filtering/smoothing, the posterior is represented as a weighted\ud particle cloud. We develop a new algorithm for extracting the smoothed\ud marginal maximum a posteriori (MAP) estimate from the available particle\ud cloud of the marginal smoother, generated using either the forwardbackward\ud smoother or the two filter smoother. The smoothed marginal\ud MAP estimator is then applied to estimate the unknown initial state of a\ud dynamic system.\ud There are many approaches to deal with the unknown static system\ud parameters within particle filtering/smoothing set up. One common approach\ud is to model the parameters as a part of the state vector. This is\ud followed by adding artificial process noises to this model and then estimate\ud the parameters along with the other state variables. Although this\ud approach may work well in (certain) practical situations, the added process\ud noises may result in a unnecessary loss of accuracy of the estimated\ud parameters. Here we propose some new particle filtering/smoothing based\ud algorithms, where we avoid any effect of the artificial dynamics on the\ud estimate of the parameters

Micromechanics of particle-coated bubbles: deformation from quasistatic to millisecond timescales

Particles adsorbed at fluid-fluid interfaces confer stability to dispersed systems such as foams and emulsions. The emergent properties associated with the interfacial microstructure underpins the creation of functional materials. In the design, synthesis and application of such materials, it is essential to understand the dynamic behaviour of structured interfaces at deformation timescales that are relevant in practical scenarios. In this experiment-driven study, a bubble is used as a probe to understand the stability mechanisms and dynamics of fluid-fluid interfaces coated with particles. First, in a model wax-based oil foam, or oleofoam, bubble dissolution time, under controlled conditions, is used as a parameter to assess the bulk and interfacial rheological contributions responsible for the remarkable stability observed. Focus is then drawn to interfacial phenomena, by removing bulk effects, through microscopic observations of crystal-coated bubbles undergoing deformation due to either bubble dissolution or ultrasound-driven volumetric oscillations. In this way phenomena at two extreme timescales, 10,000 s and 0.0001 s, are observed and interpreted. Finally, the effect of unsteady, fast deformation on a complex interface is systematically studied using a well characterised model interface, comprising of bubbles coated with optically resolvable, monodisperse latex microspheres. The bubbles are subjected to acoustic forcing, leading to the rapid cyclic compression and expansion of the colloidal monolayer. Effects of pressure amplitude, particle size and surface coverage on bubble excursions are studied. The results signify the importance of local mesoscopic phenomena in explaining the stability of oleofoams, where invoking macroscopic rheological reasoning alone is somewhat inadequate. Experimental timescales strongly influence the nature, integrity and response of complex interfaces to imposed stresses. Further, a bubble driven by ultrasound has potential in studying time-dependent interfacial mechanics.Open Acces

Estimating volatility and model parameters of stochastic volatility models with jumps using particle filter

Despite the success of particle filter, there are two factors which cause difficulties in its implementation. The first one is the choice of importance functions commonly used in the literature which are far from being optimal. The second one is the combined state and parameter estimation problem. In a widely used Heston model on stochastic volatility in financial literature, we are able to circumvent both these problems. To reflect the most realistic situation, we also include jump in the stochastic volatility model. Numerical results show the effectiveness of the algorithms

Eigenfunction localization and nodal geometry on dumbbell domains

In this article, we study the location of the first nodal line and hot spots under different boundary conditions on dumbbell-shaped domains. Apart from its intrinsic interest, dumbbell domains are also geometrically contrasting to the extensively studied convex domains. For dumbbells with Dirichlet boundary, we investigate the location of the supremum level set of the first eigenfunction and discuss the optimal positioning of obstacles. Considering the other end of level sets, the nodal sets, we establish that the first nodal set of a Neumann dumbbell (with sufficiently narrow connectors) lies within a neighborhood of the connectors. The article demonstrates the utilization of the asymptotic $L^2$-localization (or its absence, characterized by either Dirichlet or Neumann boundaries) of dumbbell domains in tackling the aforementioned nodal geometry problems.Comment: 18 pages, 4 figures. Comments are most welcome

Higher-order topological corner and bond-localized modes in magnonic insulators

We theoretically investigate a novel two-dimensional decorated honeycomb lattice framework to realize a second-order topological magnon insulator (SOTMI) phase featuring distinct corner-localized modes. Our study emphasizes the pivotal role of spin-magnon mapping in characterizing bosonic topological properties, which exhibit differences from their fermionic counterparts. We employ a symmetry indicator topological invariant to identify and characterize this SOTMI phase, particularly for systems respecting time-reversal and ${\sf{C}}_6$ rotational symmetry. Using a spin model defined on a honeycomb lattice geometry, we demonstrate that introducing "kekule" type distortions yields a topological phase. In contrast, anti-kekule" distortions result in a non-topological magnonic phase. The presence of kekule distortions manifests in two distinct topologically protected bosonic corner modes - an "intrinsic" and a "pseudo", based on the specific edge terminations. On the other hand, anti-kekule distortions give rise to bond-localized boundary modes, which are non-topological and reliant on particular edge termination. We further investigate the effects of random out-of-plane exchange anisotropy disorder on the robustness of these bosonic corner modes. The distinction between SOTMIs and their fermionic counterparts arises due to the system-specific magnonic onsite energies, a crucial feature often overlooked in prior literature. Our study unveils exciting prospects for engineering higher-order topological phases in magnon systems and enhances our understanding of their unique behavior within decorated honeycomb lattices.Comment: 4.5 Pages, 4 PDF Figures (main text) + 3 Pages, 3 PDF Figures (Supplementary Material), Comments are welcom

A detailed investigation to study the pattern of the interplay of Cyclic AMP Receptor Protein (CRP) of E. coli with its different classes of promoters

The activity of most of the promoters in Escherichia coli, involved in the metabolism of sugars other than glucose, is controlled by a CRP (cAMP receptor protein) or CAP (catabolite activator protein). CRP-dependent promoters are differentiated into various classes (Class I, Class II, and Class III) based on its cognate binding site’s position on DNA. The promoters regulated by CAP are differentially regulated by this transcriptional factor and it is also imperative to mention that these promoters vary greatly in respect to the binding site of CAP to its cognate binding site, it has also been reported that either it overlaps with the binding site of RNA polymerase or it present upstream to it. In Class I CAP-dependent promoters, a particular CAP molecule makes protein-protein interaction for the start of transcription. In Class II CAP-dependent promoters, a particular CAP molecule makes multiple interactions for the start of transcription. At last, in Class III-CAP dependent promoters, more than one CAP molecule is involved and activation of transcription is done synergistically. It has also been documented that CAP shows a kind of biphasic behavior in some promoters. So, the main focus of this work is to find out whether this biphasic behavior is true for other E. coli promoters as well. Experiments have been performed to know more about this biphasic nature and the various patterns of interactions of catabolite activator protein (CAP) of E. coli with its different classes of promoters