Implied Filtering Densities on the Hidden State of Stochastic Volatility

Abstract

We formulate and analyse an inverse problem using derivative prices to obtain an implied filtering density on volatility’s hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the market, and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as separability. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market. When applied to SPX options data, the estimated model and implied densities produce variance-swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur due to the options’ expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options.     

Investigation on the undercooling and crystallization of pure aluminum melt by DSC

The undercooling of pure aluminum melt was in situ investigated by differential scanning calorimeter with flux processing technique in this study. The highest undercooling of pure aluminum with 17.8 K was obtained as the thermal treatment temperature of the melt being 1033 K and the cooling rate being 50 K min^?1. When cooling rate is fixed, the undercooling depends on the melt processing temperature, and increases rapidly at the first stage. The effects of thermal treatment temperature and cooling rates on the undercooling are discussed in this article.     

Absolutely Pure Covers

Absolutely pure modules act in ways similar to injective modules. There are conditions on a ring which guarantee that the class of injective modules will be covering. In this article, we define conditions on the ring R which guarantee that the class of absolutely pure modules will be covering. These include R being left coherent, which we show implies a number of other necessary properties.     

Effect of pure phase decoherence on entanglement teleportation

We study entanglement teleportation in the two‐qubit XX Heisenberg model with pure phase decoherence taken into account. For some initial entangled states, pure phase decoherence has no effect on the teleported entanglement, while for others pure phase decoherence has a pronounced effect. In addition, entanglement sudden death happens in the latter case.     

A multiperiod model for estimating the cost of deposit insurance under the Basel III minimum capital requirement

Under the Basel III regime, a commercial bank is considered adequately capitalized if it maintains a ratio of capital to total risk-weighted assets or capital adequacy ratio (CAR) of at least 8%. We model a commercial bank that complies with Basel III's minimum capital requirement on an interval $[0,T]$ for $T>0$. The bank model is achieved via a specific rate of capital influx that fixes the bank's CAR at the minimum prescribed level of 8%. On the basis of this capital influx rate, we derive models for the bank's asset portfolio and capital dynamics required for maintaining the CAR at the minimum prescribed level. For the aforementioned bank, we further study a deposit insurance (DI) pricing problem with a coverage horizon equal to $T$ years. More specifically, we employ a multiperiod DI pricing model to approximate the cost of DI for the bank on the interval $[0,T]$, where the constant (minimum) CAR is maintained. We study the behaviours of the models leading to the constant (minimum) CAR, and the behaviour of the DI premium estimate by means of numerical simulations. In the simulation study pertaining to the DI premium estimate specifically, we determine the effects of changes in the bank's initial leverage level (deposit-to-asset ratio), the DI coverage horizon, and the volatility of the asset portfolio on the DI premium estimate.     

Characterization of Different Salt Forms of Chitooligosaccharides and Their Effects on Nitric Oxide Secretion by Macrophages

In this paper, chitooligosaccharides in different salt forms, such as chitooligosaccharide lactate, citrate, adipate, etc., were prepared by the microwave method. They were characterized by SEM, FTIR, NMR, etc., and the nitric oxide (NO) expression was determined in RAW 264.7 cells. The results showed that pure chitooligosaccharide was an irregular spherical shape with rough surface, and its different salt type products are amorphous solid with different honeycomb sizes. In addition to the characteristic absorption peaks of chitooligosaccharides, in FTIR, the characteristic absorption of carboxyl group, methylene group, and aromatic group in corresponding acid appeared. The characteristic absorption peaks of carbon in carboxyl group, hydrogen and carbon in methyl, methylene group, and aromatic group in corresponding acid also appeared in NMR. Therefore, the sugar ring structure and linking mode of chitooligosaccharides did not change after salt formation of chitooligosaccharides. Different salt chitooligosaccharides are completely different in promoting NO secretion by macrophages, and pure chitooligosaccharides are the best.     

Bouncing and Coalescence of Bubble Pairs Rising at High Reynolds Number in Pure Water or Aqueous Surfactant Solutions

The encounter of bubble pairs of O(1 mm) in both pure water and aqueous surfactant solutions was studied experimentally. In pure water, two equally sized bubbles were found to coalesce if the Weber number, W = V² R/, based on the velocity of approach, V, was below a critical value, W_cr = 0.18, where and are the density and surface tension of the liquid respectively and R the equivalent radius of the bubbles. After coalescence bubbles perform volume and shape oscillations.When W_cr is exceeded, bubbles bounce. After bouncing, bubbles can either coalesce or separate without coalescing. This was found to depend on the Weber number, based on the rise velocity U, We = U² R/. If this number was below a critical value, bubbles coalesced after bouncing. The relative motion of the bubbles was found to be damped out by acoustic damping due to surface oscillations rather then by viscosity.If We was above a critical value, which was close to that for path instability of a single bubble (We = 3.3), the bubbles separated after bouncing. This is probably caused by shedding of vortices which dominate the relative motion of the bubbles. This mechanism may cause bubbles in bubbly flows not aggregating in horizontal planes, as was found in calculations based on potential flow theory. For modelling bubbly flows it will therefore be essential to incorporate the influence of vorticity.When surfactants are added to the water it was found that bubbles are prevented to coalesce above a critical concentration, which is nearly identical to that of single rising bubbles. Above this critical concentration, bubbles behave as rigid spheres and trajectories cannot be predicted by potential flow theory.     

Critical comparison of radiometric and mass spectrometric methods for the determination of radionuclides in environmental, biological and nuclear waste samples

The radiometric methods, alpha (α)-, beta (β)-, gamma (γ)-spectrometry, and mass spectrometric methods, inductively coupled plasma mass spectrometry, accelerator mass spectrometry, thermal ionization mass spectrometry, resonance ionization mass spectrometry, secondary ion mass spectrometry, and glow discharge mass spectrometry are reviewed for the determination of radionuclides. These methods are critically compared for the determination of long-lived radionuclides important for radiation protection, decommissioning of nuclear facilities, repository of nuclear waste, tracer application in the environmental and biological researches, these radionuclides include ³H, ¹⁴C, ³⁶Cl, ⁴¹Ca, ^59,63Ni, ^89,90Sr, ⁹⁹Tc, ¹²⁹I, ^135,137Cs, ²¹⁰Pb, ^226,228Ra, ²³⁷Np, ²⁴¹Am, and isotopes of thorium, uranium and plutonium. The application of on-line methods (flow injection/sequential injection) for separation of radionuclides and automated determination of radionuclides is also discussed.     

Estimating the distortion parameter of the proportional hazards premium for heavy-tailed losses under Lévy-stable regime

Estimating the distorted parameter in the case of non negative heavy-tailed losses has been treated in Brahimi et al. (2011). In this paper, we extend this work to the case of the real heavy-tailed losses. We derive an asymptotic distribution of the estimator. We construct a practically implemented confidence interval for the distortion parameter and illustrate the performance of the interval in a simulation study with application to real data.     

高压熔渗生长法制备金刚石聚晶中碳的转化机制研究

在6 GPa和1500 ℃的压力和温度范围内, 利用高压熔渗生长法制备了纯金刚石聚晶, 深入研究了高温高压下金刚石聚晶生长过程中碳的转化机制. 利用光学显微镜、X-射线衍射、场发射扫描电子显微镜检测, 发现在熔渗过程中金刚石层出现了石墨化现象, 在烧结过程中金刚石颗粒表面形貌发生了变化. 根据实验现象分析, 在制备过程中存在三种碳的转化机制: 1)金属熔渗阶段金刚石颗粒表面石墨化产生石墨; 2)产生的石墨在烧结阶段很快转变为填充空隙的金刚石碳; 3)金刚石直接溶解在金属溶液中, 以金刚石形式在颗粒间析出, 填充空隙. 本文研究碳的转化机制为在高温高压金属溶剂法合成金刚石的条件下(6 GPa和1500 ℃的压力和温度范围内)工业批量化制备无添加剂、无空隙的纯金刚石聚晶提供了重要的理论指导.