Why Do Absolute Returns Predict Volatility So Well?

Market Prices of Orthogonal Risk and Risk Aversion in Complete Stochastic Volatility Models: Theoretical and Empirical

We use a discrete-time analysis, giving necessary and sufficient conditions for the almost-sure convergence of ARCH(1) and GARCH(1,1) discrete-time models, to suggest an extension of the ARCH and GARCH concepts to continuous-time processes. Our ‘COGARCH’ (continuous-time GARCH) model, based on a single background driving Lévy process, is different from, though related to, other continuous-time stochastic volatility models that have been proposed. The model generalises the essential features of discrete-time GARCH processes, and is amenable to further analysis, possessing useful Markovian and stationarity properties.

We consider a continuous-time stochastic volatility model. The model contains a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We assume that we observe the process at discrete instants in time. The sampling times will be equidistant with vanishing distance. A Fourier-type deconvolution kernel density estimator based on the logarithm of the squared processes is proposed to estimate the volatility density. An expansion of the bias and a bound on the variance are derived.

We consider variance-optimal hedging in general continuous-time affine stochastic volatility models. The optimal hedge and the associated hedging error are determined semiexplicitly in the case that the stock price follows a martingale. The integral representation of the solution opens the door to efficient numerical computation. The setup includes models with jumps in the stock price and in the activity process. It also allows for correlation between volatility and stock price movements. Concrete parametric models will be illustrated in a forthcoming paper.

In this paper, we analyze the robustness and sensitivity of various continuous-time rough Volterra stochastic volatility models in relation to the process of market calibration. Model robustness is examined from two perspectives: the sensitivity of option price estimates and the sensitivity of parameter estimates to changes in the option data structure. The following sensitivity analysis consists of statistical tests to determine whether a given studied model is sensitive to changes in the option data structure based on the distribution of parameter estimates. Empirical study is performed on a data set consisting of Apple Inc. equity options traded on four different days in April and May 2015. In particular, the results for RFSV, rBergomi and alpha RFSV models are provided and compared to the results for Heston, Bates, and AFSVJD models.

Estimates of monthly average rainfall based on satellite observations from a low Earth orbit will differ from the true monthly average because the satellite observes a given area only intermittently. This sampling error inherent in satellite monitoring of rainfall would occur even if the satellite instruments could measure rainfall perfectly. We estimate the size of this error for a satellite system being studied at NASA, the Tropical Rainfall Measuring Mission (TRMM). We first examine in detail the statistical description of rainfall on scales from 1 to 103 km, based on rainfall data from the Global Atmospheric Research Project Atlantic Tropical Experiment (GATE). A TRMM‐like satellite is flown over a two‐dimensional time‐evolving simulation of rainfall using a stochastic model with statistics tuned to agree with GATE statistics. The distribution of sampling errors found from many months of simulated observations is found to be nearly normal, even though the distribution of area‐averaged rainfall is far from normal. For a range of orbits likely to be employed in TRMM, sampling error is found to be less than 10% of the mean for rainfall averaged over a 500 × 500 km2 area.

This purpose of research is aim to know and proves empirically about monetary performance influence
 to stock price change at banking company in Indonesia Stock Exchange. Research benefit is add
 knowledge and knowledge of writer about monetary performance influence to stock price change.
 Population of Research is all listing banking company of Eflk Indonesia 26 banks the year 2008-2009.
 Research sample is all member of population. Data applied is secondary data collected through
 documentation technique. Data analytical technique applied is doubled linear regression.
 From result of research is obtained by equation of doubled linear regression is Y = - 394,031 +
 93,838X1 - 369,665X2 + 86,279X3 + 449,883X4 - 22,348X5 + 3,072X6. Mean, capital adequancy
 ratio, net margin interest, return asset on, and net profit margin influential positive to stock price
 change at banking company. While return on risked asset and loan to deposit ratio influential
 negativity to stock price change at banking company. Result of test result F, indicates that capital
 adequancy ratio, retum on risked asset, net margin interest, return asset on, loan to deposit ratio and
 net profit margin influential positive and signifikan in sirrzultan to stock price change at Perusahaan
 Perbankan in Indonesia Stock Exchange. Result of test result t, indicates that capital adequancy ratio,
 return on risked asset, net margin interest, return asset on, loan to deposit ratio and net profit margin
 influential signifikan parsially to stock price change at Perusahaan Perbankan in Indonesia Stock
 Exchange. Correlation coeflicient value ( R) 0,761. Mean, capital adequancy ratio, return on risked
 asset, net margin interest, return asset on, loan to deposit ratio and net profit margin to stock price
 change. Determinant coefiicient value ( R Square) 0,580.
 Mean, explainable stock price change by capital adequancy ratio, return on risked asset, net margin
 interest, return asset on, loan to deposit ratio and net profit margin equal to 58%, while 42% again
 explained by other factor. In simultan monetary performance variable had an effect on positive to stock
 price change, while parsially monetary performance had an ejfect on negative and positive to stock
 price change. Suggestion given to researcher hereinafter is be better if researcher hereinafter adds
 company becoming research sample.

We report on a new statistical test for detecting density dependence in univariate time series observations of population abundances. The test is a likelihood ratio test based on a discrete time stochastic logistic model. The null hypothesis is that the population is undergoing stochastic exponential growth, stochastic exponential decline, or random walk. The distribution of the test statistic under both the null and alternate hypotheses is obtained through parametric bootstrapping. We document the power of the test with extensive simulations and show how some previous tests in the literature for density dependence suffer from either excessive Type I or excessive Type II error. The new test appears robust against sampling or measurement error in the observations. In fact, under certain types of error the power of the new test is actually increased. Example analyses of elk (Cervus elaphus) and grizzly bear (Ursus arctos horribilis) data sets are provided. The model implies that density—dependent populations do not have a point equilibrium, but rather reach a stochastic equilibrium (stationary distribution of population abundance). The model and associated statistical methods have potentially important applications in conservation biology.

In this paper, we propose a fractional stochastic volatility jump-diffusion model which extends the Bates(1996) model. Where we model the volatility as a fractional process. Extensive empirical studies show that the distributions of the logarithmic returns of financial asset usually exhibit properties of self-similarity and long-range dependence and since the fractional Brownian motion has these two important properties, it has the ability to capture the behavior of underlying asset price. Further incorporating jumps into the stochastic volatility framework gives further freedom to financial mathematicians to fit both the short and long end of the implied volatility surface. We propose a stochastic model which contains both fractional and jump process. Then we price options using Monte Carlo simulations along with a variance reduction technique(antithetic variates). We use market data from the S&P 500 index and we compare our results with the Heston and Bates model using error measures. The results show our model greatly outperforms previous models in terms of estimation accuracy.

The business cycle analysis of Arthur F. Burns and Wesley C. Mitchell and the National Bureau of Economic Research presumed that aggregate economic variables evolve on a time scale defined by business cycle turning points rather than by months or quarters. Do macroeconomic variables appear to evolve on an economic rather than a calendar time scale? Evidence presented here suggests that they do. However, the estimated economic time scales are only weakly related to business cycle time scales, providing evidence against the view underlying traditional business cycle analysis. Copyright 1987 by University of Chicago Press.

This paper sets out a basic framework for solving a stochastic portfolio problem using dynamic programming (DP). Dynamic portfolio decisions are concerned with simultaneous decisions on savings and asset allocation whereby asset returns, such as on equity and bonds, are stochastic as in Campbell and Viceira (Strategic asset allocation, portfolio choice for long-term investors, 2002). In contrast to CV (2002) we do not use a local approximation method to solve the stochastic model but rather use a global solution procedure such as DP. Whereas CV (2002) solve their model by assuming a constant consumption-wealth ratio and equity premium, we can allow both to be time varying. Different variances of equity and bond returns are explored in their impact on saving and asset allocation decisions and on the value function. The stochastic dynamic portfolio decision method proposed here allows for online decisions as data on asset returns are available in real time. The method is set up in a way such that it also helps to make fund decisions online for various types of investment opportunities.

Occupancy models estimate distributions of imperfectly detected species, but violations of the closure assumption can bias results. However, researchers working with mobile animals may find it impossible to eliminate such violations. Here, we tested the hypothesis that occupancy models fit to realistic sampling data can generate unbiased occupancy estimates for an itinerant Wood Thrush (Hylocichla mustelina) population. In 2013 and 2014, we tracked movements of 41 breeding Wood Thrush males. We modelled territory shift probabilities using logistic exposure models and within‐territory movements using continuous‐time stochastic process models. We then constructed an individual‐based model, simulated (1000 iterations) spatiotemporal locations for individuals and simulated sampling these populations using 162 different point count protocols with variable spatial (sampling radius and point placement method), and temporal (survey length, between‐survey intervals and number of surveys) characteristics. We compared occupancy estimates with true values of instantaneous, daily and seasonal occupancy from the simulations. We parameterized continuous time stochastic process models based on movements within 34 unique territories and estimated a daily territory shift probability of 0.0099 (95% CI: 0.0060, 0.0152). Simulated data indicated that estimates of occupancy ranged from 0.18 (0.06, 1.00) to 0.80 (0.71, 0.89) depending on protocol characteristics. Occupancy estimates increased with increasing survey radius, survey length and between‐survey interval. Protocols using shorter surveys and between‐survey intervals were good estimators for instantaneous occupancy (low bias and mean‐squared error) but poor estimators for daily and seasonal occupancy; longer surveys and intervals generated unbiased estimators of daily occupancy but underestimated seasonal occupancy. Logistic regression models that ignored imperfect detection outperformed occupancy models for estimating instantaneous occupancy but not daily or seasonal occupancy. For mobile animals, occupancy of sampling sites changes in space and time. Consequently, the spatial and temporal aspects of a sampling protocol have strong, but predictable, effects on occupancy model parameter estimates. Our results demonstrate that how these factors interact is critical for designing surveys that produce occupancy estimates representative of the biological process of interest to a researcher.

This work provides further contribution to the linear properties in a continuous time linear model. We deal with linear sufficiency and linear completeness properties, together with the linear admissibility property. These concepts were originally introduced and characterized in a discrete time context and subsequently were extended by the authors of the present paper to a continuous time linear model. Our objective is to study in depth these properties showing a general unified context where the classical linear model appears as a particular case.

The data of general database is two-dimensional, while the general mathematical models and data analysis formula are also based on two-dimensional matrix. Nowadays, data sets based on data warehouse and some of the applied database (such as spatial database) are multi-dimensional, so there is an important problem of science and technology that is needed to be solved urgently, that is, to suit the expression of multi-dimensional matrix of multi-dimensional data sets, mathematical models and algorithms based on data warehouse. The stochastic frontier linear model, introduced and developed by statisticians, solves the objectivity and optimality problems of production function well. The main part is a linear model. In fact, linear regression may be largely deviated, and using single non-parameter regression alternatively may be inconvincible. Combined with linear regression and non-parameter regression, Stone firstly designed a model, which is popularly studied, named linear semi-parameter regression model. Now, we take advantage of this thought to study stochastic frontier problems, and present following stochastic frontier semi-parameter model. In the end of this paper, we give an example computed by DASC which is a software developed by ourself.

We consider a moving shutter and non-deterministic generalization of the diffraction in time model introduced by Moshinsky several decades ago to study a class of quantum transients. We first develop a moving-mesh finite element method (FEM) to simulate the determisitic version of the model. We then apply the FEM and multilevel Monte Carlo (MLMC) algorithm to the stochastic moving-domain model for simulation of approximate statistical moments of the density profile of the stochastic transients.