Stochastic Modeling of Stratospheric Temperature

This study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

“Asymmetric Export Volatility Shock Behaviour” of Lower Middle Income (LMI) Countries in South East Asia During COVID-19 Pandemic

COVID-19 Pandemic still affecting all countries. South Asian economies and that particularly India is no exception. Because of this “uncertainty shock”, India’s GDP has contracted by 3.1percent in the last quarter of 2020. The present empirical work covers broadly the “asymmetric spillover and related noisy shocks” surrounded with trade (export) volatility about LMI nations in “two phases” i.e. in terms of considering the During pandemic phase (DC) the period from April 2019 till June 2020 and Pre-pandemic phase (PC) from April 2013 till November 2020. A comparative trade volatility asymmetries analysis were applied using a nonlinear volatility function i.e. exponential weighted moving average (EWMA), and identification of noisy behaviour after the initial post-recovery for empirical evidence. The empirical findings discovered that there were “extended” non-smooth and noisy “shock propagation” post initial recovery across two phases by the use of VAR and VECM outcomes. Bangladesh and Pakistan were stronger “Noisy shock contributors” while Nepal and Sri Lanka were turned out to be the strongest “Noisy shock receivers”. This “noisy” behaviour implies “uncertainty” and chaos on the international trade front resulting in higherthan expected volatility in trade figures and in-built destabilized momentum in the impulses. The results also relate to the possible opportunities of intra-regional trade convergence as a policy imperative.

Stochastic modelling of stratospheric temperature

<p>A stochastic model for daily-spatial mean stratospheric temperature over a given area is suggested. The model is a sum of a deterministic seasonality function and a Lévy driven vectorial Ornstein-Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the model is an order 4 continuous-time autoregressive (CAR(4)) process, derived from data analysis suggesting an order 4 autoregressive (AR(4)) process to model the deseasonalized stochastic temperature data empirically. In this analysis, temperature data as represented in ECMWF re-analysis model products are considered. The residuals of the AR(4) process turn out to be normal inverse Gaussian distributed random variables scaled with a time dependent volatility function. In general, it is possible to show that the discrete time AR(p) process is closely related to CAR(p) processes, its continuous counterpart. An equivalent effort is made in deriving a dual stochastic model for stratospheric temperature, in the sense that the year is divided into summer and winter seasons. However, this seems to further complicate the modelling, rather than obtaining a simplified analytic framework. A stochastic characterization of the stratospheric temperature representation in model products, such as the model proposed in this paper, can be used in geophysical analyses to improve our understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modelling and prediction of large-scale middle atmospheric events like sudden stratospheric warmings. Through stratosphere-troposphere coupling, this is important in the work towards an extended predictability of long-term tropospheric weather forecasting.</p>

Patterns of 50 ETF Options Implied Volatility in China: On Implied Volatility Functions

The aim of this study is to examine the volatility smile based on the European options on Shanghai stock exchange 50 ETF. The data gives evidence of the existence of a well-known U-shaped implied volatility smile for the SSE 50 ETF options market in China. For those near-month options, the implied volatility smirk is also observed. And the implied volatility remains high for the short maturity and decreases as the maturity increases. The patterns of the implied volatility of SSE 50 ETF options indicate that in-the-money options and out-of-the-money options are more expensive relative to at-the-money options. This makes the use of at-the-money implied volatility for pricing out-of- or in-the-money options questionable. In order to investigate the implied volatility, the regression-based implied volatility functions model is considered employed to study the implied volatility in this study as this method is simple and easy to apply in practice. Several classical implied volatility functions are investigated in this paper to find whether some kind of implied volatility functions could lead to more accurate options pricing values. The potential determinants of implied volatility are the degree of moneyness and days left to expiration. The empirical work has been expressed by means of simple ordinary least squares framework. As the study shows, when valuing options, the results of using volatility functions are mixed. For far-month options, using at-the-money implied volatility performs better than other volatility functions in option valuation. For near-month options, the use of volatility functions can improve the valuation accuracy for deep in-the-money options or deep out-of-the-money options. However, no particular implied volatility function performs very well for options of all moneyness level and time to maturity.

NOISY HIGH FREQUENCY DATA-BASED ESTIMATION OF VOLATILITY FUNCTION WITH APPLICATIONS

Diffusion models have been widely used to describe the stochastic dynamics of the underlying economic variables. Renò ( 2008 ) introduced a nonparametric estimator of the volatility function, which is based on the estimation of quadratic variation between observations by means of realized variance. However, they may be misleading when one uses intraday data to implement directly the estimator, because intraday data display microstructure effects that could seriously distort the estimation. To filter out the impact of microstructure noise on the estimation of the volatility function, in this paper we propose an improved estimator when there is microstructure noise in the observed price. Also, we show that the proposed estimator has the same asymptotic properties as the Renò estimator when the step of discretization inclines to zero. Some simulations and empirical applications on Shanghai Stock Exchange data from March 3, 2002 to December 31, 2008 are used to illustrate the finite sample performance of the proposed estimator.

Nonparametric Range-Based Double Smoothing Spot Volatility Estimation for Diffusion Models

We consider nonparametric spot volatility estimation for diffusion models with discrete high frequency observations. Our estimator is carried out in two steps. First, using the local average of the range-based variance, we propose a crude estimator of the spot volatility. Second, we use usual nonparametric kernel smoothing to reconstruct the volatility function from the crude estimator. By inference, we find such a double smoothing operation can effectively reduce the estimation error.