Volatility Process Research Articles

On the Curvature of the Bachelier Implied Volatility

Our aim in this paper is to analytically compute the at-the-money second derivative of the Bachelier implied volatility curve as a function of the strike price for correlated stochastic volatility models. We also obtain an expression for the short-term limit of this second derivative in terms of the first and second Malliavin derivatives of the volatility process and the correlation parameter. Our analysis does not need the volatility to be Markovian and can be applied to the case of fractional volatility models, both with H<1/2 and H>1/2. More precisely, we start our analysis with an adequate decomposition formula of the curvature as the curvature in the uncorrelated case (where the Brownian motions describing asset price and volatility dynamics are uncorrelated) plus a term due to the correlation. Then, we compute the curvature in the uncorrelated case via Malliavin calculus. Finally, we add the corresponding correlation correction and we take limits as the time to maturity tends to zero. The presented results can be an interesting tool in financial modeling and in the computation of the corresponding Greeks. Moreover, they allow us to obtain general formulas that can be applied to a wide class of models. Finally, they provide us with a precise interpretation of the impact of the Hurst parameter H on this curvature.

Exploring when to exploit: the cognitive underpinnings of foraging-type decisions in relation to psychopathy

Impairments in reinforcement learning (RL) might underlie the tendency of individuals with elevated psychopathic traits to behave exploitatively, as they fail to learn from their mistakes. Most studies on the topic have focused on binary choices, while everyday functioning requires us to learn the value of multiple options. In this study, we evaluated the cognitive correlates of naturalistic foraging-type decision-making and their electrophysiological signatures in a community sample (n = 108) with varying degrees of psychopathic traits. Reinforcers with different salience were included in a foraging-type decision-making task. Recruitment of various cognitive processes was estimated with a computational model and electrophysiology, and the relationships to psychopathic traits were assessed. Higher Antisocial traits were associated with a bias towards expecting more volatility in the environment when high-salience reinforcers were used. Additionally, higher levels of Interpersonal traits were associated with reduced learning from personalized rewards, as evidenced by reductions in the prediction errors (PEs) about rate of change. Higher Affective traits were associated with lower PEs and aberrant learning from painful punishments. Lastly, the PEs about rate of change were reflected in the trial-wise trajectories of Feedback-Related Negativity event-related potentials. Together, our results point to the importance of volatility processing in understanding aberrant decision-making in relation to psychopathy, demonstrate the relationships between psychopathic traits and learning through reward and punishment, and emphasise the potentially more beneficial effect of personalized rewards and punishment for improving reinforcement-based decision-making in individuals with elevated psychopathic traits.

High‐Frequency Instruments and Identification‐Robust Inference for Stochastic Volatility Models

ABSTRACTWe introduce a novel class of stochastic volatility models, which can utilize and relate many high‐frequency realized volatility (RV) measures to latent volatility. Instrumental variable methods provide a unified framework for estimation and testing. We study parameter inference problems in the proposed framework with nonstationary stochastic volatility and exogenous predictors in the latent volatility process. Identification‐robust methods are developed for a joint hypothesis involving the volatility persistence parameter and the autocorrelation parameter of the composite error (or the noise ratio). For inference about the volatility persistence parameter, projection techniques are applied. The proposed tests include Anderson‐Rubin‐type tests and their point‐optimal versions. For distributional theory, we provide finite‐sample tests and confidence sets for Gaussian errors, establish exact Monte Carlo test procedures for non‐Gaussian errors (possibly heavy‐tailed), and show asymptotic validity under weaker assumptions. Simulation results show that the proposed tests outperform the asymptotic test regarding size and exhibit excellent power in empirically realistic settings. The proposed inference methods are applied to IBM's price and option data (2009–2013). We consider 175 different instruments (IVs) spanning 22 classes and analyze their ability to describe the low‐frequency volatility. IVs are compared based on the average length of the proposed identification‐robust confidence intervals. The superior instrument set mostly comprises 5‐min HF realized measures, and these IVs produce confidence sets which show that the volatility process is nearly unit‐root. In addition, we find RVs with higher frequency yield wider confidence intervals than RVs with slightly lower frequency, indicating that these confidence intervals adjust to absorb market microstructure noise. Furthermore, when we consider irrelevant or weak IVs (jumps and signed jumps), the proposed tests produce unbounded confidence intervals. We also find that both RV and BV measures produce almost identical confidence intervals across all 14 subclasses, confirming that our methodology is robust in the presence of jumps. Finally, although jumps contain little information regarding the low‐frequency volatility, we find evidence that there may be a nonlinear relationship between jumps and low‐frequency volatility.

Correction to: Electrokinetic remediation of real soils polluted with chlorinated hydrocarbons: relevance of dichlorination and volatilization processes

Correction to: Electrokinetic remediation of real soils polluted with chlorinated hydrocarbons: relevance of dichlorination and volatilization processes

The heat modulated infinite dimensional Heston model and its numerical approximation

The HEat modulated Infinite DImensional Heston (HEIDIH) is introduced as a concrete case of the general framework of infinite dimensional Heston stochastic volatility models of (F.E. Benth, I.C. Simonsen '18) for the pricing of forward contracts. It is supported by a comprehensive numerical analysis. The model consists of a one-dimensional stochastic advection equation coupled with a stochastic volatility process. This process is a Cholesky-type decomposition of the tensor product of a Hilbert-space valued Ornstein-Uhlenbeck process, the solution to a stochastic heat equation on the real half-line. The advection and heat equations are driven by independent space-time Gaussian processes which are white in time and coloured in space, with the latter covariance structure expressed by two different kernels. First, a class of weight-stationary kernels are given, under which regularity results for the HEIDIH model in fractional Sobolev spaces are formulated. In particular, the class includes weighted Matérn kernels. Second, numerical approximation of the model is considered. An error decomposition formula, pointwise in space and time, for a finite-difference scheme is proven. For a special case, essentially sharp convergence rates are obtained when this is combined with a fully discrete finite element approximation of the stochastic heat equation. The analysis takes into account a localization error, a pointwise-in-space finite element discretization error and an error stemming from the noise being sampled pointwise in space. The rates obtained in the analysis are higher than what would be obtained using a standard Sobolev embedding technique. Numerical simulations illustrate the results.

Reweighted Nadaraya–Watson estimation of stochastic volatility jump-diffusion models

In this paper, we construct the reweighted Nadaraya–Watson estimators of the infinitesimal moments for the volatility process of the stochastic volatility models, with the application of the threshold estimator of the unobserved volatility process. Our model includes jumps in both the underlying asset price and its volatility process. We derive the asymptotic properties of the estimators under the infill and long span assumptions. The results are useful for identification of the process. The finite-sample performance of the estimators is studied through Monte Carlo simulation.

A general valuation framework for rough stochastic local volatility models and applications

Rough volatility models are a new class of stochastic volatility models that have been shown to provide a consistently good fit to implied volatility smiles of SPX options. They are continuous-time stochastic volatility models, whose volatility process is driven by a fractional Brownian motion with the corresponding Hurst parameter less than a half. Albeit the empirical success, the valuation of derivative securities under rough volatility models is challenging. The reason is that it is neither a semi-martingale nor a Markov process. This paper proposes a novel valuation framework for rough stochastic local volatility (RSLV) models. In particular, we introduce the perturbed stochastic local volatility (PSLV) model as the semi-martingale approximation for the RSLV model and establish its existence, uniqueness, Markovian representation and convergence. Then we propose a fast continuous-time Markov chain (CTMC) approximation algorithm to the PSLV model and establish its convergence. Numerical experiments demonstrate the convergence of our approximation method to the true prices, and also the remarkable accuracy and efficiency of the method in pricing European, barrier and American options. Comparing with existing literature, a significant reduction in the CPU time to arrive at the same level of accuracy is observed.

STRUCTURAL BREAKS AND VOLATILITY PERSISTENCE IN HOTEL OCCUPANCY RATE

Purpose: Although Singapore has been one of the most attractive destinations for international tourists over the past 20 years, little evidence exists on the dynamics of its hotel occupancy rate. Our study aims to extend this scarce literature Design/Methodology/Approach: The present study employs time-varying volatility processes (e.g., GARCH process) and models the uncertainty associated with the hotel occupancy rate in Singapore. Findings: The main results indicate that shocks to the occupancy rate have a long run persistence and that there are asymmetric impacts in the occupancy rate. Further analysis suggests that structural breaks emanating from extreme news or shocks exert substantial impacts on the level of uncertainty for hotel occupancy rate. Originality/Value: Managers in the hotel industry could benefit from our findings while adopting active measures to reduce risk in tourism demand and hotel occupancy and attract more international tourists.

Identification of potential volatile markers for characterizing Argentine wine vinegars based on their production process

In Argentina, the production of quality wine vinegars has been barely exploited. Currently, most of the marketed vinegars are produced using rapid industrial fermentation systems obtaining vinegars with a high production rate, but with low quality and few organoleptic nuances. This work aims to study the volatile profile by headspace solid phase microextraction (HS-SPME) coupled to gas chromatography-mass spectrometry (GC–MS) and chemometrics to differentiate Argentinian wine vinegars according to their production process (industrial or traditional). A total of 92 volatile compounds were identified on the samples by using a strategy based on volatile profile processing using PARADISe® software. The complete volatile profile of all the samples was submitted to partial least squares discriminant analysis (PLS-DA) for the selection of variables with importance in the projection (VIPs). Thus, 37 volatile compounds with the potential to be markers of the manufacturing process were selected. The results obtained revealed, for the first time, the volatile profile of Argentine wine vinegars showing that the compound groups that, on average, exhibited higher relative areas were esters, acids, and alcohols. Thus, certain acids, aldehydes and terpenes were noticeably present in industrial wine vinegar. Conversely, the alcohols were strongly associated with traditional ones. In the case of esters, they were connected to the different types of wine vinegars. These compounds could be considered as potential volatile markers of quality and authenticity of these types of vinegars.

Pricing of timer volatility-barrier options under Heston’s stochastic volatility model

Timer options are financial instruments that enable investors to exercise their rights on a random maturity date the realized variance reaches the level of variance budget. These options provide a stable investment opportunity for investors under the unpredictable and complex financial markets, such as global financial crisis or COVID-19 pandemic, which can induce the drastic changes of the volatility for the underlying asset. Meanwhile, in the financial markets, investors who invest in standard timer options may face the problems caused by the postponement of the exercising time for too low volatility, compared to standard vanilla options. In this regard, to overcome such disadvantages, we propose timer volatility-barrier options, which are activated and expired when the volatility arrives at a relatively low barrier level, with the original properties of the standard timer options. In this paper, by making use of the method of images, we derive an analytical formulas for the timer volatility-barrier options so that the volatility process can be driven by Heston stochastic volatility model, and verify the pricing accuracy of the timer options by comparing our solutions with those obtained from Monte Carlo simulations. Finally, we conduct numerical studies on the timer volatility-barrier options to examine the pricing sensitivities with respect to the various model parameters, and implement the discussion for pricing formula of double volatility barrier type of the timer options.

Identifying the number of latent factors of stochastic volatility models

AbstractWe provide a procedure to identify the number of latent factors of stochastic volatility models. The methodology relies on the non-parametric Fourier estimation method introduced by Malliavin and Mancino (Finance Stoch 4:49–61, 2002) and applies to high-frequency data. Based on the Fourier analysis, we first estimate the latent volatility process and then the volatilities and covariances of the processes that are gradually identified, such as volatility of volatility and leverage. The analysis of the eigenvalue spectrum of the Gram matrix can reveal information about the actual number of factors driving the process at hand. We corroborate our analysis by numerical simulations on single and multi factor models. Finally, we apply our methodology to intraday prices from the S &P 500 index futures.

Portfolio problem for the α−hypergeometric stochastic volatility model with consumption

This paper solves the finite horizon optimal consumption-investment problem for an investor that trades in the α−hypergeometric stochastic volatility model, with preferences based on a power utility function. To find the optimal strategy, we follow the dynamic programming approach. First, we perform a suitable change of variables in order to fully transform the non-linear Hamilton-Jacobi-Bellman (HJB) equation into a semilinear one. Next, we apply the Girsanov theorem to deduce an implicit Feynman-Kac formula depending upon the volatility process. The operator defined by the Feynman-Kac representation is shown to be a contraction operator on a designed function space. Finally, the Banach fixed point theorem yields the existence of a solution to the HJB equation in the designed space. Moreover, we apply a verification theorem to guarantee that the solution of the HJB equation coincides with the value function.

Robustness of Hilbert space-valued stochastic volatility models

In this paper, we show that Hilbert space-valued stochastic models are robust with respect to perturbations, due to measurement or approximation errors, in the underlying volatility process. Within the class of stochastic-volatility-modulated Ornstein–Uhlenbeck processes, we quantify the error induced by the volatility in terms of perturbations in the parameters of the volatility process. We moreover study the robustness of the volatility process itself with respect to finite-dimensional approximations of the driving compound Poisson process and semigroup generator, respectively, when considering operator-valued Barndorff-Nielsen and Shephard stochastic volatility models. We also give results on square root approximations. In all cases, we provide explicit bounds for the induced error in terms of the approximation of the underlying parameter. We discuss some applications to robustness of prices of options on forwards and volatility.

A Barndorff-Nielsen and Shephard model with leverage in Hilbert space for commodity forward markets

We propose an extension of the model introduced by Barndorff-Nielsen and Shephard, based on stochastic processes of Ornstein–Uhlenbeck type taking values in Hilbert spaces and including the leverage effect. We compute explicitly the characteristic function of the log-return and the volatility processes. By introducing a measure change of Esscher type, we provide a relation between the dynamics described with respect to the historical and the risk-neutral measures. We discuss in detail the application of the proposed model to describe the commodity forward curve dynamics in a Heath–Jarrow–Morton framework, including the modelling of forwards with delivery period occurring in energy markets and the pricing of options. For the latter, we show that a Fourier approach can be applied in this infinite-dimensional setting, relying on the attractive property of conditional Gaussianity of our stochastic volatility model. In our analysis, we study both arithmetic and geometric models of forward prices and provide appropriate martingale conditions in order to ensure arbitrage-free dynamics.

AI-based R&D for frozen and thawed meat: Research progress and future prospects.

Frozen and thawed meat plays an important role in stabilizing the meat supply chain and extending the shelf life of meat. However, traditional methods of research and development (R&D) struggle to meet rising demands for quality, nutritional value, innovation, safety, production efficiency, and sustainability. Frozen and thawed meat faces specific challenges, including quality degradation during thawing. Artificial intelligence (AI) has emerged as a promising solution to tackle these challenges in R&D of frozen and thawed meat. AI's capabilities in perception, judgment, and execution demonstrate significant potential in problem-solving and task execution. This review outlines the architecture of applying AI technology to the R&D of frozen and thawed meat, aiming to make AI better implement and deliver solutions. In comparison to traditional R&D methods, the current research progress and promising application prospects of AI in this field are comprehensively summarized, focusing on its role in addressing key challenges such as rapid optimization of thawing process. AI has already demonstrated success in areas such as product development, production optimization, risk management, and quality control for frozen and thawed meat. In the future, AI-based R&D for frozen and thawed meat will also play an important role in promoting personalization, intelligent production, and sustainable development. However, challenges remain, including the need for high-quality data, complex implementation, volatile processes, and environmental considerations. To realize the full potential of AI that can be integrated into R&D of frozen and thawed meat, further research is needed to develop more robust and reliable AI solutions, such as general AI, explainable AI, and green AI.

Option pricing in a stochastic delay volatility model

This work introduces a new stochastic volatility model with delay parameters in the volatility process, extending the Barndorff–Nielsen and Shephard model. It establishes an analytical expression for the log price characteristic function, which can be applied to price European options. Empirical analysis on S&P500 European call options shows that adding delay parameters reduces mean squared error. This is the first instance of providing an analytical formula for the log price characteristic function in a stochastic volatility model with multiple delay parameters. We also provide a Monte Carlo scheme that can be used to simulate the model.

Comparison of plastic and glass cages on volatile compounds in protein extracted from Protaetia brevitarsis larvae

Edible insects, known for their high-protein production efficiency, are vital for enhancing food security. However, standardized breeding protocols are lacking, and research on the impact of cage materials on insect product composition is limited. This study investigated the volatile compounds and processing properties of protein from Protaetia brevitarsis larvae reared in plastic and glass cages. Protein extracts from larvae reared in plastic cages contained 14 types of hydrocarbons, 4 types of ketones, and 1 type of phenol. Those reared in glass cages contained two types of acids, seven types of alcohols, and five types of aldehydes. Notably, plastic-derived compounds, such as p-xylene (110.87 μg/mL) and o-xylene (37.98 μg/mL), were significantly higher in the extracts from plastic cages, indicating potential plastic exposure. Processing properties, including protein solubility, pH, color, foaming properties, and emulsion characteristics, showed no significant differences between the two rearing conditions (P > 0.05). Therefore, considering the detection and potential accumulation of plastic-derived volatile compounds, using glass cages may be more beneficial for rearing insects for protein production.

Strategies for regulating crystallinity and surface quality based on solvent multistage volatilization

In this paper, Bi2212 superconducting thin films were prepared with metal acetate as salt source and a mixture of acetic acid and N,N-dimethylformamide (DMF) as solvent. The volatilization process of the solvent was regulated by changing the ratio of the mixed solvent, which in turn achieved the regulation of the surface morphology and crystallinity of the Bi2212 superconducting films. The mechanism of the mixed solvents on the crystallinity and surface quality of Bi2212 superconducting films was systematically investigated. The results showed that the Bi2212 superconducting films were all (00l) epitaxial growth. The grain size of Bi2212 increased continuously with the increase of the proportion of acetic acid in the solvents. The grain size of the largest grain size was 43.8 nm when the proportion of acetic acid was 80 %. However, the high proportion of acetic acid in the mixed solvents reduced the surface quality of Bi2212 thin films. The minimum surface roughness was 15.0 nm at 40 % acetic acid. All the samples exhibited good superconducting properties. This work provides a research basis for the systematic preparation of multicomponent oxide thin films.

The Fourier–Malliavin Volatility (FMVol) MATLAB® library

This paper presents the Fourier–Malliavin Volatility (FMVol) estimation library for MATLAB®. This library includes functions that implement Fourier–Malliavin estimators (see Malliavin and Mancino (2002, 2009)) of the volatility and co-volatility of continuous stochastic volatility processes and second-order quantities, like the quarticity (the squared volatility), the volatility of volatility and the leverage (the covariance between changes in the process and changes in its volatility). The Fourier–Malliavin method is fully non-parametric, does not require equally-spaced observations and is robust to measurement errors, or noise, without any preliminary bias correction or pre-treatment of the observations. Furthermore, in its multivariate version, it is intrinsically robust to irregular and asynchronous sampling. Although originally introduced for a specific application in financial econometrics, namely the estimation of asset volatilities, the Fourier–Malliavin method is a general method that can be applied whenever one is interested in reconstructing the latent volatility and second-order quantities of a continuous stochastic volatility process from discrete observations.

Electrokinetic remediation of real soils polluted with chlorinated hydrocarbons: relevance of dichlorination and volatilization processes

Electrokinetic remediation of real soils polluted with chlorinated hydrocarbons: relevance of dichlorination and volatilization processes