Stochastic Volatility Model Research Articles

Optimal portfolio strategy of wealth process: a Lévy process model-based method

This paper is concerned with the optimal portfolio problem for a company that can invest in two risky assets, where a novel Lévy-process-driven model is constructed to describe the dynamics of the wealth process by using a constant elasticity of variance model and a jump-diffusion process. A delicately designed value function is proposed under the mean–variance criterion to reflect the optimal portfolio for the stochastic volatility model. By using the verification theorem, the desired optimal portfolio strategy is proposed by the solution to certain Hamilton–Jacobi–Bellman equations. Furthermore, the corresponding expressions are achieved by using the stochastic analysis theory. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed optimal portfolio strategy.

Stochastic Volatility Models with Skewness Selection.

This paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to overparameterization. Our proposed approach mitigates this concern by leveraging sparsity-inducing priors to automatically select the skewness parameter as dynamic, static or zero in a data-driven framework. We consider two empirical applications. First, in a bond yield application, dynamic skewness captures interest rate cycles of monetary easing and tightening and is partially explained by central banks' mandates. In a currency modeling framework, our model indicates no skewness in the carry factor after accounting for stochastic volatility. This supports the idea of carry crashes resulting from volatility surges instead of dynamic skewness.

Impact of capital market volatility on economic growth - An analysis based on stochastic volatility model

This paper delves into the relationship between the volatility of the capital market and economic growth within the broader framework of the macro capital market. By employing the Heston stochastic volatility model in tandem with macroeconomic theory, we aim to analyze the stochastic control problem between the allocation trajectory of macro-capital and economic fluctuations. Our mathematical analysis reveals that the influence of capital shifts on economic growth's volatility varies across different capital markets due to diverse risk levels inherent within the macro-capital market. To validate these mathematical findings, we embark on an empirical econometric analysis tailored to the nuances of China's capital market and its macroeconomic operations. This econometric exploration yields two primary insights: 1. Distinct components of China's capital market have varying influences on macroeconomic growth. 2. The structure of China's capital market, especially in its impact on macroeconomic development, exhibits imbalances and lacks optimal configuration.

Implied roughness in the term structure of oil market volatility

This paper analyses the attributes and the significance of the roughness of oil market volatility. We employ unspanned stochastic volatility models driven by rough Brownian motions that yield semi-analytical prices for future options entailing efficient calibration applications. By performing a Monte Carlo simulation study, we show that the semi-analytical pricing performs well thus establishing its efficiency for calibration applications. Thus we calibrate option prices written on oil futures and provide empirical evidence of the roughness in oil volatility. Introducing just one additional parameter, the Hurst parameter, indicating the roughness of the volatility improves the calibration by almost a factor of 10. The calibrated option-implied Hurst parameter varies over time, but the entire set of parameters becomes more stable than in the non-rough case corresponding to a fixed Hurst parameter 1/2. These results underscore the importance to model the time dependency of the roughness of oil market volatility.

Analytically pricing foreign exchange options under a three-factor stochastic volatility and interest rate model: A full correlation structure

The current literature usually ignores the dependence between the rate of exchange and two interest rates, i.e., domestic and foreign ones, for the availability of analytical solutions to foreign exchange option prices, while such settings potentially limit the performance of these models. To address this, we introduce two new factors into the Heston–Hull–White model when foreign exchange options are evaluated. This newly formulated three-factor Heston–Hull–White model still admits a closed-form solution to foreign exchange option prices, which is successfully figured out based on the numeraire change technique and the obtained analytical expression of the characteristic function. Based on options on foreign exchange rate between US and Australian Dollar, both the three-factor and one-factor Heston–Hull–White models are calibrated using the Adaptive Simulated Annealing. When evaluating the performance of both models with in- and out-of-sample errors, the greater forecasting ability of the new model equipped with the two new factors over the one-factor Heston–Hull–White model is identified.

What influences the dynamic spillovers of China’s financial market uncertainties?

ABSTRACT Uncertainty serves as a significant source of volatility in financial markets. The aim of this study is to examine the spillover effects of China’s financial market uncertainties (capital market, currency market, foreign exchange (FX) market and derivatives market) and their potential determinants. A large amount of economic and financial data is selected as the sample dataset to construct the financial uncertainty index by the combination of the stochastic volatility model and the Markov chain Monte Carlo algorithm. The TVP-VAR-DY model and the extreme bounds analysis model are also used to conduct spillover and determinant analyses. The results indicate that uncertainties in capital and currency markets primarily act as transmitters of spillover effects. The derivatives market uncertainty mainly serves as a recipient of influence from other markets, whereas the role of FX market uncertainty is relatively unstable. Moreover, international factors such as global economic policy uncertainty and the implied volatility index (VIX) have a more robust impact on spillover relationships among the four financial uncertainties, whereas domestic factors have the greater impact intensity.

Pricing Discretely Monitored Asian Options Under Regime-Switching and Stochastic Volatility Models with Jumps

Pricing Discretely Monitored Asian Options Under Regime-Switching and Stochastic Volatility Models with Jumps

Economic policy uncertainty and stock market volatility in China: Evidence from SV-MIDAS-t model

This study combines the stochastic volatility (SV) model with a mixed data sampling (MIDAS) structure under t-distribution to investigate the effect of economic policy uncertainty (EPU) on Chinese stock market volatility. Furthermore, we compare eight volatility models regarding using “GARCH or SV” model, “with or without” the MIDAS structure, under “normal or t” distributions. The model comparison results show that SV-MIDAS-t model is the best in terms of data fitting, AIC, BIC, and various loss function criteria. Based on the SV-MIDAS-t model, we find that a rise in EPU index significantly increases the long-term component of volatility, and this impact has a time lag effect.

Induced Garima Stochastic Volatility Models

In the present paper, a stochastic volatility model generated by a first-order induced Garima Markov sequence has been suggested for modeling financial time series. The statistical and probabilistic properties of the suggested model are studied, and the estimation of the model parameters is done using the generalized method of moments. Simulation studies and real data analysis aredone to demonstrate the applicability of the model. Also, the fit has been compared with an existing stochastic volatility model.

Co-volatility dynamics in global cryptocurrency and conventional asset classes: a multivariate stochastic factor volatility approach

Purpose This study aims to investigate the co-volatility patterns between cryptocurrencies and conventional asset classes across global markets, encompassing 26 global indices ranging from equities, commodities, real estate, currencies and bonds. Design/methodology/approach It used a multivariate factor stochastic volatility model to capture the dynamic changes in covariance and volatility correlation, thus offering empirical insights into the co-volatility dynamics. Unlike conventional research on price or return transmission, this study directly models the time-varying covariance and volatility correlation. Findings The study uncovers pronounced co-volatility movements between cryptocurrencies and specific indices such as GSCI Energy, GSCI Commodity, Dow Jones 1 month forward and U.S. 10-year TIPS. Notably, these movements surpass those observed with precious metals, industrial metals and global equity indices across various regions. Interestingly, except for Japan, equity indices in the USA, Canada, Australia, France, Germany, India and China exhibit a co-volatility movement. These findings challenge the existing literature on cryptocurrencies and provide intriguing evidence regarding their co-volatility dynamics. Originality This study significantly contributes to applying asset pricing models in cryptocurrency markets by explicitly addressing price and volatility dynamics aspects. Using the stochastic volatility model, the research adding methodological contribution effectively captures cryptocurrency volatility's inherent fluctuations and time-varying nature. While previous literature has primarily focused on bitcoin and a few other cryptocurrencies, this study examines the stochastic volatility properties of a wide range of cryptocurrency indices. Furthermore, the study expands its scope by examining global asset markets, allowing for a comprehensive analysis considering the broader context in which cryptocurrencies operate. It bridges the gap between traditional asset pricing models and the unique characteristics of cryptocurrencies.

Explore jump behaviour in China's crude oil future market during the COVID-19

ABSTRACT We have conducted a thorough analysis of four stochastic volatility models, including double exponential jumps and infinite-activity Lévy jumps. By selecting recent data from Shanghai crude oil futures and Brent crude oil, we explore the impact of the COVID-19 pandemic and characterized the price fluctuations in the Shanghai crude oil market. We estimate the model parameters using the MCMC method and discuss the significance of jumps in crude oil futures returns. Our study provides evidence that the double exponential jump model is more sensitive to asset price fluctuations and shocks and can better capture the price dynamics of the crude oil market.

Reduced-Order Modeling for Heston Stochastic Volatility Model

In this paper, we compare the intrusive proper orthogonal decomposition (POD) with Galerkin projection and the data-driven dynamic mode decomposition (DMD), for Heston's option pricing model. The full order model is obtained by discontinuous Galerkin discretization in space and backward Euler in time. Numerical results for butterfly spread, European and digital call options reveal that in general DMD requires more modes than the POD modes for the same level of accuracy. However, the speed-up factors are much higher for DMD than POD due to the non-intrusive nature of the DMD.

Time-varying effects of the gold price and the oil price on imports in Turkey

ABSTRACT The impacts of the gold price, the oil price and the exchange rate on imports are analyzed using a time-varying parameter vector autoregressive with stochastic volatility (TVP-VAR-SV) model. The impulse response functions showed that the impact of oil price shocks on imports continued for a short period of time, whereas that of the gold price became more significant and gave rise to long term effects in later periods. The results reveal important implications for policy makers reducing imports, which stimulates a trade deficit in Turkey.

Integrating Complex Derivative Models in Understanding Dollarization’s Impact on Sustainable Development Goals and Environmental Economics: A Neo-Classical Finance Perspective

Dollarization has major implications for sustainable development and environmental economics in developing countries. This paper integrates complex derivative models from neoclassical finance theory, including stochastic volatility, copula, and regime-switching models, to quantitatively analyze the impacts of dollarization. The models examine effects on poverty, inequality, economic growth, natural capital investment, and green bond financing access related to sustainable development goals and environmental economics. Despite limitations in assumptions, the models provide useful risk quantification. Results suggest dollarization exacerbates volatility and negative externalities, hindering sustainability objectives. The integration of derivative modeling and development economics provides an analytical framework for examining dollarization, indicating potential gains from gradual de-dollarization policies. Further empirical research is warranted to validate the theoretical insights.

On an asymmetric multivariate stochastic difference volatility: structure and estimation

<abstract><p>In this study, we explored an asymmetric multivariate stochastic difference volatility model that extends various probabilistic and statistical properties previously discussed in the literature. We rigorously established that the model exhibits periodic stationarity and periodic ergodicity. Additionally, we delved into the robust consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE), providing a comprehensive analysis of its theoretical underpinnings. Finally, we demonstrated the practical applicability of our major findings through a series of pertinent applications. This work not only contributes to the existing body of knowledge on stochastic volatility modeling, but also opens new avenues for further research in this domain.</p></abstract>

Expected power utility maximization with delay for insurers under the 4/2 stochastic volatility model

In this paper, we are interested in the optimal investment and reinsurance strategies of an insurer with delay under the $ 4/2 $ stochastic volatility model. Indeed, the objective of the insurer is to maximize the expected power utility of the terminal wealth and the average wealth on finite time horizon. The other objective is to maximize the growth rate of expected power utility per unit time on infinite time horizon. The wealth of the insurer is described by an approximation of the classical Cramér–Lundberg process. Then, these problems can be formulated as stochastic control problems with delay. A pair of forward-backward stochastic differential equations that are derived via the stochastic maximum principle has an explicit solution obtained by solving a Riccati differential equation. So, the optimal strategy of the finite time horizon problem can be constructed explicitly. And, by investigating asymptotics of the Riccati equation, the infinite time horizon problem can be solved explicitly. Finally, we present some numerical results to illustrate our model, optimal strategies and sensitivities of some parameters.

Markov-switching threshold stochastic volatility models with regime changes

<abstract><p>This paper introduces a comprehensive class of models known as Markov-Switching Threshold Stochastic Volatility (MS-TSV) models, specifically designed to address asymmetry and the leverage effect observed in the volatility of financial time series. Extending the classical threshold stochastic volatility model, our approach expresses the parameters governing log-volatility as a function of a homogeneous Markov chain with a finite state space. The primary goal of our proposed model is to capture the dynamic behavior of volatility driven by a Markov chain, enabling the accommodation of both gradual shifts due to economic forces and sudden changes caused by abnormal events. Following the model's definition, we derive several probabilistic properties of the MS-TSV models, including strict (or second-order) stationarity, causality, ergodicity, and the computation of higher-order moments. Additionally, we provide the expression for the covariance function of the squared (or powered) process. Furthermore, we establish the limit theory for the Quasi-Maximum Likelihood Estimator (QMLE) and demonstrate the strong consistency of this estimator. Finally, a simulation study is presented to assess the performance of the proposed estimation method.</p></abstract>

Copula Variational LSTM for High-Dimensional Cross-Market Multivariate Dependence Modeling.

We address a challenging problem-modeling high-dimensional, long-range dependencies between nonnormal multivariates, which is important for demanding applications such as cross-market modeling (CMM). With heterogeneous indicators and markets, CMM aims to capture between-market financial couplings and influence over time and within-market interactions between financial variables. We make the first attempt to integrate deep variational sequential learning with copula-based statistical dependence modeling and characterize both temporal dependence degrees and structures between hidden variables representing nonnormal multivariates. Our copula variational learning network weighted partial regular vine copula-based variational long short-term memory (WPVC-VLSTM) integrates variational long short-term memory (LSTM) networks and regular vine copula to model variational sequential dependence degrees and structures. The regular vine copula models nonnormal distributional dependence degrees and structures. VLSTM captures variational long-range dependencies coupling high-dimensional dynamic hidden variables without strong hypotheses and multivariate constraints. WPVC-VLSTM outperforms benchmarks, including linear models, stochastic volatility models, deep neural networks, and variational recurrent networks in terms of both technical significance and portfolio forecasting performance. WPVC-VLSTM shows a step-forward for CMM and deep variational learning.

Functional Stochastic Discount Factors in the Stochastic Volatility Model

Functional Stochastic Discount Factors in the Stochastic Volatility Model

Probabilistic properties and estimation methods for periodic threshold autoregressive stochastic volatility

<abstract><p>In an endeavor to encapsulate the dual aspects of volatility progression and periodicity inherent in autocorrelation frameworks demonstrated by various nonlinear time series, a novel conceptualization emerges—the periodic threshold autoregressive stochastic volatility (PTAR-SV) model. This model served as a viable alternative to the conventional periodic threshold generalized autoregressive conditional heteroskedasticity (TGARCH) process. The inherent probabilistic framework of the PTAR-SV model incorporated certain essential features, including strict periodic stationarity, enhancing its analytical robustness. Additionally, this study established the conditions for higher-order moments to exist within the PTAR-SV model. The autocovariance structure pertaining to the powers of the PTAR-SV process has been studied. The process of parameter estimation was scrutinized via the quasi-maximum likelihood technique. This estimation approach involved assessing likelihood using prediction error decomposition and Kalman filtering. Moreover, we extended our analysis to include a Bayesian Markov chain Monte Carlo (MCMC) method based on Griddy-Gibbs sampling, particularly suitable when the distribution of model innovations follows a standard Gaussian. Through a simulation study, we evaluated the performances of both the quasi-maximum likelihood (QML) and Bayesian Griddy Gibbs estimates, providing valuable insights into their respective strengths and weaknesses. Finally, we applied our newly developed methodology to model the spot rates of the euro against the Algerian dinar, demonstrating its applicability and efficacy in real-world financial modeling scenarios.</p></abstract>