Volatility Models Research Articles

Derivative Markets and Economic Growth: A South African Perspective

It is well established that financial development and innovation promote economic growth through improving the allocation of capital, enhancing risk management, contributing to price discovery, and increasing market efficiencies. While a vast empirical literature is devoted to the nexus between financial development and economic growth, however, substantially less research has been done on the relationship between derivatives and growth, especially in the emerging-market context. Derivatives can be viewed as a specific category of financial innovation, which may advance economic growth through its specialised functions of risk management and price discovery. This paper contributes to bridging this gap in the literature by exploring the impact of exchange-traded futures derivatives on South African economic growth, output, and economic growth volatility. It employs ARDL bounds tests, Granger causality tests and GARCH volatility modeling to analyse the effects of exchange-traded futures derivatives on various measures of South African economic activity. The main result is that exchange-traded futures derivatives contribute positively to South African economic growth and economic activity. This may suggest that opportunities might exist in other emerging economies, with financial structures comparable to that of South Africa, to encourage the development of organised and well-regulated derivatives markets to unlock economic growth in these economies.

A Comprehensive Study of Stock Market Volatility: Types, Determinants, and Measurement Methods

The Volatility, a critical aspect of financial markets, quantifies the uncertainty associated with asset price movements. This paper provides a comprehensive review of volatility, encompassing its definition, types, determinants, and measurement methods. Various factors, including macroeconomic indicators, market sentiment, liquidity, global events, and corporate actions, influence volatility. A range of methods, such as standard deviation, historical volatility, implied volatility, GARCH models, EWMA, and range-based volatility, are employed to measure volatility. Understanding volatility is essential for investors, traders, and risk managers to make informed decisions and manage risk effectively. Future research can delve into advanced volatility models, volatility spillovers, investor behavior, and the relationship between volatility and asset pricing.

ANALYSIS OF OPTIMAL PORTFOLIO ON FINITE AND SMALL-TIME HORIZONS FOR A STOCHASTIC VOLATILITY MODEL WITH MULTIPLE CORRELATED ASSETS

In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by [Formula: see text]-dimensional Brownian motions. At first, we derive a Hamilton–Jacobi–Bellman equation including the correlations among the standard Brownian motions. We use an approximation method for the optimization of portfolios. With such approximation, the value function is analyzed using the first-order terms of expansion of the utility function in the powers of time to the horizon. The error of this approximation is controlled using the second-order terms of expansion of the utility function. It is also shown that the one-dimensional version of this analysis corresponds to a known result in the literature. We also generate a close-to-optimal portfolio near the time to horizon using the first-order approximation of the utility function. It is shown that the error is controlled by the square of the time to the horizon. Finally, we provide an approximation scheme to the value function for all times and generate a close-to-optimal portfolio.

Option Pricing Based on REGARCH Model with High-Frequency Information

As a prevalent tool for hedging risk, the trading volume of options has been growing increasingly in the derivatives market. Precision in the estimation of volatility leads to accurate option pricing. Since volatility is time-varying and has a clustering effect, GARCH class of volatility models is effective in modeling volatility precisely. This paper utilizes the realized EGARCH (REGARCH) model combined with Monte Carlo simulation to investigate the role of high-frequency information in option pricing. The parameter estimates of the REGARCH model are obtained via joint maximum likelihood estimation using observations on returns and realized measure. Applying the model to S&P options market, the empirical results show that the REGARCH model that using high-frequency data is more efficient than the model that only use daily closing prices, including the EGARCH, NGARCH and GJR-GARCH models. This paper demonstrates that incorporating realized measures into volatility models can improve the accuracy of option pricing. The REGARCH model contained more intraday trading information from high-frequency data, can measure the additional risk premiums and specific volatility shocks.

Pricing Variable Annuity Contract with GMAB Guarantee Under a Regime Switching Local Volatility Model

Pricing Variable Annuity Contract with GMAB Guarantee Under a Regime Switching Local Volatility Model

Analytic Moments of TGARCH(1,1) Models with Polynomially Adjusted Densities

Abstract This article extends He, Silvennoinen, and Teräsvirta (2008, J Finan Econ, 6, 208–230) and Francq and Zakoïan (2010, GARCH Models) by providing analytical expressions for the moments of the unconditional distribution of the TGARCH(1,1) under alternative specifications for the conditional mean and different skewed distributions for the innovations. We consider polynomially adjusted (PA) densities, such as the PA Logistic, PA hyperbolic secant, and the PA Gaussian, along with the skewed Student-t. Our results show that (i) the main driver of the skewness of the TGARCH(1,1) is the skewness of the innovations, while the excess kurtosis has a comparatively lesser impact. However, both skewness and kurtosis of the innovations significantly affect the TGARCH(1,1) kurtosis; (ii) if the conditional mean is not constant, returns can be asymmetric even if innovations are symmetric; (iii) skewed innovations can generate cross-correlations different from zero, indicating leverage effect, even when the volatility model is symmetric. Finally, we illustrate our theoretical results with an empirical application to stock indices.

Robustness meets co-jumps: optimal consumption and portfolio choice with derivatives

In this paper, we study a robust, dynamic, continuous-time optimal consumption and portfolio allocation problem for investors with recursive preferences who have access to both stock and derivatives markets. We assume the stock price process follows a stochastic volatility model, with instantaneous precision as the unique state variable, allowing for discontinuities in all the dynamics. We obtain a closed-form approximate solution up to a system of ODEs to the optimization problem for a non-unitary value of the elasticity of intertemporal substitution of consumption, being able to derive an exact solution as a particular case. Our theoretical findings show that the optimal policies are remarkably affected by the ambiguity-aversion parameters to diffusive and jump risks. A detailed numerical analysis confirms the effectiveness of our theoretical results on real data. Finally, we prove that investors who do not believe in ambiguity may suffer considerable wealth losses.

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.

A long short-term memory enhanced realized conditional heteroskedasticity model

This paper examines the potential of using realized volatility measures for capturing financial markets’ uncertainty. Earlier studies show the usefulness of the high-frequency data based Generalized AutoRegressive Conditional Heteroskedasticity (RealGARCH) model for enhancing volatility forecasting accuracy; however, this model focuses only on linear and short-term dependencies of realized volatility measures on the underlying volatility. Recognizing the critical economic implications of this limitation, the long short-term memory neural network is integrated into RealGARCH, aiming to explore the full impact of realized volatility on volatility modeling and forecasting via capturing the nonlinear and long-term effects. A comprehensive empirical study using 31 indices from 2004 to 2021 is conducted. The results demonstrate that our proposed framework achieves superior in-sample and out-of-sample performance compared to several benchmark models. Importantly, it retains interpretability and effectively adapts to the stylized facts observed in volatility, emphasizing its significant potential for enhancing economic decision-making and risk management.

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.

High-frequency realized stochastic volatility model

A new high-frequency realized stochastic volatility model is proposed. Apart from the standard daily-frequency stochastic volatility model, the high-frequency stochastic volatility model is fit to intraday returns by extensively incorporating intraday volatility patterns. The daily realized volatility calculated using intraday returns is incorporated into the high-frequency stochastic volatility model by considering the bias in the daily realized volatility caused by microstructure noise. The volatility of intraday returns is assumed to consist of the autoregressive process, the seasonal component of the intraday volatility pattern, and the announcement component responding to macroeconomic announcements. A Bayesian method via Markov chain Monte Carlo is developed for the analysis of the proposed model. The empirical analysis using the 5-minute returns of E-mini S&P 500 futures provides evidence that our high-frequency realized stochastic volatility model improves in-sample model fit and volatility forecasting over the high-frequency stochastic volatility model.

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.

Implied volatility modeling and forecasting: evidence from China

PurposeTesting several approaches for implied volatility modeling and forecasting.Design/methodology/approachComparative empirical study with four traded options.FindingsNon-parametric higher-order spline is better than parametric stochastic volatility inspired (SVI) in China.Research limitations/implicationsOur results imply that even though popular on Wall Street, SVI seems not to be utilized by traders and market-makers in China.Practical implicationsTraders may consider higher-order spline as a better method for implied volatility modeling and forecasting.Originality/valuePropose to model and forecast implied volatility via the fifth-order spline interpolation as a first; initiates studies of the empirical performance of SVI and the fifth-order spline models in implied volatility modeling and forecasting.

FORECASTING THE REALIZED VOLATILITY OF ISLAMIC EQUITIES USING MULTIVARIATE HAR-TYPE MODELS

This study proposes nine multivariate intraday models using various realized variation measures with the aim to improve volatility forecasting in the Islamic stock market in Malaysia using a dataset from 1st April 2008 to 31st March 2018. The findings show that considering independently the jump-robust realized volatility, additional daily jump realized volatility, and continuous and discontinuous jump sample path variations improved the in-sample predictive regressions compared to using the standard realized volatility. For the out-of-sample volatility forecasts evaluation, it is observed that the volatility models that disentangled the realized volatility into its continuous and discontinuous jump components have outperformed the rest of the proposed models. This is because both the continuous and discontinuous variation of returns exhibit distinctive substantial information in yielding the final volatility dynamic and thus should be modeled disjointedly. However, the empirical results suggest that the simple autoregressive specification using the standard realized volatility is often performing better or as well as the new extension models. Lastly, this study may provide useful insight in portfolio management, risk assessment, and asset pricing, particularly in the Shariah-compliant equities.

Technological shocks and stock market volatility over a century

This paper provides a novel perspective on the innovation-stock market nexus by examining the predictive relationship between technological shocks and stock market volatility using data over a period of more than 140 years. Utilizing annual patent data for the U.S. and a large set of economies to create proxies for local and global technological shocks and a mixed-sampling data (MIDAS) framework, we present robust evidence that technological shocks capture significant predictive information regarding future realizations of stock market volatility, both in- and out-of-sample and at both the short and long forecast horizons. Further economic analysis shows that investment portfolios created by the volatility forecasts obtained from the forecasting models that incorporate technological shocks as predictors in volatility models experience significantly lower return volatility in the out-of-sample horizons, which in turn helps to improve the risk-return profile of those portfolios. Our findings present a novel take on the nexus between technological innovations and stock market dynamics and pave the way for several interesting avenues for future research regarding the role of technological innovations on asset pricing tests and portfolio models.

Option pricing under stochastic volatility on a quantum computer

We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under typical market conditions. These algorithms are based on combining well-established numerical methods for stochastic differential equations and quantum amplitude estimation technique. In particular, we empirically show that, despite its simplicity, weak Euler method achieves the same level of accuracy as the better-known strong Euler method in this task. Furthermore, by eliminating the expensive procedure of preparing Gaussian states, the quantum algorithm based on weak Euler scheme achieves drastically better efficiency than the one based on strong Euler scheme. Our resource analysis suggests that option pricing under stochastic volatility is a promising application of quantum computers, and that our algorithms render the hardware requirement for reaching practical quantum advantage in financial applications less stringent than prior art.

Joint calibration of local volatility models with stochastic interest rates using semimartingale optimal transport

We develop and implement a non-parametric method for joint exact calibration of a local volatility model and a correlated stochastic short rate model using semimartingale optimal transport. The method relies on the duality results established in Joseph et al. (Calibration of local volatility models with stochastic interest rates using optimal transport, 2023). and jointly calibrates the whole equity-rate dynamics. It uses an iterative approach which starts with a parametric model and tries to stay close to it, until a perfect calibration is obtained. We demonstrate the performance of our approach on market data using European SPX options and European cap interest rate options. Finally, we compare the joint calibration approach with the sequential calibration, in which the short rate model is calibrated first and frozen.

Modelling Multivariate Return Volatilities by Independent Components Using Johnson SU Likelihood

Time-varying volatility modelling is crucial in financial econometrics. For multivariate data, time-varying correlations across securities are important to explain the co-movement of the data. Therefore, we need to estimate the covariance matrix. Estimating a large conditional covariance matrix requires the estimation of a large number of parameters, which is a hard task and often leads to convergence difficulties in the estimation algorithm. We introduce a framework for forecasting the conditional covariance matrix of a large data set by employing a factor model to reduce dimensionality, with the factors estimated using independent components. The main contribution of our article is the estimation of the unobserved independent components using Johnson SU likelihood, which captures the skewness and excess kurtosis—stylized facts in stock returns. First, we extract the independent components using the Johnson SU distribution, maximizing their non-Gaussianity. Second, we sorted the independent components in terms of their explained variability and fit a univariate GARCH process on a few common independent components. Next, we approximate the conditional covariance matrix of the data through a linear combination of the conditional variances of those select few independent components. We apply this procedure to 50 stock returns data (listed in Nifty 50) that exhibit excess kurtosis and skewness, and the findings show that our methodology dominates other algorithms in extracting the independent components. This method enables fund managers to accurately forecast a large conditional covariance matrix, facilitating effective risk management and portfolio construction.

Assessing the Best Cryptocurrencies for Long-Term Investment Using Mean Reversion and Half-Life Volatility Models

Assessing the Best Cryptocurrencies for Long-Term Investment Using Mean Reversion and Half-Life Volatility Models

Application and Empirical Analysis of Random Volatility Model in Financial Markets

The Stochastic Volatility Model (SVM), as a key innovation in modern financial engineering, has profoundly changed our understanding of the volatility characteristics of financial markets. This model not only considers the volatility of asset prices as a time-varying random variable, but also simulates this uncertainty by introducing stochastic processes such as Brownian motion or more complex stochastic differential equations, thereby achieving a precise characterization of the dynamic characteristics of volatility. Compared to traditional fixed or historical average volatility assumptions, SVM can capture sudden changes in market sentiment, the impact of news events, and the influence of macroeconomic factors on volatility, providing investors with a more realistic perspective on the market. This article not only deeply analyzes the theoretical basis and construction methods of SVM, but also verifies its effectiveness and applicability in different financial market environments through empirical analysis and actual market data, providing valuable references and insights for financial practitioners, scholars, and policy makers.