Asset Volatility Research Articles

A novel circular dynamics in financial networks with cross-correlated volatility and asset movements

In this paper, we propose a novel application of classical directional statistics to model the cross-correlation of asset volatility in financial networks. The proposed novel Circular Volatility Model (CVM) provides a framework for studying the interdependencies of financial assets whose returns exhibit periodic behaviors. By extending traditional volatility models into a circular framework, we establish new pathways for understanding the cyclicity inherent in market dynamics. Our model is rigorously grounded in classical \& directional statistics, utilizing von Mises distributions for parameter estimation and novel circular covariance structures. We offer formal derivations, maximum likelihood estimates, and a novel goodness-of-fit testing framework for this circular model. We establish our methodologies using simulation studies.

HACKED: Understanding the stock market response to cyberattacks

Increasing levels of digitisation make firms more susceptible to cyberattacks and privacy violations. In this paper, we quantify the impact of cybercrime on company stock returns using a large international sample. On the day after the cyber event, stock returns are found to decrease by -0.24%, but the effect reverses in about two weeks. The magnitude of the decrease in the stock market is greatest for companies that have experienced reoccurring events and for breaches deemed to be most severe. We show that the extent of the stock market decline cannot be explained by national institutional and macroeconomic factors, and is related to company-specific characteristics, including size, volatility, credit ranking and asset volatility. The empirical results highlight important policy and regulatory issues, not least the need for cyber risk disclosure requirements.

The Choice of Optimal Risk Retention Forms from the Perspective of Asymmetric Information

The risk retention rule requires issuers to retain part of their securities and share the interests of investors. The different forms of risk retention chosen lead to different financing effects of enterprises. In order to explore the optimal choice of risk retention forms in different environments, according to asset pricing theory and asset securitization practice combined with risk retention rules, we obtain issuer payoff models under three forms of risk retention. Through numerical simulation and economic meaning analysis, we draw the following conclusions: hybrid retention can not only alleviate the side effects of horizontal retention but also reduce the proportion of vertical retention, which can improve the issuer payoffs; horizontal retention is more suitable for situations where asset pool losses are small or asset volatility is large, while vertical retention is the opposite. Therefore, we suggest that securities issuers should consider the assets of enterprises and macroeconomic situations to choose the optimal form of risk retention.

VOLATILITY SPILLOVER EFFECTS BETWEEN STOCK MARKETS DURING THE CRISIS PERIODS: DIAGONAL BEKK APPROACH

A rise in the yield of financial market assets could lead to variations in the returns of other assets over time due to arbitrage conditions. Consequently, this phenomenon may trigger spillover effects or cointegration among the volatilities of assets within financial markets. The aim of this study is to investigate spillover effects among American, European, Russian, and Turkish stock markets during the COVID-19 pandemic and the Russia-Ukraine war. Employing the diagonal BEKK-GARCH model from 2020 to 2023, the volatility transmissions within stock returns is examined. The results reveal significant GARCH effects alongside modest ARCH effects. Notably, during the COVID-19 period, the European market exerted the most significant influence on other markets, whereas during the war period, the US market dominated, and Turkish markets displaying the least impact for two periods. Furthermore, the findings indicate that the lagged cross-volatility persistence is lower during the Russia-Ukraine war period compared to the COVID-19 period.

The determinants of funding liquidity risk in decentralized lending

Decentralized lending in the DeFi ecosystem mirrors traditional financial intermediation but poses significant risks, particularly funding liquidity risk, due to the volatility and composbility of digital assets, high leverage, and the absence of regulatory protections. This study applies traditional financial intermediation theories to DeFi lending and empirically test which internal factors such as interest rates and user market power, as well as external factors like the USD Index, influence funding liquidity risk in DeFi lending. Analyzing high-frequency blockchain data using the ARDL model and a novel dynamic ARDL simulation from major pools such as Wrapped Bitcoin (WBTC) and Wrapped Ethereum (WETH), the research finds that current algorithmic interest rate models fail to function as effective self-stabilization mechanisms. Additionally, lower deposit concentration in these pools may exacerbate, rather than mitigate, funding liquidity risk.

Optimising Stock Market Indices for Emerging Economies: An Empirical Study of the Iraqi Stock Exchange

This research explores the efficiency of different ways to construct a stock market index in the Iraqi Stock Exchange (ISX) context, an emerging market with unique traits. Five methods are considered: Price-Weighted Index (PWI), Equal-Weighted Index (EWI), Geometric Mean Index (GMI), Risk-Weighted Index (RWI) and Volatility-Weighted Index (VWI). The ISX60 index is used as a benchmark against their performance. The study employs 57 stocks listed on the ISX from August 2022 to August 2024, covering two years. We examine each method’s stability, performance, and representativeness through graphical analysis and comparative evaluation when building an index. The results indicate that broader indices with more components show higher stability under all constructions. GMI works well in tracking general trends across the market, while RWI and VWI appear effective at controlling risk and reducing exposure to volatile assets, respectively. It also underscores diversification as critical for constructing indices and tradeoffs between representation versus stability in emerging markets. Such insights enhance understanding of how indices can be created in developing financial systems and have practical implications for investors, policymakers, and financial analysts operating within Iraqi or similar emerging economy settings.

Bonds versus Equities: Information for Investment

ABSTRACTWe provide a simple model of investment by a firm funded with debt and equity and empirical evidence to demonstrate that, once we control for the debt overhang problem with credit spreads, asset volatility is an unambiguously positive signal for investment, while equity volatility sends a mixed signal: Elevated volatility raises the option value of equity and increases investment for financially sound firms, but exacerbates debt overhang and decreases investment for firms close to default. Our study provides a simple unified understanding of the structural and empirical relationships between investment, credit spreads, equity versus asset volatility, leverage, and Tobin's .

Some bivariate options pricing in a regime-switching stochastic volatility jump-diffusion model with stochastic intensity, stochastic interest and dependent jump

This paper investigates the performance of bivariate options in the hypothesis of association between two underlying assets. Instead of the classical jump-diffusion process, the volatility of assets and the intensity of Poisson co-jump are both subject to the regime-switching square root process in this price dynamics. The endogenous and exogenous interest rate processes are introduced to examine the effect of interest rate on bivariate options pricing, respectively. An analytic pricing expression of bivariate options are deduced by joint discounted conditional characteristic function. Furthermore, the Fourier cosine expansion method is applied to obtain the approximated solutions of bivariate options price. Simulation and numerical examples are realized to examine the effect of the proposed model, the Fourier cosine expansion method, and the sensitivity of key arguments. The results indicate that embedding stochastic intensity, dependent structure of co-jump, and Markov regime-switching into the pricing dynamics have a significant influence on option pricing, and options prices are robust with respect to the choice of interest rate process.

Existence of maximal solutions for the financial stochastic Stefan problem of a volatile asset with spread

In this work, we consider the outer Stefan problem for the short-time prediction of the spread of a volatile asset traded in a financial market. The stochastic equation for the evolution of the density of sell and buy orders is the Heat Equation with a space–time white noise, posed in a moving boundary domain with velocity given by the Stefan condition. This condition determines the dynamics of the spread, and the solid phase [s−(t),s+(t)] defines the bid–ask spread area wherein the transactions vanish. We introduce a reflection measure and prove existence and uniqueness of maximal solutions up to stopping times in which the spread s+(t)−s−(t) stays a.s. non-negative and bounded. For this, we define an approximation scheme, and use some of the estimates of Hambly et al. (2020) for the Green’s function and the associated to the reflection measure obstacle problem. Analogous results are obtained for the equation without reflection corresponding to a signed density.

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.

Comparison of Triple Exponential Smoothing and ARIMA in Predicting Cryptocurrency Prices

Cryptocurrency has emerged as a prominent digital asset over the past decade, but its high price volatility presents significant challenges for investors. This study evaluates and compares the effectiveness of the Triple Exponential Smoothing (TES) and Autoregressive Integrated Moving Average (ARIMA) methods in forecasting the prices of five major cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Binance Coin (BNB), Solana (SOL), and Ripple (XRP). TES models trends and seasonality in time series data, while ARIMA captures autoregressive patterns and moving averages. The dataset is split into 80% for training and 20% for testing, with performance evaluated using Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE). TES outperforms ARIMA in predicting Bitcoin and Binance Coin, achieving MAPE values of 10.38% and 13.81%, and RMSE values of 3,985.55 and 41.28, respectively. However, ARIMA shows better performance for Ethereum, Solana, and Ripple, with MAPE ranging from 8.78% to 32.84% and RMSE between 0.08 and 204.59. Notably, Ethereum has the lowest MAPE at 8.78%, while Ripple exhibits the smallest RMSE at 0.08. These findings suggest that TES is more suitable for cryptocurrencies with relatively stable price patterns, while ARIMA is better adapted to forecasting highly volatile assets. This research underscores the importance of selecting forecasting models based on the specific characteristics of each cryptocurrency

Improvement of Real-GJR Model using Jump Variables on High Frequency Data

Volatility is a key indicator in assessing risk when making investment decisions. In the world of financial markets, volatility reflects the degree to which the value of a financial asset fluctuates over a given period. The most common way to measure the future loss potential of an investment is through volatility. Focusing on the Realized GJR (RealGJR) volatility model, which consists of return, conditional volatility, and measurement equations, this study proposes the RealGJR-CJ model developed by decomposing the exogenous variable in the volatility equation of RealGJR into continuous C and discontinuous (jump) J variables. The decomposition of exogenous variables makes the RealGJR-CJ model follow realistic financial markets, where the asset volatility is a continuous process with some jump components. As an empirical illustration, the models are applied to an index in the Japanese stock market, namely Tokyo Stock Price Index, covering from January 2004 to December 2011. The observed exogenous variable in the volatility equation of RealGJR models is Realized Volatility (RV), which is calculated using intraday data with time intervals of 1 and 5 minutes. Adaptive Random Walk Metropolis method was employed in Markov Chain Monte Carlo algorithm to estimate the model parameters by updating the parameters during sampling based on previous samples from the chain. From the results of running the MCMC algorithm 20 times, the mean of the information criteria of competing models is significantly different based on standard deviation and the result suggests that the model with continuous and jump variables can improve the model without jump. The best fit model is provided by RealGJR-CJ with the adoption of 1-minute RV data.

Deep learning enhanced volatility modeling with covariates

Exogenous information such as policy news and economic indicators can have the potential to trigger significant movements in financial asset volatility. This article presents a model, called the RECH-X model, that allows incorporating exogenous variables into a recurrent neural network for volatility modeling and forecasting. The RECH-X model can allow for abrupt changes in the volatility level and effectively capture the complex serial dependence structure in the volatility dynamics. We demonstrate in a wide range of applications that the RECH-X model consistently outperforms the benchmark models in terms of volatility modeling and forecasting.

Volatility spillover effect between cryptocurrency and stock market using MGARCH Bekk model

This paper explores the volatility spillover effects between the cryptocurrency market and the Pakistan Stock Exchange (PSX). Utilising data from January 1, 2019, to April 5, 2024, sourced from Investing and Yahoo Finance, the study employs the Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MGARCH) BEKK model to assess the dynamic interactions between these markets. Stationarity tests confirmed the non-stationarity of time series data at their levels, which became stationary after first differencing, ensuring robust econometric analysis. The results indicate significant volatility spillovers from major cryptocurrencies, such as Bitcoin and Ethereum, to the PSX, highlighting a solid interconnectedness between these markets. This suggests that digital asset volatility significantly influences traditional financial systems. The study concludes that integrating cryptocurrencies into global financial markets introduces risks and opportunities for investors and policymakers. The findings underscore the need for market participants to account for these volatility interactions in their risk management strategies. Additionally, policymakers must consider these interlinkages to maintain financial stability. This research contributes to the literature on financial market volatility by emphasising the importance of understanding the impact of emerging digital currencies on traditional stock markets.

Cost-efficient payoffs under model ambiguity

Dybvig (1988a, 1988b) solves in a complete market setting the problem of finding a payoff that is cheapest possible in reaching a given target distribution (“cost-efficient payoff”). In the presence of ambiguity, the distribution of a payoff is, however, no longer known with certainty. We study the problem of finding the cheapest possible payoff whose worst-case distribution stochastically dominates a given target distribution (“robust cost-efficient payoff”) and determine solutions under certain conditions. We study the link between “robust cost-efficiency” and the maxmin expected utility setting of Gilboa and Schmeidler (1989), as well as more generally in a possibly nonexpected robust utility setting. Specifically, we show that solutions to maxmin robust expected utility are necessarily robust cost-efficient. We illustrate our study with examples involving uncertainty both on the drift and on the volatility of the risky asset.

Analytically pricing European options in dynamic markets: Incorporating liquidity variations and economic cycles

This paper discusses the European option pricing problem in the context of asset prices being influenced by liquidity risks and economic cycles. We employ regime switching for asset volatility, and liquidity risks are captured by market-wide liquidity. We obtain an analytical formulation of European option prices, allowing for fast model calibration using real-market data. By estimating model parameters using real option data, we show that pricing errors can be significantly reduced using our model that considers stochastic liquidity, indicating that our model has real-world applications. Our results can help investors and regulators better understand the market and provide a potentially effective risk management tool.

The Impact of Financial Stress and Uncertainty on Green and Conventional Bonds and Stocks: A Nonlinear and Nonparametric Quantile Analysis

This study aims to investigate the impact of financial stress and uncertainty on the returns of green and conventional bonds and stocks in the United States from 2010 to 2022. The research utilizes nonlinear and nonparametric analysis, which includes the quantile-on-quantile and nonparametric causality-in-quantiles approaches to examine the relationship between variables. The data analyzed using R programming language show that financial stress positively impacts the middle quantiles of both conventional and green equity, while financial uncertainty negatively impacts upper quantiles. The study also finds that financial stress has a more significant impact on all types of bonds compared to financial uncertainty, with conventional bonds being more affected. This study proposes a pyramid that classifies financial assets based on their susceptibility to financial stress, which could help investors evaluate risk levels and make better investment decisions. The study recommends that policymakers should encourage green investments by offering incentives, such as tax credits. They should also focus on enhancing the efficiency of volatile assets by implementing new investment rules and regulations.

Volatility spillover and dynamic correlation between Islamic, conventional, cryptocurrency and precious metal markets during the immediate outbreak of COVID-19 pandemic

PurposeThis paper aims to investigate the immediate effect of the outbreak of the COVID-19 pandemic by investigating volatility transmission and dynamic correlation between stock (conventional and Islamic) markets, bitcoin and major commodities such as gold, oil and silver at different investment horizons before and after 161 trading days of the outbreak of the COVID-19 pandemic.Design/methodology/approachThe MGARCH-DCC and maximum overlap discrete wavelet transform -based cross-correlation were used in the estimation of the volatility spillover and continuous wavelet transform in the estimation of the time-varying volatility and correlation between the assets at different investment horizons.FindingsThe authors observed a sudden correlation breakdown following the COVID-19 shock. Oil (Bitcoin) was a major volatility transmitter before (during) COVID-19. Digital gold (Bitcoin), gold and silver became highly correlated during COVID-19. The highest co-movement between the assets was observed at medium and long-term investment horizons.Practical implicationsThe study findings have a financial implication for day traders, investors and policymakers in the understanding of volatility transmission and intercorrelation in a bid to actively manage stylized and well-diversified asset portfolios.Originality/valueThis study is unique for its employment in estimating the time-varying conditional volatility of the investable assets and cross-correlations between them at different investment horizons, particularly before and after COVID-19 outbreak.

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.

Modelling the Volatility of NFTs and Traditional Financial Assets using MGARCH Family Models

Modelling the Volatility of NFTs and Traditional Financial Assets using MGARCH Family Models