Volatility Of Financial Assets Research Articles

Borsa Endeksi, Döviz Kuru, Faiz Oranları ve CDS Primleri Arasındaki Oynaklık Yayılımları: Türkiye Örneği

In recent years, the volatility of financial assets has significantly increased. High volatility causes instability in financial markets and increases portfolio risks. Under these conditions, modeling the volatility, determining the volatility relationships, and volatility spillovers are important for market actors. In this study, for the period January 2, 2010 - April 10, 2020, it was investigated the volatility spillover and correlation relationship between the Borsa Istanbul (BIST) 100 Index, the exchange rates ($/ ), interest rates, and credit default swap (CDS) premiums. It was also examined the effects of economic, political, and social factors on the correlation relationship. In the study, it was seen that the bidirectional volatility spillover between the BIST 100 index - exchange rates, interest rates - exchange rates, and CDS premiums – interest rates, on the other hand, unidirectional volatility spillover from CDS premiums to the exchange rates. A positive volatility relationship was determined between CDS premiums - interest rates and CDS premiums - exchange rates while the negative volatility relationship between interest rates - BIST 100 index and CDS premiums - BIST 100 index. It was also determined that political, economic, and social factors affect the relationships of correlation between variables.

Forecasting Volatility of Stock Index: Deep Learning Model with Likelihood‐Based Loss Function

Volatility is widely used in different financial areas, and forecasting the volatility of financial assets can be valuable. In this paper, we use deep neural network (DNN) and long short‐term memory (LSTM) model to forecast the volatility of stock index. Most related research studies use distance loss function to train the machine learning models, and they gain two disadvantages. The first one is that they introduce errors when using estimated volatility to be the forecasting target, and the second one is that their models cannot be compared to econometric models fairly. To solve these two problems, we further introduce a likelihood‐based loss function to train the deep learning models and test all the models by the likelihood of the test sample. The results show that our deep learning models with likelihood‐based loss function can forecast volatility more precisely than the econometric model and the deep learning models with distance loss function, and the LSTM model is the better one in the two deep learning models with likelihood‐based loss function.

Archmodels.Jl: Estimating Arch Models in Julia

This paper introduces ARCHModels.jl, a package for the Julia programming language that implements a number of univariate and multivariate ARCH-type models. This model class is the workhorse tool for modelling the conditional volatility of financial assets. Their distinguishing feature is that they model the latent volatility as a (deterministic) function of past returns and volatilities. This recursive structure results in loop-heavy code which, due to its just-in-time compiler, Julia is well-equipped to handle. As such, the entire package is written in Julia, without any binary dependencies. We benchmark the performance of ARCHModels.jl against popular implementations in MATLAB, R, and Python, and illustrate its use in a detailed case study.

MODELING THE VOLATILITY FOR LONG TERM INTEREST RATE RETURNS IN THE NIGERIA BOND MARKET USING CONDITIONALY HETEROSCEDASTIC MODELS

Investigating the volatility of financial assets is fundamental to risk management. This study used generalized Autoregressive Conditional Heteroscedastic Volatility models to evaluate the volatility of the long term interest rate of Nigeria's financial market. We also incorporated three innovations distributions viz: the Gaussian, the student-t, and the Generalized Error Distribution (GED) in the modeling process under the maximum likelihood estimation method. The results show that GARCH (GED) is the most performing model for describing the volatility of three and twenty-year interest rate returns while TARCH (GED) is the most suitable model for describing the volatility of five and ten-year interest rate returns in Nigeria. The preferred models will help in the development of tools for effective risk management by monitoring the behavior of long term interest rates.

Modelling volatility of Kuala Lumpur composite index (KLCI) using SV and garch models

It is well-known that financial time series exhibits changing variance and this can have important consequences in formulating economic or financial decisions. In much recent evidence shows that volatility of financial assets is not constant, but rather that relatively volatile periods alternate with more tranquil ones. Thus, there are many opportunities to obtain forecasts of this time-varying risk. The paper presents the modelling volatility of the Kuala Lumpur Composite Index (KLCI) using SV and GARCH models. Thus, the aim of this study is to model the KLCI stock market using two models; Stochastic Volatility (SV) and Generalized Auto-Regressive Conditional Heteroscedasticity (GARCH). This study employs an SV model with Bayesian approach and Markov Chain Monte Carlo (MCMC) sampler; and GARCH model with MLE estimator. The best model will be used to forecast the future volatility of stock returns. The study involves 971 daily observations of KLCI Closing price index, from 2 January 2008 to 10 November 2016, excluding public holidays. SV model is found to be the best based on the lowest RMSE and MAE values.

Does Aggregate Economic Uncertainty Predict the Volatility of Financial Assets?

We investigate the effects of economic uncertainty on the return volatility of financial assets, including equities, bonds, foreign exchange and commodities. We use several popular measures of economic uncertainty, and find the uncertainty displays significant but heterogeneous effect on financial volatility. Economic uncertainty constructed in a data rich environment shows strong effects for most financial assets. In particular, the first principal component of the economic uncertainty measures provides a good balance of the effects. The effects of economic uncertainty on financial volatility appear to be closely related to the state of the economy and are more pronounced around recession periods. Furthermore, our out-of-sample analysis shows that investors can use economic uncertainty to predict financial volatility, from both the statistical and economic perspectives.

Estimation of structural mean breaks for long-memory data sets

ABSTRACTIn long-memory data sets such as the realized volatilities of financial assets, a sequential test is developed for the detection of structural mean breaks. The long memory, if any, is adjusted by fitting an HAR (heterogeneous autoregressive) model to the data sets and taking the residuals. Our test consists of applying the sequential test of Bai and Perron [Estimating and testing linear models with multiple structural changes. Econometrica. 1998;66:47–78] to the residuals. The large-sample validity of the proposed test is investigated in terms of the consistency of the estimated number of breaks and the asymptotic null distribution of the proposed test. A finite-sample Monte-Carlo experiment reveals that the proposed test tends to produce an unbiased break time estimate, while the usual sequential test of Bai and Perron tends to produce biased break times in the case of long memory. The experiment also reveals that the proposed test has a more stable size than the Bai and Perron test. The proposed test is applied to two realized volatility data sets of the S&P index and the Korea won-US dollar exchange rate for the past 7 years and finds 2 or 3 breaks, while the Bai and Perron test finds 8 or more breaks.

PREDICTIVE ACCURACY OF FUTURES OPTIONS IMPLIED VOLATILITY: THE CASE OF THE EXCHANGE RATE FUTURES MEXICAN PESO-US DOLLAR

There has been substantial research effort aimed to forecast futures price return volatilities of financial assets. A significant part of the literature shows that volatility forecast accuracy is not easy to estimate regardless of the forecasting model applied. This paper examines the volatility accuracy of several volatility forecast models for the case of the Mexican peso-USD exchange rate futures returns. The models applied here are a univariate GARCH, a multivariate ARCH (the BEKK model), two option implied volatility models and a composite forecast model. The composite model includes time-series (historical) and option implied volatility forecasts. Different to other works in the literature, in this paper there is a more rigorous analysis of the option implied volatilities calculations. The results show that the option implied models are superior to the historical models in terms of accuracy and that the composite forecast model was the most accurate one (compared to the alternative models) having the lowest mean-squared-errors. However, the results should be taken with caution given that the coefficient of determination in the regressions was relatively low. According to these findings it is recommended to use a composite forecast model if both types of data are available i.e. the time-series (historical) and the option implied.

A conditional autoregressive range model with gamma distribution for financial volatility modelling

The commonly used conditional autoregressive range model with Weibull distribution (henceforth WCARR) suffers from serious inlier problem. We conjecture that this problem is due to a misspecified distribution to the disturbance, and propose a conditional autoregressive range model with gamma distribution (henceforth GCARR) to model the volatility of financial assets. In this paper, we first discuss the theoretical properties of the GCARR model and then compare its empirical performance with the WCARR. Empirical studies are performed on a broad set of stock indices in different countries over different time horizons. Consistent with the conjecture, we find that the GCARR model can reduce not only the inlier problem but also the outlier problem of the WCARR model. The results indicate that our GCARR model describes the dynamics of the range-based volatility better than the WCARR model and thus serves as a better benchmark.

The economic value of using range-based volatility for international REIT diversification

Conditional volatility of financial assets can be estimated through either a return-based estimator or a range-based estimator. This paper investigates whether the range-based estimator can lead to economic benefits over a return-based benchmark. We take an asset-allocation perspective and compare the performances of an all-REIT international portfolio using the two estimators. We find that the portfolio constructed based on the range-based estimator significantly outperforms the one constructed based on the return-based estimator. This conclusion is robust to different portfolio performance measures and asset allocation periods. We also demonstrate the implementability of the range-based portfolio by showing that the economic value of using it is sufficient to compensate for transaction costs. Overall, our findings suggest that using range-based volatility adds value to international diversification among real estate markets.

Estimation of long memory in volatility using wavelets

AbstractThis work studies wavelet-based Whittle estimator of the fractionally integrated exponential generalized autoregressive conditional heteroscedasticity (FIEGARCH) model often used for modeling long memory in volatility of financial assets. The newly proposed estimator approximates the spectral density using wavelet transform, which makes it more robust to certain types of irregularities in data. Based on an extensive Monte Carlo study, both behavior of the proposed estimator and its relative performance with respect to traditional estimators are assessed. In addition, we study properties of the estimators in presence of jumps, which brings interesting discussion. We find that wavelet-based estimator may become an attractive robust and fast alternative to the traditional methods of estimation. In particular, a localized version of our estimator becomes attractive in small samples.

The price of granularity and fractional finance

The purpose of this paper is to assess the risk premium a fractional financial lognormal (Black-Scholes or BS) process relative to a non-fractional and complete financial pricing model. While fractional Brownian BS models based on the Duncan and Wicks calculus were shown to define a no arbitrage financial model, this paper claim is that this martingale need not be the pricing martingale. There may be many martingales corresponding to a no-arbitrage financial model. In this vein, the intent of this paper are twofold. On the one hand, provide a definition of the risk premium implied by the discount rate applied to future fractional returns as well as justify this premium compared to a non-fractional financial model. To do so, an insurance rationale for the risk implied by the financial asset volatility is used when defining a no-arbitrage risk neutral probability measure. A “granular risk premium”, is then defined relative to the model granularity. On the other, the paper highlights the effects of a model granularity and its Hurst index on financial risk management. In particular, we argue that that such an index is defined by both the granularity underlying the model as well as the effects of mixed models (combining both diffusion and jump processes) on relative range and volatility variations (and thus the measurement of the Hurst index). To present simply the ideas underlying this paper, we price an elementary fractional risk free bond and its risk premium relative to a known spot interest rate. Similarly, the Black-Scholes no arbitrage model is presented in both its non-fractional conventional form and in its fractional framework. The granularity risk premium is then calculated.

Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model

Market crashes often appear in daily trading activities and such instantaneous occurring events would affect the stock prices greatly. In an unstable market, the volatility of financial assets changes sharply, which leads to the fact that classical option pricing models with constant volatility coefficient, even stochastic volatility term, are not accurate. To overcome this problem, in this paper we put forward a dynamic elasticity of variance (DEV) model by extending the classical constant elasticity of variance (CEV) model. Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. In addition, Kalman filtering method is employed to estimate the volatility term of our model. Our main finding is that the prices of European call option under our model are more accurate than those calculated by Black-Scholes model and CEV model in financial crashes.

Modeling and Forecasting Financial Volatilities Using a Joint Model for Range and Realized Volatility

There exist many ways to measure financial asset volatility. In this paper, we introduce a new joint model for the high-low range of assets prices and realized measure of volatility: Realized CARR. In fact, the high-low range and realized volatility, both are efficient estimators of volatility. Hence, this new joint model can be viewed as a model of volatility. The model is similar to the Realized GARCH model of Hansen et al. (2012), and it can be estimated by the quasi-maximum likelihood method. Out-of-sample volatility forecasting using Standard and Poors 500 stock index (S&P), Dow Jones Industrial Average index (DJI) and National Association of Securities Dealers Automated Quotation (NASDAQ) 100 equity index shows that the Realized CARR model does outperform the Realized GARCH model.

The Price of Granularity and Fractional Finance

The purpose of this paper is to assess the risk premium a fractional financial lognormal (Black-Scholes or BS) process relative to a non-fractional and complete financial pricing model. While fractional Brownian BS models based on the Duncan and Wicks calculus were shown to define a no arbitrage financial model, this paper claim is that this martingale need not be the pricing martingale. There may be many martingales corresponding to a no-arbitrage financial model. In this vein, the intent of this paper are twofold. On the one hand, provide a definition of the risk premium implied by the discount rate applied to future fractional returns as well as justify this premium compared to a non-fractional financial model. To do so, an insurance rationale for the risk implied by the financial asset volatility is used when defining a no-arbitrage risk neutral probability measure. A “granular risk premium”, is then defined relative to the model granularity. On the other, the paper highlights the effects of a model granularity and its Hurst index on financial risk management. In particular, we argue that that such an index is defined by both the granularity underlying the model as well as the effects of mixed models (combining both diffusion and jump processes) on relative range and volatility variations (and thus the measurement of the Hurst index). To present simply the ideas underlying this paper, we price an elementary fractional risk free bond and its risk premium relative to a known spot interest rate. Similarly, the Black-Scholes no arbitrage model is presented in both its non-fractional conventional form and in its fractional framework. The granularity risk premium is then calculated.

Semiparametric Conditional Quantile Models for Financial Returns and Realized Volatility

This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex-post variation in asset prices as well as option-implied volatility. We work in the flexible quantile regression framework and rely on recently developed model-free measures of integrated variance, upside and downside semivariance, and jump variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show that simple linear quantile regressions for returns and heterogenous quantile autoregressions for realized volatility perform very well in capturing the dynamics of the respective conditional distributions, both in absolute terms as well as relative to a couple of well-established benchmark models. The models can therefore serve as useful risk management tools for investors trading the futures contracts themselves or various derivative contracts written on realized volatility.

Semi-parametric Conditional Quantile Models for Financial Returns and Realized Volatility

This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex post variation in asset prices as well as option-implied volatility. We work in the flexible quantile regression framework and rely on recently developed model-free measures of integrated variance, upside and downside semivariance, and jump variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show that simple linear quantile regressions for returns and heterogenous quantile autoregressions for realized volatility perform very well in capturing the dynamics of the respective conditional distributions, both in absolute terms as well as relative to a couple of well-established benchmark models. The models can therefore serve as useful risk management tools for investors trading the futures contracts themselves or various derivative contracts written on realized volatility.

Stochastic Volatility of Financial Assets and Default Risk

We present the non-Gaussian extension of the traditional Merton framework, which takes into account slowly relaxing fluctuations of the volatility of the firm’s market value of financial assets. The minimal version of the model depends on the Tsallis entropic parameter q and the generalized “distance to default”. For , related to the normal statistics, the new approach replicates results of traditional structural models. For q > 1, corresponding to complex systems with non-additive Tsallis entropy, the model leads to much higher 1-year probability of default for investment grade issuers. The empirical foundation and implications of the model are illustrated by the study of 645 North American industrial firms during the financial crisis, 2006-2012. All defaulters in the sample have exceptionally large q. Using Receiver Operating Characteristic curves, we demonstrate the high forecasting power of the model in prediction of 1-year defaults. We report excellent fitting capabilities of the derived formulae to multi-period default data in both investment-grade and high-yield categories of credit ratings initially assigned to future defaulters. Our study suggests that the level of complexity (“turbulence”) of the time series, quantified by q, should be taken into account to improve valuations of default risk.

Garch model indentification using neural network

GARCH models are being largely used to estimate the volatility offinancial assets, and GARCH(1,1) is the one most used. However, identificationof GARCH models is not fully explored. Some specialist systems technology havebeen used in some applications of time series models such as time seriesclassification problems, ARMA models identification, as well as SARIMA. The aim of this paper is to develop an intelligent system that can accurately identifythe specification of GARCH models providing the right choice of the model to beused, thus avoiding the indiscriminate usage of GARCH(1,1) model.

Bayesian testing volatility persistence in stochastic volatility models with jumps

Whether or not there is a unit root persistence in volatility of financial assets has been a long-standing topic of interest to financial econometricians and empirical economists. The purpose of this article is to provide a Bayesian approach for testing the volatility persistence in the context of stochastic volatility with Merton jump and correlated Merton jump. The Shanghai Composite Index daily return data is used for empirical illustration. The result of Bayesian hypothesis testing strongly indicates that the volatility process doesn’t have unit root volatility persistence in this stock market.