An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is...An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.展开更多
Based on the weekly closing price of Shenzhen Integrated Index, this article studies the volatility of Shenzhen Stock Market using three different models： Logistic, AR（1） and AR（2）. The time-variable parameters o...Based on the weekly closing price of Shenzhen Integrated Index, this article studies the volatility of Shenzhen Stock Market using three different models： Logistic, AR（1） and AR（2）. The time-variable parameters of Logistic regression model is estimated by using both the index smoothing method and the time-variable parameter estimation method. And both the AR（1） model and the AR（2） model of zero-mean series of the weekly dosing price and its zero-mean series of volatility rate are established based on the analysis results of zero-mean series of the weekly closing price, Six common statistical methods for error prediction are used to test the predicting results. These methods are： mean error （ME）, mean absolute error （MAE）, root mean squared error （RMSE）, mean absolute percentage error （MAPE）, Akaike＇s information criterion （AIC）, and Bayesian information criterion （BIC）. The investigation shows that AR（1） model exhibits the best predicting result, whereas AR（2） model exhibits predicting results that is intermediate between AR（1） model and the Logistic regression model.展开更多
This paper aims to investigate the effectiveness of four volatility forecasting models, i.e. Exponential Weighted Moving Average （EWMA）, Autoregressive Integrated Moving Average （ARIMA） and Generalized Auto-Regres...This paper aims to investigate the effectiveness of four volatility forecasting models, i.e. Exponential Weighted Moving Average （EWMA）, Autoregressive Integrated Moving Average （ARIMA） and Generalized Auto-Regressive Conditional Heteroscedastic （GARCH）, in four stock markets Indonesia, Malaysia, Japan and Hong Kong. Using monthly closing stock index prices collected from 1 st January 1998 to 31 st December 2015 for the four selected countries, results obtained confirm that volatility in developed markets is not necessarily always lower than the volatility in emerging markets. Among all the three models, GARCH （1, l） model is found to be the best forecasting model for stock markets in Malaysia, Indonesia, and Japan, while EWMA model is found to be the best forecasting model for Hong Kong stock market. The outperformance of GARCH （1, 1） found supports again what is found in Minkah （2007）.展开更多
A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC...A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.展开更多
Since market uncertainty,or volatility,serves as a crucial gauge for assessing the traits of market fluctuations,the link between stock market volume and price continues to be a focal point of interest in finance.This...Since market uncertainty,or volatility,serves as a crucial gauge for assessing the traits of market fluctuations,the link between stock market volume and price continues to be a focal point of interest in finance.This study examines the dynamic,nonlinear correlations between Chinese stock volatility,trading volume,and return using a hybrid approach that combines the Markov-switching regime with the vector autoregressive model(MS-VAR).The empirical findings are as follows:(1)The Chinese stock market can be divided into three regional systems:steady downward,steady upward,and high volatility.The three states have similar frequencies of occurrence,and their corresponding stable probabilities are not high,indicating that the Chinese stock market is unstable.(2)Asymmetric dynamic relationships exist between market volatility,investment return,and trading volume.For different regimes,while the effect of trading volume on volatility and return appears to be insignificant,the impacts of volatility and return on trading volume are considerably strong.(3)A regime-dependent,contemporaneous correlation between volatility and return is observed,which also reflects the behavior of the Chinese stock market“chasing up and down”.However,a positive contemporaneous correlation always exists between volatility and trading volumes in different regimes,indicating that uncertainty in the Chinese stock market is closely related to information inflow.展开更多
In this work we consider a stochastic volatility model, commonly used in financial time series studies, to analyse ozone data. The model considered depends on some parameters and in order to estimate them a Markov cha...In this work we consider a stochastic volatility model, commonly used in financial time series studies, to analyse ozone data. The model considered depends on some parameters and in order to estimate them a Markov chain Monte Carlo algorithm is proposed. The algorithm considered here is the so-called Gibbs sampling algorithm which is programmed using the language R. Its code is also given. The model and the algorithm are applied to the weekly ozone averaged measurements obtained from the monitoring network of Mexico City.展开更多
The aim of this paper is to use the General Autoregressive Conditional Heteroscedastic (GARCH) type models for the estimation of volatility of the daily returns of the Kenyan stock market: that is Nairobi Securities E...The aim of this paper is to use the General Autoregressive Conditional Heteroscedastic (GARCH) type models for the estimation of volatility of the daily returns of the Kenyan stock market: that is Nairobi Securities Exchange (NSE). The conditional variance is estimated using the data from March 2013 to February 2016. We use both symmetric and asymmetric models to capture the most common features of the stock markets like leverage effect and volatility clustering. The results show that the volatility process is highly persistent, thus, giving evidence of the existence of risk premium for the NSE index return series. This in turn supports the positive correlation hypothesis: that is between volatility and expected stock returns. Another fact revealed by the results is that the asymmetric GARCH models provide better fit for NSE than the symmetric models. This proves the presence of leverage effect in the NSE return series.展开更多
In this paper, we consider the leverage effect on the CSI 300 Index yield and Hong Kong Hang Seng Index yield. It is modeled by the SV model with leverage. In this model, we compare the mainland and the Hong Kong stoc...In this paper, we consider the leverage effect on the CSI 300 Index yield and Hong Kong Hang Seng Index yield. It is modeled by the SV model with leverage. In this model, we compare the mainland and the Hong Kong stock market with stock market long-term effect, the degree on fluctuation reply and leverage effect so on. The analysis results show that the leverage stochastic volatility model can well fitting rate of return on the CSI300 index and the Hang Seng index in Hong Kong;The Shanghai and Shenzhen stock market volatility and leverage effect obviously stronger than the Hong Kong stock market.展开更多
An explicit formula for the transition probability density function of the Hull and White stochastic volatility model in presence of nonzero correlation between the stochastic differentials of the Wiener processes on ...An explicit formula for the transition probability density function of the Hull and White stochastic volatility model in presence of nonzero correlation between the stochastic differentials of the Wiener processes on the right hand side of the model equations is presented. This formula gives the transition probability density function as a two dimensional integral of an explicitly known integrand. Previously an explicit formula for this probability density function was known only in the case of zero correlation. In the case of nonzero correlation from the formula for the transition probability density function we deduce formulae (expressed by integrals) for the price of European call and put options and closed form formulae (that do not involve integrals) for the moments of the asset price logarithm. These formulae are based on recent results on the Whittaker functions [1] and generalize similar formulae for the SABR and multiscale SABR models [2]. Using the option pricing formulae derived and the least squares method a calibration problem for the Hull and White model is formulated and solved numerically. The calibration problem uses as data a set of option prices. Experiments with real data are presented. The real data studied are those belonging to a time series of the USA S&P 500 index and of the prices of its European call and put options. The quality of the model and of the calibration procedure is established comparing the forecast option prices obtained using the calibrated model with the option prices actually observed in the financial market. The website: http://www.econ.univpm.it/recchioni/finance/w17 contains some auxiliary material including animations and interactive applications that helps the understanding of this paper. More general references to the work of the authors and of their coauthors in mathematical finance are available in the website: http://www.econ.univpm.it/recchioni/finance.展开更多
Stochastic volatility models are used in mathematical finance to describe the dynamics of asset prices. In these models, the asset price is modeled as a stochastic process depending on time implicitly defined by a sto...Stochastic volatility models are used in mathematical finance to describe the dynamics of asset prices. In these models, the asset price is modeled as a stochastic process depending on time implicitly defined by a stochastic differential Equation. The volatility of the asset price itself is modeled as a stochastic process depending on time whose dynamics is described by a stochastic differential Equation. The stochastic differential Equations for the asset price and for the volatility are coupled and together with the necessary initial conditions and correlation assumptions constitute the model. Note that the stochastic volatility is not observable in the financial markets. In order to use these models, for example, to evaluate prices of derivatives on the asset or to forecast asset prices, it is necessary to calibrate them. That is, it is necessary to estimate starting from a set of data the values of the initial volatility and of the unknown parameters that appear in the asset price/volatility dynamic Equations. These data usually are observations of the asset prices and/or of the prices of derivatives on the asset at some known times. We analyze some stochastic volatility models summarizing merits and weaknesses of each of them. We point out that these models are examples of stochastic state space models and present the main techniques used to calibrate them. A calibration problem for the Heston model is solved using the maximum likelihood method. Some numerical experiments about the calibration of the Heston model involving synthetic and real data are presented.展开更多
This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid t...This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid the COVID-19 pandemic. Initially, a univariate GARCH model is developed to derive residual sequences, which are then used to estimate the DCC model parameters. The research reveals a significant rise in the interconnection between the Chinese and U.S. stock markets during the pandemic. The S&P 500 index displayed higher sensitivity and greater volatility in response to the pandemic, whereas the CSI 300 index showed superior resilience and stability. Analysis and model estimation suggest that the market’s dependence on historical data has intensified and its sensitivity to recent shocks has heightened. Predictions from the model indicate increased market volatility during the pandemic. While the model is proficient in capturing market trends, there remains potential for enhancing the accuracy of specific volatility predictions. The study proposes recommendations for policymakers and investors, highlighting the importance of improved cooperation in international financial market regulation and investor education.展开更多
Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
This paper mainly through the comparison of GARCH-VaR China stock market board,small board and gem in the United States correspond to the three stock index volatility,volatility between stock indexes obtained U.S.stoc...This paper mainly through the comparison of GARCH-VaR China stock market board,small board and gem in the United States correspond to the three stock index volatility,volatility between stock indexes obtained U.S.stock market volatility risk multi-level market differences.As a suggestion and reference for investors,it can also provide reference for the supervision department of stock market risk.Based on the empirical research,analyzes the advantages and disadvantages of traditional risk measurement methods,and combined with GARCH model with high degree of complexity and the practice effect analysis,trying to find the objective measure stock model analysis.In the specific study of the volatility of the stock market,through the comparison of China’s three major plates and the market classification mechanism of mature U.S.stock market,combined with the objective situation of the market,draw conclusions and change expectations.From the empirical results,the U.S.stock market has recovered after the financial crisis,and its performance on risk volatility is better than China’s three major plates.From the comparison of the stock market in the same country,the small and medium-sized plates tend to have greater risks,while the risks of the main board and the gem have the characteristics of low average value but frequent fluctuations.展开更多
Determining which variables affect price realized volatility has always been challenging.This paper proposes to explain how financial assets influence realized volatility by developing an optimal day-to-day forecast.T...Determining which variables affect price realized volatility has always been challenging.This paper proposes to explain how financial assets influence realized volatility by developing an optimal day-to-day forecast.The methodological proposal is based on using the best econometric and machine learning models to forecast realized volatility.In particular,the best forecasting from heterogeneous autoregressive and long short-term memory models are used to determine the influence of the Standard and Poor’s 500 index,euro-US dollar exchange rate,price of gold,and price of Brent crude oil on the realized volatility of natural gas.These financial assets influenced the realized volatility of natural gas in 87.4% of the days analyzed;the euro-US dollar exchange rate was the primary financial asset and explained 40.1% of the influence.The results of the proposed daily analysis differed from those of the methodology used to study the entire period.The traditional model,which studies the entire period,cannot determine temporal effects,whereas the proposed methodology can.The proposed methodology allows us to distinguish the effects for each day,week,or month rather than averages for entire periods,with the flexibility to analyze different frequencies and periods.This methodological capability is key to analyzing influences and making decisions about realized volatility.展开更多
The financial market is the core of national economic development,and stocks play an important role in the financial market.Analyzing stock prices has become the focus of investors,analysts,and people in related field...The financial market is the core of national economic development,and stocks play an important role in the financial market.Analyzing stock prices has become the focus of investors,analysts,and people in related fields.This paper evaluates the volatility of Apple Inc.(AAPL)returns using five generalized autoregressive conditional heteroskedasticity(GARCH)models:sGARCH with constant mean,GARCH with sstd,GJR-GARCH,AR(1)GJR-GARCH,and GJR-GARCH in mean.The distribution of AAPL’s closing price and earnings data was analyzed,and skewed student t-distribution(sstd)and normal distribution(norm)were used to further compare the data distribution of the five models and capture the shape,skewness,and loglikelihood in Model 4-AR(1)GJR-GARCH.Through further analysis,the results showed that Model 4,AR(1)GJR-GARCH,is the optimal model to describe the volatility of the return series of AAPL.The analysis of the research process is both,a process of exploration and reflection.By analyzing the stock price of AAPL,we reflect on the shortcomings of previous analysis methods,clarify the purpose of the experiment,and identify the optimal analysis model.展开更多
Since the establishment of financial models for risk prediction,the measurement of volatility at risky market has improved,and its significance has also grown.For high-frequency financial data,the degree of investment...Since the establishment of financial models for risk prediction,the measurement of volatility at risky market has improved,and its significance has also grown.For high-frequency financial data,the degree of investment risk,which has always been the focus of attention,is measured by the variance of residual sequence obtained following model regression.By integrating the long short-term memory(LSTM)model with multiple generalized autoregressive conditional heteroscedasticity(GARCH)models,a new hybrid LSTM model is used to predict stock price volatility.In this paper,three GARCH models are used,and the model that can best fit the data is determined.展开更多
This study investigates the static and dynamic return and volatility spillovers between non-fungible tokens(NFTs)and conventional currencies using the time-varying parameter vector autoregressions approach.We reveal t...This study investigates the static and dynamic return and volatility spillovers between non-fungible tokens(NFTs)and conventional currencies using the time-varying parameter vector autoregressions approach.We reveal that the total connectedness between these markets is weak,implying that investors may increase the diversification benefits of their multicurrency portfolios by adding NFTs.We also find that NFTs are net transmitters of both return and volatility spillovers;however,in the case of return spillovers,the influence of NFTs on conventional currencies is more pronounced than that of volatility shock transmissions.The dynamic exercise reveals that the returns and volatility spillovers vary over time,largely increasing during the onset of the Covid-19 crisis,which deeply affected the relationship between NFTs and the conventional currencies markets.Our findings are useful for currency traders and NFT investors seeking to build effective cross-currency and cross-asset hedge strategies during systemic crises.展开更多
基金National Natural Science Foundation of China(No.62073071)Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University,China(No.CUSF-DH-D-2021045)。
文摘An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.
基金The research is supported by the National Natural Science Foundation of China (60574069)the Soft Science Foundation of Guangdong Province (2005B70101044)
文摘Based on the weekly closing price of Shenzhen Integrated Index, this article studies the volatility of Shenzhen Stock Market using three different models： Logistic, AR（1） and AR（2）. The time-variable parameters of Logistic regression model is estimated by using both the index smoothing method and the time-variable parameter estimation method. And both the AR（1） model and the AR（2） model of zero-mean series of the weekly dosing price and its zero-mean series of volatility rate are established based on the analysis results of zero-mean series of the weekly closing price, Six common statistical methods for error prediction are used to test the predicting results. These methods are： mean error （ME）, mean absolute error （MAE）, root mean squared error （RMSE）, mean absolute percentage error （MAPE）, Akaike＇s information criterion （AIC）, and Bayesian information criterion （BIC）. The investigation shows that AR（1） model exhibits the best predicting result, whereas AR（2） model exhibits predicting results that is intermediate between AR（1） model and the Logistic regression model.
文摘This paper aims to investigate the effectiveness of four volatility forecasting models, i.e. Exponential Weighted Moving Average （EWMA）, Autoregressive Integrated Moving Average （ARIMA） and Generalized Auto-Regressive Conditional Heteroscedastic （GARCH）, in four stock markets Indonesia, Malaysia, Japan and Hong Kong. Using monthly closing stock index prices collected from 1 st January 1998 to 31 st December 2015 for the four selected countries, results obtained confirm that volatility in developed markets is not necessarily always lower than the volatility in emerging markets. Among all the three models, GARCH （1, l） model is found to be the best forecasting model for stock markets in Malaysia, Indonesia, and Japan, while EWMA model is found to be the best forecasting model for Hong Kong stock market. The outperformance of GARCH （1, 1） found supports again what is found in Minkah （2007）.
基金Sponsored by the National Natural Science Foundation of China(70571010)
文摘A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.
基金This work was partially supported by the National Natural Science Foundation of China(Grant No.:72171192)the MOE Layout Foundation of Humanities and Social Sciences(Grant No.:22YJA790007)+1 种基金the Science and Technology Innovation Program of Hunan Province(Grant No.:2021RC3057)the Youth Innovation Team of Shanxi University,and the Fundamental Research Funds for the Central Universities.
文摘Since market uncertainty,or volatility,serves as a crucial gauge for assessing the traits of market fluctuations,the link between stock market volume and price continues to be a focal point of interest in finance.This study examines the dynamic,nonlinear correlations between Chinese stock volatility,trading volume,and return using a hybrid approach that combines the Markov-switching regime with the vector autoregressive model(MS-VAR).The empirical findings are as follows:(1)The Chinese stock market can be divided into three regional systems:steady downward,steady upward,and high volatility.The three states have similar frequencies of occurrence,and their corresponding stable probabilities are not high,indicating that the Chinese stock market is unstable.(2)Asymmetric dynamic relationships exist between market volatility,investment return,and trading volume.For different regimes,while the effect of trading volume on volatility and return appears to be insignificant,the impacts of volatility and return on trading volume are considerably strong.(3)A regime-dependent,contemporaneous correlation between volatility and return is observed,which also reflects the behavior of the Chinese stock market“chasing up and down”.However,a positive contemporaneous correlation always exists between volatility and trading volumes in different regimes,indicating that uncertainty in the Chinese stock market is closely related to information inflow.
文摘In this work we consider a stochastic volatility model, commonly used in financial time series studies, to analyse ozone data. The model considered depends on some parameters and in order to estimate them a Markov chain Monte Carlo algorithm is proposed. The algorithm considered here is the so-called Gibbs sampling algorithm which is programmed using the language R. Its code is also given. The model and the algorithm are applied to the weekly ozone averaged measurements obtained from the monitoring network of Mexico City.
文摘The aim of this paper is to use the General Autoregressive Conditional Heteroscedastic (GARCH) type models for the estimation of volatility of the daily returns of the Kenyan stock market: that is Nairobi Securities Exchange (NSE). The conditional variance is estimated using the data from March 2013 to February 2016. We use both symmetric and asymmetric models to capture the most common features of the stock markets like leverage effect and volatility clustering. The results show that the volatility process is highly persistent, thus, giving evidence of the existence of risk premium for the NSE index return series. This in turn supports the positive correlation hypothesis: that is between volatility and expected stock returns. Another fact revealed by the results is that the asymmetric GARCH models provide better fit for NSE than the symmetric models. This proves the presence of leverage effect in the NSE return series.
文摘In this paper, we consider the leverage effect on the CSI 300 Index yield and Hong Kong Hang Seng Index yield. It is modeled by the SV model with leverage. In this model, we compare the mainland and the Hong Kong stock market with stock market long-term effect, the degree on fluctuation reply and leverage effect so on. The analysis results show that the leverage stochastic volatility model can well fitting rate of return on the CSI300 index and the Hang Seng index in Hong Kong;The Shanghai and Shenzhen stock market volatility and leverage effect obviously stronger than the Hong Kong stock market.
文摘An explicit formula for the transition probability density function of the Hull and White stochastic volatility model in presence of nonzero correlation between the stochastic differentials of the Wiener processes on the right hand side of the model equations is presented. This formula gives the transition probability density function as a two dimensional integral of an explicitly known integrand. Previously an explicit formula for this probability density function was known only in the case of zero correlation. In the case of nonzero correlation from the formula for the transition probability density function we deduce formulae (expressed by integrals) for the price of European call and put options and closed form formulae (that do not involve integrals) for the moments of the asset price logarithm. These formulae are based on recent results on the Whittaker functions [1] and generalize similar formulae for the SABR and multiscale SABR models [2]. Using the option pricing formulae derived and the least squares method a calibration problem for the Hull and White model is formulated and solved numerically. The calibration problem uses as data a set of option prices. Experiments with real data are presented. The real data studied are those belonging to a time series of the USA S&P 500 index and of the prices of its European call and put options. The quality of the model and of the calibration procedure is established comparing the forecast option prices obtained using the calibrated model with the option prices actually observed in the financial market. The website: http://www.econ.univpm.it/recchioni/finance/w17 contains some auxiliary material including animations and interactive applications that helps the understanding of this paper. More general references to the work of the authors and of their coauthors in mathematical finance are available in the website: http://www.econ.univpm.it/recchioni/finance.
文摘Stochastic volatility models are used in mathematical finance to describe the dynamics of asset prices. In these models, the asset price is modeled as a stochastic process depending on time implicitly defined by a stochastic differential Equation. The volatility of the asset price itself is modeled as a stochastic process depending on time whose dynamics is described by a stochastic differential Equation. The stochastic differential Equations for the asset price and for the volatility are coupled and together with the necessary initial conditions and correlation assumptions constitute the model. Note that the stochastic volatility is not observable in the financial markets. In order to use these models, for example, to evaluate prices of derivatives on the asset or to forecast asset prices, it is necessary to calibrate them. That is, it is necessary to estimate starting from a set of data the values of the initial volatility and of the unknown parameters that appear in the asset price/volatility dynamic Equations. These data usually are observations of the asset prices and/or of the prices of derivatives on the asset at some known times. We analyze some stochastic volatility models summarizing merits and weaknesses of each of them. We point out that these models are examples of stochastic state space models and present the main techniques used to calibrate them. A calibration problem for the Heston model is solved using the maximum likelihood method. Some numerical experiments about the calibration of the Heston model involving synthetic and real data are presented.
文摘This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid the COVID-19 pandemic. Initially, a univariate GARCH model is developed to derive residual sequences, which are then used to estimate the DCC model parameters. The research reveals a significant rise in the interconnection between the Chinese and U.S. stock markets during the pandemic. The S&P 500 index displayed higher sensitivity and greater volatility in response to the pandemic, whereas the CSI 300 index showed superior resilience and stability. Analysis and model estimation suggest that the market’s dependence on historical data has intensified and its sensitivity to recent shocks has heightened. Predictions from the model indicate increased market volatility during the pandemic. While the model is proficient in capturing market trends, there remains potential for enhancing the accuracy of specific volatility predictions. The study proposes recommendations for policymakers and investors, highlighting the importance of improved cooperation in international financial market regulation and investor education.
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
文摘This paper mainly through the comparison of GARCH-VaR China stock market board,small board and gem in the United States correspond to the three stock index volatility,volatility between stock indexes obtained U.S.stock market volatility risk multi-level market differences.As a suggestion and reference for investors,it can also provide reference for the supervision department of stock market risk.Based on the empirical research,analyzes the advantages and disadvantages of traditional risk measurement methods,and combined with GARCH model with high degree of complexity and the practice effect analysis,trying to find the objective measure stock model analysis.In the specific study of the volatility of the stock market,through the comparison of China’s three major plates and the market classification mechanism of mature U.S.stock market,combined with the objective situation of the market,draw conclusions and change expectations.From the empirical results,the U.S.stock market has recovered after the financial crisis,and its performance on risk volatility is better than China’s three major plates.From the comparison of the stock market in the same country,the small and medium-sized plates tend to have greater risks,while the risks of the main board and the gem have the characteristics of low average value but frequent fluctuations.
文摘Determining which variables affect price realized volatility has always been challenging.This paper proposes to explain how financial assets influence realized volatility by developing an optimal day-to-day forecast.The methodological proposal is based on using the best econometric and machine learning models to forecast realized volatility.In particular,the best forecasting from heterogeneous autoregressive and long short-term memory models are used to determine the influence of the Standard and Poor’s 500 index,euro-US dollar exchange rate,price of gold,and price of Brent crude oil on the realized volatility of natural gas.These financial assets influenced the realized volatility of natural gas in 87.4% of the days analyzed;the euro-US dollar exchange rate was the primary financial asset and explained 40.1% of the influence.The results of the proposed daily analysis differed from those of the methodology used to study the entire period.The traditional model,which studies the entire period,cannot determine temporal effects,whereas the proposed methodology can.The proposed methodology allows us to distinguish the effects for each day,week,or month rather than averages for entire periods,with the flexibility to analyze different frequencies and periods.This methodological capability is key to analyzing influences and making decisions about realized volatility.
文摘The financial market is the core of national economic development,and stocks play an important role in the financial market.Analyzing stock prices has become the focus of investors,analysts,and people in related fields.This paper evaluates the volatility of Apple Inc.(AAPL)returns using five generalized autoregressive conditional heteroskedasticity(GARCH)models:sGARCH with constant mean,GARCH with sstd,GJR-GARCH,AR(1)GJR-GARCH,and GJR-GARCH in mean.The distribution of AAPL’s closing price and earnings data was analyzed,and skewed student t-distribution(sstd)and normal distribution(norm)were used to further compare the data distribution of the five models and capture the shape,skewness,and loglikelihood in Model 4-AR(1)GJR-GARCH.Through further analysis,the results showed that Model 4,AR(1)GJR-GARCH,is the optimal model to describe the volatility of the return series of AAPL.The analysis of the research process is both,a process of exploration and reflection.By analyzing the stock price of AAPL,we reflect on the shortcomings of previous analysis methods,clarify the purpose of the experiment,and identify the optimal analysis model.
文摘Since the establishment of financial models for risk prediction,the measurement of volatility at risky market has improved,and its significance has also grown.For high-frequency financial data,the degree of investment risk,which has always been the focus of attention,is measured by the variance of residual sequence obtained following model regression.By integrating the long short-term memory(LSTM)model with multiple generalized autoregressive conditional heteroscedasticity(GARCH)models,a new hybrid LSTM model is used to predict stock price volatility.In this paper,three GARCH models are used,and the model that can best fit the data is determined.
基金supported by FCT,I.P,the Portuguese national funding agency for science,research and technology under the Project UIDB/04521/2020.
文摘This study investigates the static and dynamic return and volatility spillovers between non-fungible tokens(NFTs)and conventional currencies using the time-varying parameter vector autoregressions approach.We reveal that the total connectedness between these markets is weak,implying that investors may increase the diversification benefits of their multicurrency portfolios by adding NFTs.We also find that NFTs are net transmitters of both return and volatility spillovers;however,in the case of return spillovers,the influence of NFTs on conventional currencies is more pronounced than that of volatility shock transmissions.The dynamic exercise reveals that the returns and volatility spillovers vary over time,largely increasing during the onset of the Covid-19 crisis,which deeply affected the relationship between NFTs and the conventional currencies markets.Our findings are useful for currency traders and NFT investors seeking to build effective cross-currency and cross-asset hedge strategies during systemic crises.
