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
.Option pricing is a major problem in quantitative finance.The Black-Scholes model proves to be an effective model for the pricing of options.In this paper a com-putational method known as the modified differential tr....Option pricing is a major problem in quantitative finance.The Black-Scholes model proves to be an effective model for the pricing of options.In this paper a com-putational method known as the modified differential transform method has been em-ployed to obtain the series solution of Black-Scholes equation with boundary condi-tions for European call and put options paying continuous dividends.The proposed method does not need discretization to find out the solution and thus the computa-tional work is reduced considerably.The results are plotted graphically to establish the accuracy and efficacy of the proposed method.展开更多
The stock market, as one of the hotspots in the financial field, forms a data system with a huge volume of data and complex relationships between various factors, making stock price prediction an area of keen interest...The stock market, as one of the hotspots in the financial field, forms a data system with a huge volume of data and complex relationships between various factors, making stock price prediction an area of keen interest for further in-depth mining and research. Mathematical statistics methods struggle to deal with nonlinear relationships in practical applications, making it difficult to explore deep information about stocks. Meanwhile, machine learning methods, particularly neural network models and composite models, which have achieved outstanding results in other fields, are being applied to the stock market with significant results. However, researchers have found that these methods do not grasp the essential information of the data as well as expected. In response to these issues, researchers are exploring better neural network models and combining them with other methods to analyze stock data. Thus, this paper proposes the ABiGRU composite model, which combines the attention mechanism and bidirectional gated recurrent unit (GRU) that can effectively extract data features for stock price prediction research. Models such as LSTM, GRU, and Bi-LSTM are selected for comparative experiments. To ensure the credibility and representativeness of the research data, daily stock price indices of BYD are chosen for closing price prediction studies across different models. The results show that the ABiGRU model has a lower prediction error and better fitting effect on three index-based stock prices, enhancing the learning efficiency of the neural network model and demonstrating good prediction stability. This suggests that the ABiGRU model is highly adaptable for stock price prediction.展开更多
Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermedi...Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black_Scholes model is generalized to the case where the risk_less asset (bond or bank account) earns a time_dependent interest rate and risk asset (stock) has time_dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put_call parity of European option are obtained. The general approach of option pricing is given for the general Black_Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put_call parity of European option on a stock whose price process is driven by general Ornstein_Uhlenback (O_U) process are given by actuarial approach.展开更多
Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics...Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics,the other based on uncertain description (i.e., the statistic theory)is the assumption of Black_Scholes's model (A.B_S.M.) in which the density function of stock price obeys logarithmic normal distribution, can be shown to be completely the same under certain equivalence relation of coefficients. The range of the solution of S.D.E. has been shown to be suited only for normal cases (no profit, or lost profit news, etc.) of stock market, so the same range is suited for A.B_ S.M. as well.展开更多
This paper develops a closed-form solution to an extended Black-Scholes (EBS) pricing formula which admits an implied drift parameter alongside the standard implied volatility. The market volatility smiles for vanilla...This paper develops a closed-form solution to an extended Black-Scholes (EBS) pricing formula which admits an implied drift parameter alongside the standard implied volatility. The market volatility smiles for vanilla call options on the S&P 500 index are recreated fitting the best volatility-drift combination in this new EBS. Using a likelihood ratio test, the implied drift parameter is seen to be quite significant in explaining volatility smiles. The implied drift parameter is sufficiently small to be undetectable via historical pricing analysis, suggesting that drift is best considered as an implied parameter rather than a historically-fit one. An overview of option-pricing models is provided as background.展开更多
Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing...Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.展开更多
This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the au...This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.展开更多
The oil industries are an important part of a country’s economy.The crude oil’s price is influenced by a wide range of variables.Therefore,how accurately can countries predict its behavior and what predictors to emp...The oil industries are an important part of a country’s economy.The crude oil’s price is influenced by a wide range of variables.Therefore,how accurately can countries predict its behavior and what predictors to employ are two main questions.In this view,we propose utilizing deep learning and ensemble learning techniques to boost crude oil’s price forecasting performance.The suggested method is based on a deep learning snapshot ensemble method of the Transformer model.To examine the superiority of the proposed model,this paper compares the proposed deep learning ensemble model against different machine learning and statistical models for daily Organization of the Petroleum Exporting Countries(OPEC)oil price forecasting.Experimental results demonstrated the outperformance of the proposed method over statistical and machine learning methods.More precisely,the proposed snapshot ensemble of Transformer method achieved relative improvement in the forecasting performance compared to autoregressive integrated moving average ARIMA(1,1,1),ARIMA(0,1,1),autoregressive moving average(ARMA)(0,1),vector autoregression(VAR),random walk(RW),support vector machine(SVM),and random forests(RF)models by 99.94%,99.62%,99.87%,99.65%,7.55%,98.38%,and 99.35%,respectively,according to mean square error metric.展开更多
In this paper,we apply the spatial panel model to explore the relationship between the dynamic of two types of crude oil prices(WTI and Brent crude oil)and their refined products over time.Considering the turbulent mo...In this paper,we apply the spatial panel model to explore the relationship between the dynamic of two types of crude oil prices(WTI and Brent crude oil)and their refined products over time.Considering the turbulent months of 2011,when Cushing Oklahoma had reached capacity and the crude oil export ban removal in 2015 as breakpoints,we apply this method both in the full sample and the three resultant regimes.First,results suggest our results show that both WTI and Brent display very similar behaviour with the refined products.Second,when attending to each regime,results derived from the first and third regimes are quite similar to the full sample results.Therefore,during the second regime,Brent crude oil became the benchmark in the petrol market,and it influenced the distillate products.Furthermore,our model can let us determine the price-setters and price-followers in the price formation mechanism through refined products.These results possess important considerations to policymakers and the market participants and the price formation.展开更多
Considering the widening of the peak-valley difference in the power grid and the difficulty of the existing fixed time-of-use electricity price mechanism in meeting the energy demand of heterogeneous users at various ...Considering the widening of the peak-valley difference in the power grid and the difficulty of the existing fixed time-of-use electricity price mechanism in meeting the energy demand of heterogeneous users at various moments or motivating users,the design of a reasonable dynamic pricing mechanism to actively engage users in demand response becomes imperative for power grid companies.For this purpose,a power grid-flexible load bilevel model is constructed based on dynamic pricing,where the leader is the dispatching center and the lower-level flexible load acts as the follower.Initially,an upper-level day-ahead dispatching model for the power grid is established,considering the lowest power grid dispatching cost as the objective function and incorporating the power grid-side constraints.Then,the lower level comprehensively considers the load characteristics of industrial load,energy storage,and data centers,and then establishes a lower-level flexible load operation model with the lowest user power-consuming cost as the objective function.Finally,the proposed method is validated using the IEEE-118 system,and the findings indicate that the dynamic pricing mechanism for peaking shaving and valley filling can effectively guide users to respond actively,thereby reducing the peak-valley difference and decreasing users’purchasing costs.展开更多
The mutton industry plays a pivotal role in the animal husbandry industry of Xinjiang Uygur Autonomous Region.To better monitor the volatility movement and risk warning of mutton price,the fluctuation characteristics ...The mutton industry plays a pivotal role in the animal husbandry industry of Xinjiang Uygur Autonomous Region.To better monitor the volatility movement and risk warning of mutton price,the fluctuation characteristics of mutton prices and the future trend of prices are analyzed systematically.On the one hand,the Hodrick Prescott(HP)filter method is used to analyze the long-term trends and cyclical characteristics of mutton prices in Xinjiang and explored the spatial evolution characteristics of mutton price fluctuations in various regions of Xinjiang.On the other hand,the Threshold Auto-Regressive(TAR)model is used to analyze the linkage relationship between mutton prices and the prices of other livestock products.The empirical results show that 1)the overall volatility of mutton price in Xinjiang is high,showing a trend of rising first,then falling and then rising from the temporal perspective.2)At the regional level,the price in the south is higher than that of the north,showing a decreasing trend from south to north on the whole from the spatial viewpoint.3)From the linkage relationship perspective,mutton and beef are complementary in the short term,but they are substitutes each other in the long term.This paper explores the characteristics of mutton price fluctuations in Xinjiang from the single time series of mutton prices and the linkage with other livestock products,which provides a reliable basis for the monitoring and risk warning of mutton price fluctuation.展开更多
In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging e...In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.展开更多
The consumer price index (CPI) measures the relative number of changes in the price level of consumer goods and services over time, reflecting the trend and degree of changes in the price level of goods and services p...The consumer price index (CPI) measures the relative number of changes in the price level of consumer goods and services over time, reflecting the trend and degree of changes in the price level of goods and services purchased by residents. This article uses the ARMA model to analyze the fluctuation trend of the CPI (taking Chongqing as an example) and make short-term predictions. To test the predictive performance of the model, the observation values from January to December 2023 were retained as the reference object for evaluating the predictive accuracy of the model. Finally, through trial predictions of the data from May to August 2023, it was found that the constructed model had good fitting performance.展开更多
This paper uses the HS2 extension cancellation in November 2021 as a quasi-experiment to study its impact on house prices and rents in Leeds.Using a DiD approach on repeat sales and monthly rents,I compare property va...This paper uses the HS2 extension cancellation in November 2021 as a quasi-experiment to study its impact on house prices and rents in Leeds.Using a DiD approach on repeat sales and monthly rents,I compare property values near the HS2 station and proposed construction site before and after the announcement.Results show a 3.6%decrease in house prices and a 3.9%decline in rents near the station,while properties near the construction site experienced a 2.4%increase in prices and a 2.1%rise in rents.This is the first paper to analyse the HS2 cancellation effect using panel data methods.展开更多
Using VAR-DCC-GARCH model,the literature on commodity price was extended by exploring the co-movement between Chinese nonferrous metal prices and global nonferrous metal prices represented by the nonferrous metal pric...Using VAR-DCC-GARCH model,the literature on commodity price was extended by exploring the co-movement between Chinese nonferrous metal prices and global nonferrous metal prices represented by the nonferrous metal prices from London Metal Exchange(LME).The results show that LME nonferrous metals prices still have a greater impact on Chinese nonferrous metals prices.However,the impact of Chinese nonferrous metals prices on LME nonferrous metals prices is still weak except for lead price.The co-movement of nonferrous metal prices between LME and China presents hysteretic nature,and it lasts for 7-8trading days.Furthermore,the co-movement between LME nonferrous metals prices and Chinese nonferrous metals prices has the characteristics of time-varying,and the correlation of lead prices between LME and China is the more stable than all other nonferrous metals prices.展开更多
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.Option pricing is a major problem in quantitative finance.The Black-Scholes model proves to be an effective model for the pricing of options.In this paper a com-putational method known as the modified differential transform method has been em-ployed to obtain the series solution of Black-Scholes equation with boundary condi-tions for European call and put options paying continuous dividends.The proposed method does not need discretization to find out the solution and thus the computa-tional work is reduced considerably.The results are plotted graphically to establish the accuracy and efficacy of the proposed method.
文摘The stock market, as one of the hotspots in the financial field, forms a data system with a huge volume of data and complex relationships between various factors, making stock price prediction an area of keen interest for further in-depth mining and research. Mathematical statistics methods struggle to deal with nonlinear relationships in practical applications, making it difficult to explore deep information about stocks. Meanwhile, machine learning methods, particularly neural network models and composite models, which have achieved outstanding results in other fields, are being applied to the stock market with significant results. However, researchers have found that these methods do not grasp the essential information of the data as well as expected. In response to these issues, researchers are exploring better neural network models and combining them with other methods to analyze stock data. Thus, this paper proposes the ABiGRU composite model, which combines the attention mechanism and bidirectional gated recurrent unit (GRU) that can effectively extract data features for stock price prediction research. Models such as LSTM, GRU, and Bi-LSTM are selected for comparative experiments. To ensure the credibility and representativeness of the research data, daily stock price indices of BYD are chosen for closing price prediction studies across different models. The results show that the ABiGRU model has a lower prediction error and better fitting effect on three index-based stock prices, enhancing the learning efficiency of the neural network model and demonstrating good prediction stability. This suggests that the ABiGRU model is highly adaptable for stock price prediction.
文摘Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black_Scholes model is generalized to the case where the risk_less asset (bond or bank account) earns a time_dependent interest rate and risk asset (stock) has time_dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put_call parity of European option are obtained. The general approach of option pricing is given for the general Black_Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put_call parity of European option on a stock whose price process is driven by general Ornstein_Uhlenback (O_U) process are given by actuarial approach.
文摘Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics,the other based on uncertain description (i.e., the statistic theory)is the assumption of Black_Scholes's model (A.B_S.M.) in which the density function of stock price obeys logarithmic normal distribution, can be shown to be completely the same under certain equivalence relation of coefficients. The range of the solution of S.D.E. has been shown to be suited only for normal cases (no profit, or lost profit news, etc.) of stock market, so the same range is suited for A.B_ S.M. as well.
文摘This paper develops a closed-form solution to an extended Black-Scholes (EBS) pricing formula which admits an implied drift parameter alongside the standard implied volatility. The market volatility smiles for vanilla call options on the S&P 500 index are recreated fitting the best volatility-drift combination in this new EBS. Using a likelihood ratio test, the implied drift parameter is seen to be quite significant in explaining volatility smiles. The implied drift parameter is sufficiently small to be undetectable via historical pricing analysis, suggesting that drift is best considered as an implied parameter rather than a historically-fit one. An overview of option-pricing models is provided as background.
文摘Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.
文摘This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.
文摘The oil industries are an important part of a country’s economy.The crude oil’s price is influenced by a wide range of variables.Therefore,how accurately can countries predict its behavior and what predictors to employ are two main questions.In this view,we propose utilizing deep learning and ensemble learning techniques to boost crude oil’s price forecasting performance.The suggested method is based on a deep learning snapshot ensemble method of the Transformer model.To examine the superiority of the proposed model,this paper compares the proposed deep learning ensemble model against different machine learning and statistical models for daily Organization of the Petroleum Exporting Countries(OPEC)oil price forecasting.Experimental results demonstrated the outperformance of the proposed method over statistical and machine learning methods.More precisely,the proposed snapshot ensemble of Transformer method achieved relative improvement in the forecasting performance compared to autoregressive integrated moving average ARIMA(1,1,1),ARIMA(0,1,1),autoregressive moving average(ARMA)(0,1),vector autoregression(VAR),random walk(RW),support vector machine(SVM),and random forests(RF)models by 99.94%,99.62%,99.87%,99.65%,7.55%,98.38%,and 99.35%,respectively,according to mean square error metric.
文摘In this paper,we apply the spatial panel model to explore the relationship between the dynamic of two types of crude oil prices(WTI and Brent crude oil)and their refined products over time.Considering the turbulent months of 2011,when Cushing Oklahoma had reached capacity and the crude oil export ban removal in 2015 as breakpoints,we apply this method both in the full sample and the three resultant regimes.First,results suggest our results show that both WTI and Brent display very similar behaviour with the refined products.Second,when attending to each regime,results derived from the first and third regimes are quite similar to the full sample results.Therefore,during the second regime,Brent crude oil became the benchmark in the petrol market,and it influenced the distillate products.Furthermore,our model can let us determine the price-setters and price-followers in the price formation mechanism through refined products.These results possess important considerations to policymakers and the market participants and the price formation.
基金supported in part by Technology Project of State Grid Jiangsu Electric Power Co.,Ltd.,China,under Grant J2022011.
文摘Considering the widening of the peak-valley difference in the power grid and the difficulty of the existing fixed time-of-use electricity price mechanism in meeting the energy demand of heterogeneous users at various moments or motivating users,the design of a reasonable dynamic pricing mechanism to actively engage users in demand response becomes imperative for power grid companies.For this purpose,a power grid-flexible load bilevel model is constructed based on dynamic pricing,where the leader is the dispatching center and the lower-level flexible load acts as the follower.Initially,an upper-level day-ahead dispatching model for the power grid is established,considering the lowest power grid dispatching cost as the objective function and incorporating the power grid-side constraints.Then,the lower level comprehensively considers the load characteristics of industrial load,energy storage,and data centers,and then establishes a lower-level flexible load operation model with the lowest user power-consuming cost as the objective function.Finally,the proposed method is validated using the IEEE-118 system,and the findings indicate that the dynamic pricing mechanism for peaking shaving and valley filling can effectively guide users to respond actively,thereby reducing the peak-valley difference and decreasing users’purchasing costs.
文摘The mutton industry plays a pivotal role in the animal husbandry industry of Xinjiang Uygur Autonomous Region.To better monitor the volatility movement and risk warning of mutton price,the fluctuation characteristics of mutton prices and the future trend of prices are analyzed systematically.On the one hand,the Hodrick Prescott(HP)filter method is used to analyze the long-term trends and cyclical characteristics of mutton prices in Xinjiang and explored the spatial evolution characteristics of mutton price fluctuations in various regions of Xinjiang.On the other hand,the Threshold Auto-Regressive(TAR)model is used to analyze the linkage relationship between mutton prices and the prices of other livestock products.The empirical results show that 1)the overall volatility of mutton price in Xinjiang is high,showing a trend of rising first,then falling and then rising from the temporal perspective.2)At the regional level,the price in the south is higher than that of the north,showing a decreasing trend from south to north on the whole from the spatial viewpoint.3)From the linkage relationship perspective,mutton and beef are complementary in the short term,but they are substitutes each other in the long term.This paper explores the characteristics of mutton price fluctuations in Xinjiang from the single time series of mutton prices and the linkage with other livestock products,which provides a reliable basis for the monitoring and risk warning of mutton price fluctuation.
基金Supported by the National Natural Science Foundation of China(11671115)the Natural Science Foundation of Zhejiang Province(LY14A010025)
文摘In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.
文摘The consumer price index (CPI) measures the relative number of changes in the price level of consumer goods and services over time, reflecting the trend and degree of changes in the price level of goods and services purchased by residents. This article uses the ARMA model to analyze the fluctuation trend of the CPI (taking Chongqing as an example) and make short-term predictions. To test the predictive performance of the model, the observation values from January to December 2023 were retained as the reference object for evaluating the predictive accuracy of the model. Finally, through trial predictions of the data from May to August 2023, it was found that the constructed model had good fitting performance.
文摘This paper uses the HS2 extension cancellation in November 2021 as a quasi-experiment to study its impact on house prices and rents in Leeds.Using a DiD approach on repeat sales and monthly rents,I compare property values near the HS2 station and proposed construction site before and after the announcement.Results show a 3.6%decrease in house prices and a 3.9%decline in rents near the station,while properties near the construction site experienced a 2.4%increase in prices and a 2.1%rise in rents.This is the first paper to analyse the HS2 cancellation effect using panel data methods.
基金Project(71073177)supported by the National Natural Science Foundation of ChinaProject(12JJ4077)supported by the Natural Science Foundation of Hunan Province of ChinaProject(2012zzts002)supported by the Fundamental Research Funds of Central South University,China
文摘Using VAR-DCC-GARCH model,the literature on commodity price was extended by exploring the co-movement between Chinese nonferrous metal prices and global nonferrous metal prices represented by the nonferrous metal prices from London Metal Exchange(LME).The results show that LME nonferrous metals prices still have a greater impact on Chinese nonferrous metals prices.However,the impact of Chinese nonferrous metals prices on LME nonferrous metals prices is still weak except for lead price.The co-movement of nonferrous metal prices between LME and China presents hysteretic nature,and it lasts for 7-8trading days.Furthermore,the co-movement between LME nonferrous metals prices and Chinese nonferrous metals prices has the characteristics of time-varying,and the correlation of lead prices between LME and China is the more stable than all other nonferrous metals prices.
