Application of Elzaki Transform Method to Market Volatility Using the Black-Scholes Model

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.

Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends

.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.

Stock Price Prediction Based on the Bi-GRU-Attention Model

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.

NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

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.

SIMPLEST DIFFERENTIAL EQUATION OF STOCK PRICE,ITS SOLUTION AND RELATION TO ASSUMPTION OF BLACK-SCHOLES MODEL

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.

Black-Scholes Option Pricing Model Modified to Admit a Miniscule Drift Can Reproduce the Volatility Smile

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.

Option Pricing beyond Black-Scholes Model:Quantum Mechanics Approach

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.

GENERAL BLACK-SCHOLES MODEL OF SECURITY VALUATION

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.

A Deep Learning Ensemble Method for Forecasting Daily Crude Oil Price Based on Snapshot Ensemble of Transformer Model

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.

Brent vs.West Texas Intermediate in the US petro derivatives price formation

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.

Flexible Load Participation in Peaking Shaving and Valley Filling Based on Dynamic Price Incentives

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.

On discrete time hedging errors in a fractional Black-Scholes model

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.

The Prediction for the Consumer Price Index of Residents in Perspective of Time Series Method in Case of Chongqing

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.

基于Black-Scholes实物期权定价模型的发电商投资决策分析

从电源投资建设项目的特点出发,结合电源建设投资的期权特性,得出了与Black—Scholes期权定价模型相对应的电源建设投资实物期权内容。通过建立基于Black-Scholes实物期权定价模型,并将其运用到电源建设投资决策中,避免了传统的电源投资决策方法依赖项目净现值等缺点。通过算例对电源建设投资项目的期权进行了估价,表明将实物期权理论应用到电源建设投资决策中是可行的。

广义Black-Scholes模型期权定价新方法——保险精算方法

利用公平保费原则和价格过程的实际概率测度推广了MogensBladt和TinaHviidRydberg的结果· 在无中间红利和有中间红利两种情况下,把Black＿Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具有时间相依的连续复利预期收益率和波动率的情况,在此情况下获得了欧式期权的精确定价公式以及买权与卖权之间的平价关系· 给出了风险资产(股票)

一种无风险利率时变条件下的Black-Scholes期权定价模型

本文研究了无风险利率改进的Black-Scholes期权定价模型问题.利用指数函数和Ito公式的方法,获得了一种改进的Black-Scholes期权定价模型,推广了现有Black-Scholes期权定价模型的结果.

修正的Black-Scholes模型下的欧式期权定价

通常情况下,期权定价研究都假定股票价格的波动率和期望收益率为常数.假定波动率和期望收益率为股票价格的一般函数.利用金融市场复制策略及布朗运动的Ito公式,得到欧式未定权益的一般Black-Scholes偏微分方程,并通过求解偏微分方程获得欧式期权定价公式.

基于Black-Scholes模型的公司资本结构模型

】对考虑代理成本的公司资本结构问题进行了研究，引入期权理论及其定价模型给出确定这一情况下的公司最优资本结构的方法。

关于Black-Scholes期权定价模型的证明

lack-Scholes期权定价模型是20世纪70年代以来金融理论发展的最重要的基石,但是在各类文献中却几乎没有关于它的详细、准确的证明.本文将有关文献中出现的错误加以更正,并优化了证明过程,给出一个关于Black-Scholes期权定价模型严格的数学证明.

基于二叉树和Black-Scholes模型的期权定价实证研究——以阿里巴巴股票为例

期权定价对于投资者在金融市场上进行期权交易时非常重要,一个合理良好的定价与众多因素都有着密切的关系,例如股票的价格、到期日、市场利率与波动率等。因此本文将采用经典的二叉树模型与Black-Scholes模型,并基于分析与处理后的股票数据对期权进行定价分析。其中对欧式期权进行定价与分析,最后对比两种模型所得到的结果与验证结果的真实性。通过上述两模型的分析与比较,并且能看出两模型的适用条件和情形,每种模型有其优点和缺点,因此要根据各自模型的特点予以特殊的考虑以及应用,以便达到期权定价的良好效果。