Stock Price Model Research Articles

Pemodelan Harga Saham PT. Telekomunikasi Indonesia Tbk Menggunakan Model TSR Linier

The movement of the stock price of PT. Telekomunikasi Indonesia Tbk from time to time is relatively erratic, but in 2020 the movement shows an decreasing trend pattern in January-October and an increasing trend pattern in November-December. There needs a stock price modeling for PT. Telekomunikasi Indonesia Tbk which is useful for investors as a consideration in making decisions to invest. In this study, modeling the stock price of PT. Telekomunikasi Indonesia Tbk uses a Time Series Regression (TSR) Linear model. The results of this study obtained a model for the proportion of data in sample 90, a model for the proportion of data in sample 80, and a model for the proportion of data in sample 70. It was found that the residual value of the TSR linear model the white noise assumption and normally distributed is not valid, so it can be concluded that TSR Linear model has not been able to understand all information on stock price data of PT. Telekomunikasi Indonesia Tbk.

PREDIKSI HARGA SAHAM MENGGUNAKAN GEOMETRIC BROWNIAN MOTION WITH JUMP DIFFUSION DAN ANALISIS RISIKO DENGAN EXPECTED SHORTFALL (Studi Kasus: Harga Penutupan Saham PT. Waskita Karya Persero Tbk.)

Investment is an activity that is quite popular among investors in recent years. One of the forms of investment in the financial sector is investing in the capital market by buying stocks in a company. The level of profit from stock investment activities can be seen from the value of stock returns. Factors that can affect the value of stock returns are stock prices. However, stock prices often experience unpredictable changes so that they experience fluctuating movements with increasing time and developing situations, therefore a stock price model is needed to predict stock prices in the future period. The Geometric Brownian Motion with Jump Diffusion’s method is more appropriate to be used in predicting stock prices if there is a jump in stock price data. Predicted stock prices can be used as a basis for measuring the value of investment risk. The results of data processing indicate that the stock return data of PT. Waskita Karya Persero Tbk has a kurtosis value > 3 which means there is a jump in stock return data so that it is more accurately modeled using the Geometric Brownian Motion with Jump Diffusion’s method. The prediction results have a good level of accuracy based on the MAPE value of 18,733%. Furthermore, in order to measure the investment risk of the predicted stock price of PT. Waskita Karya Persero Tbk used the Expected Shortfall Historical Simulation’s method with a significance level of α = 5%, the results were 0,10939, and for the significance level α = 10%, the results were 0,07596. The calculation results show that the greater the trust level used, the greater the risk borne by investors.Keywords: Jump Diffusion Process, Expected Shortfall, Risk, Extreme Value

VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION

The Option is widely applied in the financial sector. The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the process exponential model. The process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK). The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various values until convergent result was obtained.

Modeling Stock Price of Transnational companies using Brownian motion

This article is concerned with creating a model for stock price using the Brownian motion. At first, we consider the notion of a discrete time stochastic process, simple random walk, and then move on to its continuous analogue, the Brownian motion. Next we identify the problem with using regular Calculus for stochastic differential equations and derive Ito’s Lemma. After that we derive a model for stock prices and use lognormal distribution to determine its expected value and variance. Finally, we use sample volatility to make predictions for Apple and Gazprom stock prices.

Call warrants pricing formula under mixed-fractional Brownian motion with Merton jump-diffusion

Mixed fractional Brownian motion (MFBM) is a linear combination of a Brownian motion and an independent fractional Brownian motion which may overcome the problem of arbitrage, while a jump process in time series is another problem to be address in modeling stock prices. This study models call warrants with MFBM and includes the jump process in its dynamics. The pricing formula for a warrant with mixed-fractional Brownian motion and jump, is obtained via quasi-conditional expectation and risk-neutral valuation.

How Can Random Walk Be Applied to Analysis Stock

This paper discuss how the model of random walk applies in analyzing the stock price. Firstly, the graph of symmetric random walk and the graph of the stock price of the company AMD are shown to observe the similarity of them directly. Secondly, we give the stock price model driven by random walk theoretically. The result of our research helps us to understand the application of random walk on analyzing the stock price by deriving the equations.

Poisson Process Modeling of Pure Jump Equities on the Ghana Stock Exchange

Although Geometric Brownian Motion and Jump Diffusion Models have largely dominated the literature on asset price modeling, studies of the empirical stock price data on the Ghana Stock Exchange have led to the conclusion that there are some stocks in which the return processes consistently depart from these models in theory as well as in its statistical properties. This paper gives a fundamental review of the development of a stock price model based on pure jump processes to capture the unique behavior exhibited by some stocks on the Exchange. Although pure jump processes have been examined thoroughly by other authors, there is a lack of mathematical clarity in terms of deriving the underlying stock price process. This paper provides a link between stock prices existing on a measure space to its development as a pure jump Levy process. We test the suitability of the model to the empirical evidence using numerical procedures. The simulation results show that the trajectories of the model are a better fit for the empirical data than those produced by the diffusion and jump diffusion models.

A sentiment-based modeling and analysis of stock price during the COVID-19: U- and Swoosh-shaped recovery

In the aftermath of stock market crash due to COVID-19, not all sectors recovered in the same way. Recently, a stock price model is proposed by Mahata et al. (2021) that describes V- and L-shaped recovery of the stocks and indices, but fails to simulate the U- and Swoosh-shaped recovery that arises due to sharp fall, continuation at the low price and followed by quick recovery, slow recovery for longer period, respectively. We propose a modified model by introducing a new parameter θ=+1,0,−1 to quantify investors’ positive, neutral and negative sentiments, respectively. The model explains movement of sectoral indices with positive financial anti-fragility (ϕ) showing U- and Swoosh-shaped recovery. Simulation using synthetic fund-flow with different shock lengths, ϕ, negative sentiment period and portion of fund-flow during recovery period show U- and Swoosh-shaped recovery. It shows that recovery of indices with positive ϕ becomes very weak with extended shock and negative sentiment period. Stocks with higher ϕ and fund-flow show quick recovery. Simulation of Nifty Bank, Nifty Financial and Nifty Realty show U-shaped recovery and Nifty IT shows Swoosh-shaped recovery. Simulation results are consistent with stock price movement. The estimated time-scale of shock and recovery of these indices are also consistent with the time duration of change of negative sentiment from the onset of COVID-19. We conclude that investors need to evaluate sentiment along with ϕ before investing in stock markets because negative sentiment can dampen the recovery even in financially anti-fragile stocks.

Generalization of affine feedback stock trading results to include stop-loss orders

The main question we would like to address in this paper is as follows: Given a geometric Brownian motion (GBM) as the underlying stock price model, what is the cumulative distribution function (CDF) for the trading profit or loss, call it g(t), when an affine feedback control strategy with stop-loss order is considered? Moreover, is it possible to obtain a closed-form characterization for the desired CDF for g(t) so that a theoretician or practical trader might be benefited from it? The answers to these questions are affirmative. In this paper, we provide a closed-form expression for the cumulative distribution function for the trading profit or loss. In addition, we show that the affine feedback controller with stop-loss order indeed generalizes the result without stop order in the sense of distribution function. Some simulations and illustrative examples are also provided as supporting evidence of the theory.

On Multilevel and Control Variate Monte Carlo Methods for Option Pricing under the Rough Heston Model

The rough Heston model is a form of a stochastic Volterra equation, which was proposed to model stock price volatility. It captures some important qualities that can be observed in the financial market—highly endogenous, statistical arbitrages prevention, liquidity asymmetry, and metaorders. Unlike stochastic differential equation, the stochastic Volterra equation is extremely computationally expensive to simulate. In other words, it is difficult to compute option prices under the rough Heston model by conventional Monte Carlo simulation. In this paper, we prove that Euler’s discretization method for the stochastic Volterra equation with non-Lipschitz diffusion coefficient E[|Vt−Vtn|p] is finitely bounded by an exponential function of t. Furthermore, the weak error |E[Vt−Vtn]| and convergence for the stochastic Volterra equation are proven at the rate of O(n−H). In addition, we propose a mixed Monte Carlo method, using the control variate and multilevel methods. The numerical experiments indicate that the proposed method is capable of achieving a substantial cost-adjusted variance reduction up to 17 times, and it is better than its predecessor individual methods in terms of cost-adjusted performance. Due to the cost-adjusted basis for our numerical experiment, the result also indicates a high possibility of potential use in practice.

Empirical deep hedging

Existing hedging strategies are typically based on specific financial models: either the strategies are directly based on a given option pricing model or stock price and volatility models are used indirectly by generating synthetic data on which an agent is trained with reinforcement learning. In this paper, we train an agent in a pure data-driven manner. Particularly, we do not need any specifications on volatility or jump dynamics but use large empirical intra-day data from actual stock and option markets. The agent is trained for the hedging of derivative securities using deep reinforcement learning (DRL) with continuous actions. The training data consists of intra-day option price observations on S&P500 index over 6 years, and top of that, we use other data periods for validation and testing. We have two important empirical results. First, a DRL agent trained using synthetic data generated from a calibrated stochastic volatility model outperforms the classic Black–Scholes delta hedging strategy. Second, and more importantly, we find that a DRL agent, which is empirically trained directly using actual intra-day stock and option prices without the prior specification of the underlying volatility or jump processes, has superior performance compared with the use of synthetic data. This implies that DRL can capture the dynamics of S&P500 from the actual intra-day data and to self-learn how to hedge actual options efficiently.

Mixtures of higher-order fractional Brownian motions

In this article, we show that the nth-order fractional Brownian motions (fBm) introduced by Perrin et al. are non Markovian special semimartingales. Their infinite mixtures are also presented and shown to be semimartingales satisfying mixed self-similarity property and accounting for long-range dependence phenomena. As result, they are alternative to mixed fBm in modeling stock prices in arbitrage-free financial markets.

Research on a hybrid prediction model for stock price based on long short-term memory and variational mode decomposition

Research on a hybrid prediction model for stock price based on long short-term memory and variational mode decomposition

THE VIX AND FUTURE INFORMATION

In this paper, we propose an innovative VIX model which takes future market information available to the traders into account. The future information is modeled by an initially enlarged filtration in our setup. We derive an explicit representation for the anticipative VIX process and obtain the associated time dynamics. We also investigate the pricing of variance swaps under both backward- and forward-looking information. We finally deduce the optimal mean variance hedging portfolio in a financial market consisting of a bank account and a VIX futures. In order to have some benchmark model available, we introduce a non-anticipative stochastic volatility stock price model right at the beginning and infer representations for the related VIX index, the VIX futures and a VIX call option.

Performance of advanced stock price models when it becomes exotic: an empirical study

We calibrate several advanced stock price models to a time series of real market data of European options on the DAX. Via a Monte Carlo simulation, we price barrier down-and-out call options for all models and compare the modeled prices to given real market data of the barrier options. The Bates model reproduces barrier option prices very well. The BNS model overvalues and Lévy models with stochastic time-change and leverage undervalue the exotic options. The Heston model and a local volatility model undervalue the barrier option prices by about 5–6%. A heuristic analysis suggests that the different degree of fluctuation of the random paths of the models are responsible of producing different prices for the barrier options. Higher margins or additional risks like liquidity, calibration or model risk might economically explain why many advanced models undervalue barrier options.

Transformations of Telegraph Processes and Their Financial Applications

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac’s conditions, which may be interpreted as the equation for a diffusion process on a circle. This general case includes, for example, classical cases, such as limiting diffusion and geometric Brownian motion under some specifications of non-linear transformations (i.e., linear, exponential, etc.). We also give three applications of non-linear transformed telegraph process in finance: (1) application of classical telegraph process in the case of balance, (2) application of classical telegraph process in the case of dis-balance, and (3) application of asymmetric telegraph process. For these three cases, we present European call and put option prices. The novelty of the paper consists of new results for non-linear transformed classical telegraph process, new models for stock prices based on transformed telegraph process, and new applications of these models to option pricing.

Optimizing the Prediction Model of Stock Price in Pharmaceutical Companies Using Multiple Objective Particle Swarm Optimization Algorithm (MOPSO)

The purpose of this study is to optimize the stock price forecasting model with meta-innovation method in pharmaceutical companies.In this research, stock portfolio optimization has been done in two separate phases.The first phase is related to forecasting stock futures based on past stock information, which is forecasting the stock price using artificial neural network.The neural network used was a multilayer perceptron network using the error propagation learning algorithm.After predicting the stock price with the neural network, the forecast price data in the second phase has been used to optimize the stock portfolio.In this phase, a multi-objective genetic algorithm is used to optimize the portfolio, and the optimal weights are assigned to the stock and the optimal stock portfolio is created.Having a regression model, the design of the relevant genetic algorithm has been done using MATLAB software.The results show that the stock portfolio created by MOPSO algorithm has a better performance compared to the algorithms used in the article under comparison under all four risk criteria except the criterion of conditional risk exposure. In all models, except the conditional risk-averaged value model, the stock portfolios created by the MOPSO algorithm used in the research have more and more appropriate performance.

Bayesian neural networks for stock price forecasting before and during COVID-19 pandemic.

Recently, there has been much attention in the use of machine learning methods, particularly deep learning for stock price prediction. A major limitation of conventional deep learning is uncertainty quantification in predictions which affect investor confidence. Bayesian neural networks feature Bayesian inference for providing inference (training) of model parameters that provides a rigorous methodology for uncertainty quantification in predictions. Markov Chain Monte Carlo (MCMC) sampling methods have been prominent in implementing inference of Bayesian neural networks; however certain limitations existed due to a large number of parameters and the need for better computational resources. Recently, there has been much progress in the area of Bayesian neural networks given the use of Langevin gradients with parallel tempering MCMC that can be implemented in a parallel computing environment. The COVID-19 pandemic had a drastic impact in the world economy and stock markets given different levels of lockdowns due to rise and fall of daily infections. It is important to investigate the performance of related forecasting models during the COVID-19 pandemic given the volatility in stock markets. In this paper, we use novel Bayesian neural networks for multi-step-ahead stock price forecasting before and during COVID-19. We also investigate if the pre-COVID-19 datasets are useful of modelling stock price forecasting during COVID-19. Our results indicate due to high volatility in the stock-price during COVID-19, it is more challenging to provide forecasting. However, we found that Bayesian neural networks could provide reasonable predictions with uncertainty quantification despite high market volatility during the first peak of the COVID-19 pandemic.

Hybrid evolutionary intelligent system and hybrid time series econometric model for stock price forecasting

In this paper, a hybrid evolutionary intelligent system is proposed for dimensionality reduction and tuning the learnable parameters of artificial neural network (ANN) that can forecast the future (1-day-ahead) close price of the stock market using various technical indicators. Although the ANN possesses the ability to model highly uncertain and complex nonlinear data but the key challenge in ANN is tuning its parameters and minimizing the feature set that can be used in the input layer. The backpropagation approach used for training the ANN has a limitation to get trapped in local minima and overfitting the data. Motivated by this, we proposed a hybrid intelligent system for optimizing the initial parameters and for reducing the dimensions of the feature set. The proposed model is a combination of feature extraction technique, namely principal component analysis (PCA), particle swarm optimization (PSO), and Levenberg-Marquardt (LM) algorithm for training the feed-forward neural networks (FFNN). This paper also compares the forecasting efficiency of the proposed model with PSO-FFNN, regular FFNN, two standard benchmark approaches viz. GA and DE and another hybrid model obtained by the combination of PCA and a time series econometric model viz. auto-regressive distributed lag model. The presented technique has been tested to predict the close price of three stock indices viz. Nifty 50, Sensex, and S&P 500. Simulation results indicate that the proposed model shows superior forecasting accuracy as compared with other methods.

Modeling and analysis of the effect of COVID-19 on the stock price: V and L-shape recovery

The emergence of the COVID-19 pandemic, a new and novel risk factor, leads to the stock price crash due to the investors’ rapid and synchronous sell-off. However, within a short period, the quality sectors start recovering from the bottom. A stock price model has been developed to capture the price dynamics during shock and recovery phases of such crisis. The main variable and parameter of the model are the net fund flow (Ψt) due to institutional investors, and financial antifragility (ϕ) of a company, respectively. We assume that during the crash, the stock price fall is independent of the ϕ. We study the effects of shock length (TS) and ϕ on the stock price during the crisis period using the Ψt obtained from both the synthetic fund flow data and real fund flow data. We observed that the possibility of recovery of stock with ϕ>0, termed as quality stock, decreases with an increase in TS beyond a specific period. A quality stock with higher ϕ shows V-shape recovery and outperform others. The TS and recovery period of quality stock are almost equal in the Indian market. Financially stressed stocks, i.e., the stocks with ϕ<0, show L-shape recovery during the pandemic. The stock data and model analysis show that the investors, in the uncertainty like COVID-19, invest in the quality stocks to restructure their portfolio to reduce the risk. The study may help the investors to make the right investment decision during a crisis.