Journal of mathematic and modeling in Finance
Volume:2 Issue: 1, Winter - Spring 2022

Cryptocurrencies, which are digitally encrypted and decentralized, continue to attract attention of  nancial market players across the world. Because of high volatility in cryptocurrency market, predicting price of cryptocurrencies has become one of the most complicated  elds in  nan-cial markets. In this paper, we use Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) models to predict price of four well- known cryptocurrencies of Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), and Ripple (XRP). These models are subdivisions of Arti cial Intelligence, machine learning and data science. The main aim of this paper is to compare the accuracy of above-mentioned models in forecasting time series data, to  nd out which model can better predict price in these four cryptocurrencies. 43 variables consisting of 28 technical indicators and t+10 lags were calculated and appended to the Open, High, Low, Close and Volume (OHLCV) data for selected cryptocurrencies. Applying random forest as feature selection, 25 variables were chosen, 24 of them selected as feature (independent variables) and one as a dependent variable. Each attribute value was converted into a relative standard score, followed by Min-max scaling; we compare models and results of Dieblod Mariano test that is used to examine whether the differences in predictive accuracy with these two models are signi cant, reveal that LSTM reaches better accuracy than GRU for BTC and ETH, but both models convey the same accuracy for LTC and XRP.

This research has been investigated, economy and balance-sheet effects of the money growth rate targeting. According to financial statements of the banking network and national accounts, using dynamic stochastic general equilibrium New Keynesian and statistical data for the period 1991-2019.For estimating parameters, is used New Keynesian DSGE model and Bayesian method. This paper verify the validity of the model by analyzing the impulse response functions and Brooks and Goleman test. The results of the model indicate that the effect of negative the money growth rate targeting, reduce deposits, reduce loans interest rates, lead to reducing banks' resources, bank lending and then the health of the banks would compromise. In this way, investment and production will be reduced. Also, the effect of stock prices increasing, deposit, loan decrease and investment and production increase. Therefore, this research suggests the policy of negative the money growth rate targeting coincide with the policy of raising interest rates and stock price rising.

This study seeks to investigate the performance as well as the performance consistency of Iranian mutual funds during the current and subsequent periods. To this end, the Capital Asset Pricing Model along with CARHART’s four-factor model have been utilized to analyze the performance and performance consistency of investment funds. In order to examine persistency, all models are divided into 10 portfolios (10 distributions) based on the performance of the past one year. Then we considered succeeding 12 months later. Our results revealed that mutual funds in Iran have not outperformed the market, but there is performance consistency. This means mutual funds with the best performance (worst performance) will perform the same (better or worse) in the upcoming years. However, the extent of the best and worst performance of mutual funds is not significantly different. The historical performance of mutual funds can, to some extent, explain future performance. Therefore, investors' reliance on the backgrounds of investment funds as a recourse for investment is well justified. In other words, if investors spend on mutual funds with a past outperformance, there is a reasonable assurance to be repeated the past and will be among the winning funds in future periods. The opposite is also true

Pricing catastrophe swap as an instrument for insurance companies risk management, has received trivial attention in the previous studies, but in most of them, damage severities caused by the disaster has been considered to be fixed. In this study, through considering jumps for modeling the occurrence of disasters as in Unger [32] and completing it through considering damages caused by natural disasters as stochastic, an integro-differential model was extracted to value catastrophe swap contracts. In determining the swap price changes, the Ito command was followed and to achieve the catastrophic swap model, the generalization of the Black and Scholes modeling method was used. [3]. With regard to the initial and boundary conditions, extracted model does not have an analytical solution; thus, its answer was approximated using the finite difference numerical method and the effect of considering the damage as stochastic on swap value was analyzed. In addition, the model and the extracted numerical solution were separately implemented on the data about the earthquake damage in the United States and Iran. The results showed that prices will experience a regular upward trend until damage growth, damage severities, and occurrence probability of a catastrophe are not so high that the buyer of the swap is forced to pay compensation to the swap’s seller. Of course, the prices will fall sharply as soon as they reach and cross the threshold.

‎In this article supply demand based on prices volumes are extracted as measure of swaps between two or more indexes by neural network for recommend Market Makers to increase performance of Large Traded Volumes in real time Markets Quotes‎. ‎Neural network are widely applicable tools for develop operators performances in financial market applications‎. ‎In classic economy when an equilibrium was Unbalanced must be a side of supply or demand was over than other one.in more indexes decisions for check balance condition between more than two indexes in real time market a neural network classification trigger is good suggestion‎. ‎other methods such as indicators oscillators and numerical methods and statistical methods were been slow‎. ‎The latency of candle data in clients solved by time stamp in log file and export of these triggers can draw by graphical Line or shape in data.an equilibrium point as middle of these balances for pairs of indexes are connected with triangle shape‏‎.

It is known that the original Kaldor-Kalecki model of business cycle was an example of a difference differential model. In the literature there are many results about this model and how it relates to an extended form representing an economic growth model and how the role of government and its simultaneous monetary, fiscal policies can affect the economic stability. The authors proposed and studied business models using ordinary differential equations, nonlinear investment and saving functions. They showed that periodic solutions exist under the assumption of nonlinearity. Since then, similar models were also analyzed by several researchers and the existence of limit cycles was established due to the nonlinearity. In this paper, a three coupled Kaldor-Kalecki model with multiple delays is investigated. By means of the generalized Chafee’s criterion, some sufficient conditions to guarantee the existence of oscillatory solution for the model are obtained. Computer simulations are provided to demonstrate the proposed results.

‎The bond market is an important part of the financial markets‎ . ‎The coupon bonds are issued by companies or banks for increasing capital ‎, ‎and the interest is paid by banks or companies‎, ‎periodically ‎.‎ ‎In terms of maturities ‎, ‎bonds are divided into three categories as follows‎ : ‎short term‎ , ‎medium term‎ , ‎and long ‎term‎ .‎‎In this paper‎ , ‎we model the fractional bond pricing under fractional stochastic differential equation ‎. ‎We implement the multiquadric approximation for solving the fractional bond pricing equation‎ . ‎The equation is discretized in the time direction base on modified Riemann-- Liouville derivative and finite difference methods and is approximated by using the multiquadric approximation method in the space direction which achives the semi-- discrete solution‎ . ‎We investigate the unconditional stability and convergence of the proposed method‎. ‎Numerical results demonstrate the efficiency and ability of the presented method ‎.

The capital or stock market along with the money market is one of the most important parts of financial sector of the nation’s economy, providing long-term financing required for efficient production and service activities. The total stock price index as reflector of stock market fluctuation is important for finance practitioners and policy-makers. Therefore, in this research, a comparative investigation was presented on two superior deep-learning-based models, including long short-term memory (LSTM), and convolutional neural network long short-term memory (CNN)-LSTM, applied for analysing prediction of the total stock price index of Tehran stock exchange (TSE) market. The complete dataset utilized in the current analysis covered the period from September 23, 2011 to June 22, 2021 with a total of 3,739 trading days in the TSE market. Forecasting accuracy and performance of the two proposed models were appraised using root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) criteria. Based on the results, the CNN-LSTM showed the lowest values of the aforementioned metrics compared to the LSTM model, and it was found that the CNN-LSTM model could be effective in providing the best prediction performance of the total stock price index on the TSE market. Eventually, graphically and numerically, various prediction results obtained from the proposed models were analysed for more comprehensive analysis.

‎Given the significant increase in fraudulent claims and the resulting financial losses‎, ‎it is important to adopt a scientific approach to detect and prevent such cases‎. ‎In fact‎, ‎not equipping companies with an intelligent system to detect suspicious cases has led to the payment of such losses‎, ‎which may in the short term lead to customer happiness but eventually will have negative financial consequences for both insurers and insured‎. ‎Since data labeled fraud is really limited‎, ‎this paper‎, ‎provides insurance companies with an algorithm for identifying suspicious cases‎. ‎This is obtained with the help of an unsupervised algorithm to detect anomalies in the data set‎. ‎The use of this algorithm enables insurance companies to detect fraudulent patterns that are difficult to detect even for experienced experts‎. ‎According to the outcomes‎, ‎the frequency of financial losses‎, ‎the time of and the type of incident are the most important factors to in detecting suspicious cases‎.

In this study, based on the monetary behavior theory, which considers the mean and standard deviation of GDP per capita besides the inflation difference between two countries, we first present a model for determining the fair value of the Russian ruble in the long run from 1999 to 2021 based on macroeconomic indicators including inflation, and GDP per capita. And then we modeled the effect of widespread Russian economic sanctions on the value of the Russian ruble during the turbulent days of February 9 to April 9. Our research results show that there is not much difference between market value and fair value in the long run. Also, by observing the behavior of the ruble during the turbulent days of February 25, 2022, to April 26, 2022, and by entering the conditional risk factor and weighted average of the ruble, the USD to ruble equality between 76.23 and 91.6 was evaluated

We consider European style options with risk-neutral parameters and time-fractional Levy diffusion equation of the exponential option pricing model in this paper. In a real market, volatility is a measure of the quantity of inflation in asset prices and changes. This makes it essential to accurately measure portfolio volatility, asset valuation, risk management, and monetary policy. We consider volatility as a function of time. Estimating volatility in the time-fractional Levy diffusion equation is an inverse problem. We use a numerical technique based on Chebyshev wavelets to estimate volatility and the price of European call and put options. To determine unknown values, the minimization of a least-squares function is used. Because the obtained corresponding system of linear equations is ill-posed, we use the Levenberg-Marquardt regularization technique. Finally, the proposed numerical algorithm has been used in a numerical example. The results demonstrate the accuracy and effectiveness of the methodology used.

‎This article's primary goal is to compute an explicit transmutation-based solution to a degenerate hyperbolic equation of second order in terms of time‎. ‎To reduce a new problem to a problem that has already been solved‎, ‎or at the very least to a smaller problem‎, ‎is a standard mathematics strategy known as the transmutations method‎. ‎similar to utilizing heat equations to solve wave equations‎. ‎Using transmutation methods‎, ‎we solve this problem using the well-known Kolmogorov equation‎. We present the solution of wave equations using transmutation methods and show that it is equivalent to the solution obtained by applying the Fourier transform in order to support our methodology‎.