Journal of mathematic and modeling in Finance
Volume:1 Issue: 1, Winter - Spring 2021

This paper presents a nonlinear autoregressive model with ‎Ornstein ‎Uhlenbeck processes innovation driven with white noise. ‎‎‎‎Notations ‎and ‎preliminaries ‎are ‎presented ‎about ‎the ‎Ornstein ‎Uhlenbeck ‎processes ‎that ‎have ‎important ‎applications ‎in ‎finance. ‎The ‎parameter ‎estimation ‎for ‎these ‎processes ‎is ‎constructed ‎from ‎the ‎time ‎continuous ‎likelihood ‎function ‎that ‎leads ‎to ‎an ‎explicit ‎maximum ‎likelihood ‎estimator.‎ A semiparametric method is proposed to estimate the nonlinear autoregressive function using the conditional least square method for parametric estimation and the nonparametric kernel approach by using the nonparametric factor that is derived by a local L2-fitting criterion for the regression adjustment ‎estimation‎‎‎. Then the ‎Monte ‎Carlo‎‎ numerical simulation studies are carried out to show the efficiency and accuracy of the present ‎work.‎ The ‎mean square error (‎MSE) is a measure of the average squared deviation of the ‎estimated ‎function‎ values from the actual ones. The values of MSE indicate ‎that ‎the ‎innovation ‎in ‎noise ‎structure ‎is ‎performed ‎well ‎in ‎comparison ‎with ‎the ‎existing ‎noise ‎in ‎the ‎nonlinear ‎autoregressive ‎models.‎ ‎‎‎

In this study, Robust Net Present Value (RNPV) has been developed for evaluation of projects with infinite life. In this method, the changes of uncertain net incomes in a financial cash flow are postulated in a convex, continuous, and closed region. It has been indicated that RNPV, in the infinite life horizon, is calculable only when the net incomes are uncorrelated. Compared to traditional methods, this study considers the variance matrix of net incomes, takes uncertainty into account during the evaluation of investment projects with infinite life period. One important finding when using this method is that one does not need to calculate the covariance matrix in the evaluation of projects with infinite life. The only requirement is to estimate the value of maximum variance for the given financial cash flow. The proposed method is also easy to both calculate and understand in practice. MATLAB software is used for implementation. Lastly, the features of the developed method have been analyzed using some numerical examples for a project with infinite lifetime.

‎Determining the optimal selling price for different commodities has always been one of the main topics of scientific and industrial research‎. ‎Perishable products have a short life and due to their deterioration over time‎, ‎they cause great damage if not managed‎. ‎Many industries‎, ‎retailers‎, ‎and service providers have the opportunity to increase their revenue through optimal pricing of perishable products that must be sold within a certain period‎. ‎In the pricing issue‎, ‎a seller must determine the price of several units of a perishable or seasonal product to be sold for a limited time‎. ‎This article examines pricing policies that increase revenue for the sale of a given inventory with an expiration date‎. ‎Booster learning algorithms are used to analyze how companies can simultaneously learn and optimize pricing strategy in response to buyers‎. ‎It is also shown that using reinforcement learning we can model a demand-dependent problem‎. ‎This paper presents an optimization method in a model-independent environment in which demand is learned and pricing decisions are updated at the moment‎. ‎We compare the performance of learning algorithms using Monte Carlo simulations‎.

According to the rule of equality of equal prices, the price of a foreign commodity within a country depends on the price of the commodity at the origin as well as the exchange rate of that country. According to this rule, if the foreign exchange costs are insignificant, the price of a single commodity will be the same everywhere in terms of price, and ideally the purchasing power of a currency inside and outside the country will be the same‏. ‎Due to the effect of the exchange rate on financial assets‎, ‎study of regime change ‎in ‎exchange rate fluctuations is importance and ‎Regime Switching model is the most complete and populare regime change‎. ‎The aim of this research is to modeling Euro-Rial exchange rate under the model of Markov regime switching and Markov random regime switching model‎. ‎In order to evaluate the achieved results‎, ‎unit root test‎, ‎which included the Dickey-Fuller test and the Phillips-Peron test, ‎is used to estimates Markov regime switching and Markov random regime switching parameters in order to find the best fluctuations model.‎‎

In financial markets , dynamics of underlying assets are often specified via stochasticdifferential equations of jump - diffusion type . In this paper , we suppose that two financialassets evolved by correlated Brownian motion . The value of a contingent claim written on twounderlying assets under jump diffusion model is given by two - dimensional parabolic partialintegro - differential equation ( PIDE ) , which is an extension of the Black - Scholes equation witha new integral term . We show how basket option prices in the jump - diffusion models , mainlyon the Merton model , can be approximated using finite difference method . To avoid a denselinear system solution , we compute the integral term by using the Trapezoidal method . Thenumerical results show the efficiency of proposed method .Keywords: basket option pricing, jump-diffusion models, finite difference method.

According to the literature on risk, bad news induces higher volatility than good news. Although parametric procedures used for conditional variance modeling are associated with model risk, this may affect the volatility and conditional value at risk estimation process either due to estimation or misspecification risks. For inferring non-linear financial time series, various parametric and non-parametric models are generally used. Since the leverage effect refers to the generally negative correlation between an asset return and its volatility, models such as GJRGARCH and EGARCH have been designed to model leverage effects. However, in some cases, like the Tehran Stock Exchange, the results are different in comparison with some famous stock exchanges such as the S&P500 index of the New York Stock Exchange and the DAX30 index of the Frankfurt Stock Exchange. The purpose of this study is to show this difference and introduce and model the "reversed leverage effect bias" in the indices and stocks in the Tehran Stock Exchange.

Since noise present in financial series, often as a result of existence of fraudulent transactions, arbitrage and other factors, causes noise in financial data therefore false estimation of the parameters and hence distorts portfolio allocation strategy, in this paper wavelet transform is used for noise reduction in mean-variance portfolio theory. I apply conditional estimation of the mean and variance of returns along with the simple one obtaining “optimal weights” which later combines with smooth and non-smooth series, result in four optimal portfolio weights and therefore four portfolio returns. After this, I impose the non-negativity constraint (for weights) deduced from the Kuhn-Tucker approach to simulate the no short selling circumstance in Tehran Stock Exchange. Weights and portfolio returns changed dramatically in this step but the main result (which asset to hold) did not. Comparing Sharp ratios, I observed that Regardless of the psychological characteristics of the investor, holding the risk-free asset is almost the optimal choice in this case.

In this paper, we analyze the strong convergence and stability of the Compensated Splite-step $theta$ (CSS$theta$) and Forward-Backward Euler-Maruyama (FBEM) methods for Numerical solutions of Stochastic Differential Equations with jumps (SDEwJs),where ‎$sqrt{2}-1leqthetaleq 1‎$. The drift term $f$ has a one-sided Lipschitz condition, the diffusion term $g$ and jump term $h$ satisfy global Lipschitz condition. Furthermore, we discuss about the stability of SDEwJs with constant coefficients and present new useful relations between their coefficients. Finally we examine the correctness and efficiency of theorems with some examples.In this paper, we analyze the strong convergence and stability of the Compensated Splite-step $theta$ (CSS$theta$) and Forward-Backward Euler-Maruyama (FBEM) methods for Numerical solutions of Stochastic Differential Equations with jumps (SDEwJs),where ‎$sqrt{2}-1leqthetaleq 1‎$. The drift term $f$ has a one-sided Lipschitz condition, the diffusion term $g$ and jump term $h$ satisfy global Lipschitz condition. Furthermore, we discuss about the stability of SDEwJs with constant coefficients and present new useful relations between their coefficients. Finally we examine the correctness and efficiency of theorems with some examples.

The European option can be exercised only at the expiration date while an American option can be exercised on or at any time before the expiration date.In this paper, we will study the numerical solutions of a class of complex partial differential equations (PDE) systems with free boundary conditions. This kind of problems arise naturally in pricing (finite-maturity) American options, which is applies to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump-diffusion (HEJD) and the finite moment log stable (FMLS) models. Developing efficient numerical schemes will have significant applications in finance computation. These equations have already been solve by the Hybrid Laplace transformfinite difference methods and the Laplace transform method(LTM). In this paper we will introduce a method to solve these equations by Tau method. Also, we will show that using this method will end up to a faster convergence. Numerical examples demonstrate the accuracy and velocity of the method in CEV models.

This study emphasizes on the mathematical modeling procedure of stock price behavior and option valuation in order to highlight the role and importance of advanced mathematics and subsequently computer software in financial analysis. To this end, following price process modeling and explaining the procedure of option pricing based on it, the resulting model is solved using advanced numerical methods and is executed by MATLAB software. As derivatives pricing models are based on price behavior of underling assets and are subject to change as a result of variation in the behavior of the asset, studying the price behavior of underlying asset is of significant importance. A number of such models (such as Geometric Brownian Motion and jump-diffusion model) are, therefore, analyzed in this article, and results of their execution based on real data from Tehran Stock Exchange total index are presented by parameter estimation and simulation methods and also by using numerical methods.

In this article, the price adjustment equation has been proposed and studied in the frame of fractal calculus which plays an important role in market equilibrium. Fractal time has been recently suggested by researchers in physics due to the self-similar properties and fractional dimension. We investigate the economic models from the viewpoint of local and non-local fractal Caputo derivatives. We derive some novel analytical solutions via the fractal Laplace transform. In fractal calculus, a useful local fractal derivative is a generalized local derivative in the standard computational sense, and the non-local fractal Caputo fractal derivative is a generalization of the non-local fractional Caputo derivative. The economic models involving fractal time provide a new framework that depends on the dimension of fractal time. The suggested fractal models are considered as a generalization of standard models that present new models to economists for fitting the economic data. In addition, we carry out a comparative analysis to understand the advantages of the fractal calculus operator on the basis of the additional fractal dimension of time parameter, denoted by $alpha$, which is related to the local derivative, and we also indicate that when this dimension is equal to $1$, we obtain the same results in the standard fractional calculus as well as when $alpha$ and the nonlocal memory effect parameter, denoted by $gamma$, of the nonlocal fractal derivative are both equal to $1$, we obtain the same results in the standard calculus.

A large number of investors have been attracted to the Iran Mercantile Exchange as a result of launching Bahar Azadi Coin future contracts, also known as gold coin future contracts, since 2007. The nature of gold price as a physical-commodity and financial asset, as well as other contributing factors to the gold futures market, extremely complicates the analysis of the relationship between the underlying variables.One of the methods to forecast the price volatility is the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. However, the high percentage of errors in such prediction has forced researchers to apply a variety of techniques in the hope of more accurate projections. Similarly, in this study, a hybrid model of the GARCH and Artificial Neural Network model (ANN) was used to predict the volatility of gold coin spot and future prices in the Iran Mercantile Exchange.In this study, variables such as global gold price, spot or future gold coin price (depending on which one is analyzed), US Dollar/IR Rial, world price of OPEC crude oil, and Tehran Stock Exchange Index were considered as factors affecting the price of gold coin. The results of the study indicate that the ANN-GARCH model provides a better prediction model compared to the Autoregressive models. Moreover, the ANN-GARCH model was utilized to compare the predictive power of spot and future gold coin prices, and it revealed that gold coin future price fluctuations predicted spot price of gold coin more accurately.