Journal of Mathematics and Modeling in Finance
https://jmmf.atu.ac.ir/
Journal of Mathematics and Modeling in Financeendaily1Tue, 22 Jun 2021 00:00:00 +0430Tue, 22 Jun 2021 00:00:00 +0430Estimating the term structure of mortality: an application to actuarial studies
https://jmmf.atu.ac.ir/article_12780.html
Insurance companies and pension funds which deal with human lifetime are interested in mortality forecasting to minimize the longevity risk. In this paper, we studied the mortality forecasting model based on the age-specific death rates by the usage of the state-space framework and Kalman filtering technique. To capture the volatility of time, the time varying trend has been added to the Lee-Carter (LC) model, which is the benchmark methodology in modeling and forecasting mortality since it was introduced in 1992. So, this model is a random walk with time varying drift (TV). We illustrated the performance of the proposed model using Iranian mortality data over the period 1950&ndash;2015. Numerical results show that, both models have good fitness and are tangent. So the TV model acts as well as the LC model, but the TV model has the advantages of fewer calculations and the time-varying drift which can be beneficial in time varying data sets.The Effect of Volatility Temporal Changes on the Predictability and Return of Optimal Portfolio Using the DMA Model
https://jmmf.atu.ac.ir/article_12781.html
According to most financial experts, it is not possible to study the predictability of stock prices without considering the risks affecting stock returns. On the other hand, identify-ing risks requires determining the share of risk in the total risk and the probability of risk occurrence in different regimes. Accordingly, different DMA models with full dy-namics compared to TVP-BMA, BMA and TVP models have been used in the present study to provide this predictability. Findings showed that the DMA model is more effi-cient than other research models based on MAFE and MSFE indices. The present re-search was conducted in the period of 1-2003 to 12-2013 (including 144 periods) and was implemented in MATLAB 2014 software space. As the research results show, the bank interest rate coefficient in 45 periods, the first lag rate of the bank interest rate in 37 periods, the inflation rate coefficient in 17 periods, first lag coefficient of inflation rate in 26 periods, oil price coefficient in 78 periods, first lag rate of oil price in 85 peri-ods, exchange rate coefficient in 64 periods and first lag rate of the exchange rate in 35 periods have a significant effect on stock returns. The final conclusion shows that the stock variables of oil price and the exchange rate had the highest impact on stock returns during the studied period.Prediction of outstanding IBNR liabilities using delay probability
https://jmmf.atu.ac.ir/article_12782.html
&lrm;An important question in non life insurance research is the &lrm;estimation of number of future payments and corresponding &lrm;amount of them. A &lrm;loss reserve is the money set aside by insurance companies to pay &lrm;policyholders claims on their policies. The policyholder behavior for reporting claims after its &lrm;occurrence have significant effect on the costs of the insurance &lrm;company. This article considers the problem of predicting the amount and number &lrm;of claims that have been incurred but not reported, &lrm;say IBNR&lrm;. &lrm;Using the delay probabilities in monthly level, &lrm;calculated by the Zero Inflated Gamma Mixture distribution, &lrm;it predicts IBNR's&lrm; &lrm;loss reserve. &lrm;&lrm;The model advantage in the IBNR reserve is insurers can predict &lrm;the number of future claims for each future date. &lrm;This enables &lrm;them to change the claim reporting process. The practical applications of our findings are applied against a third party liability (TPL) insurance loss portfolio. Additional information about claim can be considered in the loss reserving &lrm;model and making the prediction of amount more accurate.Designing an Updatable Long Term Health Insurance
https://jmmf.atu.ac.ir/article_12783.html
In this paper, we considered the long-term health insurance as a sequence of annual health insurance policies. To improve the disadvantages of long-term health insurance, we specify the optimal contract including optimal insurance premiums and optimal insurance coverage for the healthcare costs using a negotiation model. We considered two case of known and unknown initial health state. The predictive model for healthcare costs was determined as a time series and state-contingent models. Since the health state changes over time, the insured tends not only to be insured against risk according to her health state, but also to be insured against reclassification of risk. The insurer also seeks a fair premium appropriate to the insured&#039;s risk. To achieve this, we determined the optimal contract based on the negotiation model, in which the negotiation parameter is calculated based on the Nash solution. The optimal premium is independent of health state so that the insured is safe against reclassification. However, the insurer coverage is state-contingent and protects the insurer from detriment. Moreover, due to the uncertainty in estimating the parameters of the prediction model, we specified the projection interval by using the bootstrap method for optimal insurance premiums in the coming years. Thus, the insured is aware of the premium intervals at the time of signing the contract with the insurer.An Application of Stochastic Approximation in Simulated Method of Moments
https://jmmf.atu.ac.ir/article_12949.html
Identifying the structures of dependence between financial assets is one of the interesting topics to researchers. However, there are challenges to this purpose. One of them is the modelling of heavy tail distributions. Distributions of financial assets generally have heavier tails than other distributions, such as exponential distributions. Also, the dependence of financial assets in crashes is stronger than in booms and consequently the skewed parameter in the left tail is more.To address these challenges, there is a function called Copula. So, copula functions are suggested for modelling dependency structure between multivariate data without any assumptions on marginal distributions, which they solve the problems of dependency measures such as linear correlation coefficient. Also, tail dependency measures have analytical formulas with copula functions. In general, the copula function connects the joint distribution functions to the marginal distribution of every variables.With regard, we have introduced a factor copula model that is useful for models where variables are based on latent factor structures. Finally, we have estimated the parameters of factor copula by Simulated method of Moment, Newton-Raphson method and Robbins-Monroe algorithm and have compared the results of these methods to each other.The first order nonlinear autoregressive model with Ornstein Uhlenbeck processes driven by white noise
https://jmmf.atu.ac.ir/article_11850.html
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. Robust Net Present Value With Infinite Lifetime
https://jmmf.atu.ac.ir/article_11849.html
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.Using Reinforcement Learning Methods to Price a Perishable Product, Case Study: Orange
https://jmmf.atu.ac.ir/article_11848.html
&lrm;Determining the optimal selling price for different commodities has always been one of the main topics of scientific and industrial research&lrm;. &lrm;Perishable products have a short life and due to their deterioration over time&lrm;, &lrm;they cause great damage if not managed&lrm;. &lrm;Many industries&lrm;, &lrm;retailers&lrm;, &lrm;and service providers have the opportunity to increase their revenue through optimal pricing of perishable products that must be sold within a certain period&lrm;. &lrm;In the pricing issue&lrm;, &lrm;a seller must determine the price of several units of a perishable or seasonal product to be sold for a limited time&lrm;. &lrm;This article examines pricing policies that increase revenue for the sale of a given inventory with an expiration date&lrm;. &lrm;Booster learning algorithms are used to analyze how companies can simultaneously learn and optimize pricing strategy in response to buyers&lrm;. &lrm;It is also shown that using reinforcement learning we can model a demand-dependent problem&lrm;. &lrm;This paper presents an optimization method in a model-independent environment in which demand is learned and pricing decisions are updated at the moment&lrm;. &lrm;We compare the performance of learning algorithms using Monte Carlo simulations&lrm;.Comparing the different types of Markov switching model for Euro to Iran Rial exchange rate
https://jmmf.atu.ac.ir/article_11863.html
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&rlm;. &lrm;Due to the effect of the exchange rate on financial assets&lrm;, &lrm;study of regime change &lrm;in &lrm;exchange rate fluctuations is importance and &lrm;Regime Switching model is the most complete and populare regime change&lrm;. &lrm;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&lrm;. &lrm;In order to evaluate the achieved results&lrm;, &lrm;unit root test&lrm;, &lrm;which included the Dickey-Fuller test and the Phillips-Peron test, &lrm;is used to estimates Markov regime switching and Markov random regime switching parameters in order to find the best fluctuations model.&lrm;&lrm;Finite difference method for basket option pricing under Merton model
https://jmmf.atu.ac.ir/article_12255.html
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 ( P I D E ) , 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.Unusual behavior: Reversed Leverage Effect Bias
https://jmmf.atu.ac.ir/article_11894.html
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.Impacts of No Short Selling and Noise Reduction on Portfolio Allocation
https://jmmf.atu.ac.ir/article_11911.html
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.Mean-square Stability and Convergence of Compensated Split-Step $theta$-method for Nonlinear Jump Diffusion Systems
https://jmmf.atu.ac.ir/article_11917.html
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 &lrm;$sqrt{2}-1leqthetaleq 1&lrm;$. 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 &lrm;$sqrt{2}-1leqthetaleq 1&lrm;$. 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.TAU METHOD FOR PRICING AMERICAN OPTIONS UNDER COMPLEX MODELS
https://jmmf.atu.ac.ir/article_11920.html
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.Mathematical Modeling of Stock Price Behavior and Option Valuation
https://jmmf.atu.ac.ir/article_12044.html
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.Economic Models Involving Time Fractal
https://jmmf.atu.ac.ir/article_12193.html
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.Forecasting Spot and Future Gold Coin Price Volatility and Their Predictive Power on Each Other by Using ANN-GARCH Model
https://jmmf.atu.ac.ir/article_12416.html
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.Spectral Graph Embedding for Dimension Reduction in Financial Risk Assessment
https://jmmf.atu.ac.ir/article_12996.html
The economic downturn in recent years has had a significant negative impact on corporates performance. In the last two years, as in the last years of 2010s, many companies have been influenced by the economic conditions and some have gone bankrupt. This has led to an increase in companies&#039; financial risk. One of the significant branches of financial risk is the emph{company&#039;s credit risk}. Lenders and investors attach great importance to determining a company&#039;s credit risk when granting a credit facility. Credit risk means the possibility of default on repayment of facilities received by a company. There are various models for assessing credit risk using statistical models or machine learning. \In this paper, we will investigate the machine learning task of the binary classification of firms into bankrupt and healthy based on the emph{spectral graph theory}. We first construct an emph{adjacency graph} from a list of firms with their corresponding emph{feature vectors}. Next, we first embed this graph into a one-dimensional Euclidean space and then into a two-dimensional Euclidean space to obtain two lower-dimensional representationsof the original data points. Finally, we apply the emph{support vector machine} and the emph{multi-layer perceptron} neural networktechniques to proceed binary emph{node classification}. The results of the proposed method on the given dataset (selected firms of Tehran stock exchange market) show a comparative advantage over PCA method of emph{dimension reduction}. Finally, we conclude the paper with some discussions on further research directions.