Journal of Mathematics and Modeling in Finance

Abstract This research has three main goals. The first goal is to investigate the contagion of the risk from the financial sector to other industries. The second objective is to examine the impact of the competitiveness of industries on the spread of the risk sequence from the financial sector to the industries, and the third objective is to examine the effect of three main industrial indicators, namely, net debt, value spread and investment spread, on the risk contagion from the financial sector to other industries. In this research, a new measurement method of the spillover of the risk sequence from the financial sector to other industries has been introduced as the occurrence of similar conditions, which for each industry in each period is equal to the number of simultaneous occurrences of severe negative returns in that industry and the financial sector. Empirical findings show that the contagion of the risk from the financial sector to other industries was significant and this contagion was greater for competitive industries due to the greater need for external financing. The occurrence of similar conditions in each sector has a positive relationship with the net debt of that industry. Also, there is no relationship between the value spread and the investment spread with the occurrence of similar conditions.

Abstract In this paper, we address the problem of analyzing and computing all steady states of an overlapping generation (OLG) model with production and many generations. The characterization of steady states coincides with a geometrical representation of the algebraic variety of a polynomial ideal, and, in principle, one can apply computational algebraic geometry methods to solve the problem. However, it is infeasible for standard methods to solve problems with a large number of variables and parameters. Instead, we use the specific structure of the economic problem to develop a new algorithm that does not employ the usual steps for the computation of Grobner basis such as the computation of successive S-polynomial and expensive division.

Abstract In this article, according to the importance of the hazard rate function criterion in the

evaluation of statistical distributions, its estimation methods are presented. Here, we suggest

estimators for the hazard rate function. First, we use the standard deconvolution kernel

density estimator and suggest a plug-in estimator. In the following we investigate asymptotic

behavior of our estimator. For another estimator, we construct the new estimation the

hazard rate function according plug-in and CDF. Finally, we consider the performance of

the suggested estimators by simulation. Mean square error of estimators λˆ(t, p), λˆ(t) and λˆ

c(t) present in tables 1 till 6.

Abstract This paper proposes a new approach to pricing European options using deep learning techniques under the Heston and Bates models of random fluctuations. The deep learning network is trained with eight input hyper-parameters and three hidden layers, and evaluated using mean squared error, correlation coefficient, coefficient of determination, and computation time. The generation of data was accomplished through the use of Monte Carlo simulation, employing variance reduction techniques. The results demonstrate that deep learning is an accurate and efficient tool for option pricing, particularly under challenging pricing models like Heston and Bates, which lack a closed-form solution. These findings highlight the potential of deep learning as a valuable tool for option pricing in financial markets.

Abstract The use of variance as a risk measure is limited by its non-coherent

nature. On the other hand, standard deviation has been demonstrated as a

coherent and effective measure of market volatility. This paper suggests the

use of standard deviation in portfolio optimization problems with cardinality

constraints and short selling, specifically in the mean-conditional value-at risk

framework. It is shown that, subject to certain conditions, this approach leads

to lower standard deviation. Empirical results obtained from experiments on

the SP index data set from 2016-2021 using various numbers of stocks and

confidence levels indicate that the proposed model outperforms existing models

in terms of Sharpe ratios.

Abstract Stock trading is a significant decision-making problem in asset management. This study introduces a financial trading system (FTS) that leverages artificial intelligence (AI) techniques to automate buy and sell orders specifically in Iran's stock market. Due to limited availability of labeled data in financial markets, the FTS utilizes reinforcement learning (RL), a subset of AI, for training. The model incorporates technical analysis and a constrained policy to enhance decision-making capabilities. The proposed algorithm is applied to the Tehran Securities Exchange, evaluating its efficiency across 45 periods using three different stock market indices. Performance comparisons are made against common strategies such as buy and hold, randomly selected actions, and maintaining the initial stock portfolio, with and without transaction costs. The results indicate that the FTS outperforms these methods, exhibiting excellent performance metrics including Sharp ratio, PP, PF, and MDD. Consequently, the findings suggest that the FTS serves as a valuable asset management tool in the Iranian financial market.

Abstract The purpose of this study is to investigate the effects and risk spillover from the global crude oil market on Tehran Stock Exchange Oil Group. For this purpose, we used a combination of copula models and switching models in this research. First, we will examine marginal models and examine Heston switching and Markov switching models in this market. Then we create the multivariate distribution function using Clayton's copula. The data analyzed in this research are related to the global crude oil markets and the Tehran Stock Exchange Oil Group from December 2011 to January 2023. This time period was chosen due to the examination of different regimes in the above markets and also the selection of the appropriate marginal model for these markets. The results show the crude oil market has influenced on Tehran Stock Exchange and also the Tehran Stock Exchange Oil Group indices. Volatility in this global market cause turbulence in the Tehran stock market and this market is affected by the global crude oil market. This is due to the influence of the global crude oil market on total prices in these markets. Heston switching model and its combination with copula models including Clayton copula can bring good results. This is confirmed by comparing this model with other models such as copula Markov switching models.

Abstract The financial markets reveal stylized facts that could not be captured by Black-Scholes partial differential equations (PDEs).  In this research, we investigate 3/2 stochastic volatility to pricing options which is more compatible with the interpretation of implied volatility. Numerical study and calibrations show that the 3/2 model incorporating jumps effectively encompasses key market characteristics attributed. However, it requires more estimating parameters in comparison to the pure diffusion model. Stochastic volatility models with jumps describe the log return features of the financial market although more parameters are involved in estimations.

Abstract Safe investment can be experienced by incorporating human experience and modern predicting

science. Artificial Intelligence (AI) plays a vital role in reducing errors in this winning layout. This study

aims at performance analysis of Deep Learning (DL) and Machine Learning (ML) methods in modelling

and predicting the stock returns time series based on the return rate of previous periods and a set of

exogenous variables. The data used includes the weekly data of the stock return index of 200 companies

included in the Tehran Stock Exchange market from 2016 to 2021. Two Long Short-Term Memory (LSTM)

and Deep Q-Network (DQN) models as DL processes and two Random Forest (RF) and Support Vector

Machine (SVM) models as ML algorithms were selected. The results showed the superiority of DL

algorithms over ML, which can indicate the existence of strong dependence patterns in these time series,

as well as relatively complex nonlinear relationships with uncertainty between the determinant variables.

Meanwhile, LSTM with R-squared equals to 87 percent and the analysis of the results of five other

evaluation models have shown the highest accuracy and the least error of prediction. On the other hand, the

RF model results in the least prediction accuracy by including the highest amount of error.

Abstract This paper investigates the effects of contingent capital, a debt instrument that automatically converts into equity if the value of the asset is below a predetermined threshold on the pricing process of a bank assets’. A traceable form of the contingent convertible bond is analyzed to find a closed-form solution for the price of this bond using barrier and growth options. We examine the interaction between growth options and financing policy in a dynamic business model. The contribution of this paper is to extend Hilscher and Raviv [10] and Tan and Yang [22] research to include the evaluation of all aspects of banks' financial structure, with an emphasis on explicitly calculating the likelihood of the default event. The fundamental theorem of asset pricing and the first passage of time method have been used to generate closed formulas that are amenable to practical analysis. The potential benefits from contingent capital as financing and risk management instrument can be assessed through their contribution to reducing the probability of default. The appropriate choice of contingent capital parameters, the rate, and the conversion threshold can reduce shareholders incentives to change risk.

Abstract One of central bank regulations that has direct impact on the banking industry is loan benchmark interest rate. Banks use it as a reference rate to determine their loan interest rate. In this paper, we study the role of loan benchmark interest rate on banking loan dynamics. The model is in the form of a difference equation that follows a gradient adjustment process. We study the loan equilibrium's stability via bifurcation theory. It is found that the benchmark rate must be set between the flip and transcritical values. Some numerical simulations are performed to confirm the analytical result. The stochastic case of the benchmark rate is also studied. In addition, we perform numerical sensitivity analysis of the benchmark rate with the model's other parameters.

Abstract Modern research often requires the use of economic models with multiple agents that interact over time. In this paper we research overlapping generations models, hereinafter OLG. In these models, the phenomenon of the multiplicity of long-term equilibrium may arise. This fact proves to be important for the theoretical justification of some economic effects, such as the collapse of the market and others. However, there is little theoretical research on the possibility of multiple equilibria in these models. At the same time, the works that exist are devoted to models with only few periods. This is due to the fact that the complexity of algorithms that calculate all long-term equilibria grows too fast with realistically selected lifespan values. However, solutions of some OLG models after the introduction of additional variables can become polynomial systems. Thus it is possible to represent many long-term equilibria as an algebraic variety. In particular, the Gr¨obner basis method became popular. However, this approach can only be used effectively when there are few variables. In this paper we consider the task of finding long-term equilibrium in overlapping generations models with many periods. We offer an algorithm for finding the system’s solutions and use it to investigate the presence of multiple solutions in realistically calibrated models with long-lived agents. We also examine these models for multiple equilibria using the Monte Carlo method and replicate previously known results using a new algorithm.