Journal of mathematic and modeling in Finance
Volume:4 Issue: 1, Winter-Spring 2024

The stress-strength model is a commonly utilized topic in reliability studies. In many reliability analyses involving stress-strength models, it is typically assumed that the stress and strength variables are unrelated. Nevertheless, this assumption is often impractical in real-world scenarios. This research assumes that the strength and stress variables follow the Pareto distribution, and a Gumbel copula is employed to represent their relationship. Additionally, the data is gathered through the Type-I progressively hybrid censoring scheme. The method of maximum likelihood estimation is used for point estimation, while asymptotic and Bootstrap percentile confidence intervals are employed for interval estimation of the unknown parameters and system reliability. Simulation is employed to assess the effectiveness of the suggested estimators. Subsequently, an actual dataset is examined to showcase the practicality of the stress-strength model. Simulation is employed to assess the effectiveness of the suggested estimators. Subsequently, a real dataset is examined to demonstrate the practicality of the stress-strength model.

This article proposes a new numerical technique for pricing asset-or-nothing options using the Black-Scholes partial differential equation (PDE). We first use the θ−weighted method to discretize the time domain, and then use Haar wavelets to approximate the functions and derivatives with respect to the asset price variable. By using some vector and matrix calculations, we reduce the PDE to a system of linear equations that can be solved at each time step for different asset prices. We perform an error analysis to show the convergence of our technique. We also provide some numerical examples to compare our technique with some existing methods and to demonstrate its efficiency and accuracy.

Usage-based Insurance (UBI) is an innovation that differs from traditional car insurance and seeks to distinguish between high-risk and low-risk drivers. The premium in this policy is calculated based on the distance traveled and telematics variables such as road type, time, speed, etc. This study measured the UBI acceptance rate and the factors that influence it. Global surveys and expert opinions were used to design a questionnaire, which was then administered to 396 randomly selected respondents, meeting the requirements of Cochran's formula for indeterminate populations (at least 384). Multinomial and binary logistic regression models were employed to measure acceptance and the willingness to purchase UBI based on distance, as well as distance and driving behaviors. These investigations were carried out across five and three scenarios, respectively, considering value-added services, awareness levels, and the importance of factors. Finally, a confirmatory factor analysis model was utilized to validate the UBI acceptance model, with the indicators affirming its appropriateness. The findings suggest the need for plans to enhance the information and awareness levels of insurance policyholders regarding UBI. Additionally, variables such as providing warnings to policyholders to improve driving, policy price, awareness of UBI, awareness of providing UBIs by some insurance companies in Iran, and providing rewards/discounts are identified as influential in driving UBI purchases, warranting investment by insurance companies to boost sales.

In this article, we discuss the numerical implementation of the Multilevel Monte-Carlo (MLMC) scheme for option pricing within the Heston asset model. The Heston model is a stochastic volatility model that captures the dynamics of the underlying asset price and its volatility. The MLMC method is a variance reduction technique that exploits the difference between two consecutive levels of discretization to estimate the expected value of a quantity of interest. We begin by providing an overview of the MLMC method, followed by an introduction to the weak methods used to approximate the Heston model. Weak methods are numerical schemes that preserve the distributional properties of the solution, rather than its pathwise behavior. Subsequently, we present the results of some numerical experiments conducted to evaluate the performance of the approach. Two different cases are surveyed.

‎This study suggests a novel approach for calibrating European option pricing model by a hybrid model based on the optimized artificial neural network and Black-Scholes model‎. ‎In this model‎, ‎the inputs of the artificial neural network are the Black-Scholes equations with different maturity dates and strike prices‎. ‎The presented calibration process involves training the neural network on historical option prices and adjusting its parameters using the Levenberg-Marquardt optimization algorithm‎. ‎The resulting hybrid model shows superior accuracy and efficiency in option pricing on both in sample and out of sample dataset‎.

‎Data envelopment analysis (DEA) is a methodology widely used for evaluating the relative performance of portfolios under a mean–variance framework‎. ‎However‎, ‎there has been little discussion of whether nonlinear models best suit this purpose‎. ‎Moreover‎, ‎when using DEA linear models‎, ‎the portfolio efficiency obtained is not comparable to those on the efficient portfolio frontier‎. ‎This is because a separable piecewise linear boundary usually below the efficient frontier is considered the efficient frontier‎, ‎so the model does not fully explore the possibility of portfolio benchmarks‎. ‎In this paper‎, ‎and with use of the dual-Lagrangian function‎, ‎we propose a linear model under a mean–variance framework to evaluate better the performance of portfolios relative to those on the efficient frontier‎.

Cardinality constrained portfolio optimization problems are widely used portfolio optimization models which incorporate restriction on the number of assets in the portfolio. Being mixed-integer programming problems make them NP-hard thus computationally challenging, specially for large number of assets. In this paper, we consider cardinality constrained mean-variance (CCMV) and cardinality constrained mean-CVaR (CCMCVaR) models and propose a hybrid algorithm to solve them. At first, it solves the relaxed model by replacing L_0-norm, which bounds the number of assets, by L_1-norm. Then it removes those assets that do not significantly contribute on the portfolio and apply the original CCMV or CCMCVaR model to the remaining subset of assets. To deal with the large number of scenarios in the CCMCVaR model, conditional scenario reduction technique is applied. Computational experiments on 3 large data sets show that the proposed approach is competitive with the original models from risk, return and Sharpe ratio perspective while being significantly faster.

‎Since pension funds are part of the social security system and have a socio-economic function, in order to maintain the value of the insured's savings, they should invest them, which will have a direct relationship with the money market and the capital market of each country. Due to the significant resources they have, pension funds affect the country's economic variables and, of course, are mostly affected by economic variables. This issue reveals the importance of examining how macroeconomic variables affect pension funds and the intensity of each one's impact, as well as the management of funds' resources in the face of the fluctuations of these variables‏. Therefore, in this ‎paper‎, the impact of pension funds on economic variables in 8 countries is investigated. Based on the results obtained in this research, the variables of short-term interest rate, exchange rate, and unemployment rate have an effect on the ratio of pension fund assets to GDP (as an indicator of performance).

This paper investigates the complexities surrounding uncertain portfolio selection in cases where security returns are not well-represented by historical data. Uncertainty in security returns is addressed by treating them as uncertain variables. Portfolio selection models are developed using the quadratic-entropy of these uncertain variables, with entropy serving as a standard measure of diversification. Additionally, the study underscores the superior risk estimation accuracy of Average Value-at-Risk (AVaR) compared to variance. The research concentrates on the computational challenges of portfolio optimization in uncertain environments, utilizing the Mean-AVaR-Quadratic Entropy paradigm to meet investor requirements and assuage concerns. Two illustrative examples are provided to show the efficiency of the proposed models in this paper.

This study compares the performance of the classic Black-Scholes model and the generalized Liu and Young model in pricing European options and calculating derivatives sensitivities in high volatile illiquid markets. The generalized Liu and Young model is a more accurate option pricing model that incorporates both the efficacy of the number of invested stocks and the abnormal increase of volatility during a financial crisis for hedging pur- poses and the financial risk management. To evaluate the performance of these models, we use numerical methods such as finite difference schemes and Monte-Carlo simulation with antithetic variate variance reduction tech- nique. Our results show that the generalized Liu and Young model outper- forms the classic Black-Scholes model in terms of accuracy, especially in high volatile illiquid markets. Additionally, we find that the finite differ- ence schemes are more efficient and faster than the Monte-Carlo simulation in this model. Based on these findings, we recommend using the general- ized Liu and Young model with finite difference schemes for the European options and Greeks valuing in high volatile illiquid markets.

In recent years, precise analysis and prediction of financial time series data have received significant attention. While advanced linear models provide suitable predictions for short and medium-term periods, market studies have indicated that stock behavior adheres to nonlinear patterns and linear models capturing only a portion of the market's stock behavior. Nonlinear exponential autoregressive models have proven highly practical in solving financial problems. This article introduces a new nonlinear model that allocates coefficients to significant variables. To achieve this, existing exponential autoregressive models are analyzed, tests are conducted to validate data integrity and identify influential factors in data trends, and an appropriate model is determined. Subsequently, a novel coefficient allocation method for optimizing the nonlinear exponential Autoregressive model is proposed. The article then proves the ergodicity of the new model and determines its order using the Akaike Information Criterion (AIC). Model parameters are estimated using the nonlinear least squares method. To demonstrate the performance of the proposed model, numerical simulations of Kayson Corporation's stocks are analyzed using existing methods and the new approach. The numerical simulation results confirm the effectiveness and prediction accuracy of the proposed method compared to existing approaches.

The main purpose of this paper is to propose a high order numerical method based on the finite difference methods for solving nonlinear Itˆo stochastic Volterra integral equations (SVIEs) of the second kind. To develop the method, a fourth-order implicit finite difference method and the explicit Milstein method are implemented for the discretization of non-stochastic and stochastic integral parts, respectively. To solve the original SVIEs, the proposed method has the deterministic fourth-order and strong stochastic first-order accuracy. The convergence analysis of the proposed method is proved. The finite difference method under consideration requires solving a 2×2 system of equations at each step for one-dimensional SVIE. Therefore, the proposed method is very simple to implement and does not require a lot of computational cost. Some numerical examples are prepared to indicate the verity and efficiency of the new method. Moreover, the comparative numerical results show that this method is more accurate than those existing methods given in the literature.