ali foroush bastani

In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization. A second order finite difference formula is used to time discretization and space discretization is done by a spectral method based on Chelyshkov wavelets and an operational process by defining Chelyshkov wavelets operational matrices. Convergence and error analysis for Chelyshkov wavelets approximation and also for the proposed method are discussed. The method is validated and its accuracy, convergency and efficiency are demonstrated through some cases with given accurate solutions. The method is also utilize for pricing various European options conducted by a time-fractional Black-Scholes model

Compliance with the capital adequacy requirements provided by the Basel Committee on Banking Supervisions is one of the most vital needs of banking in Iran. In this regard, this article reviews the methods for estimating the loss given default (LGD) as one of the two main variables in determining the credit risk of a debt. This variable is used in various areas of credit risk management, including loan pricing, loss reserve determination, credit rating, and determining capital adequacy. Therefore, in this study, while reviewing the methods of estimating this variable in the various approaches in Basel accords including “fundamental internal rating” and “advanced internal rating,” the common practice that is currently used to implement the advanced internal rating approach to estimate loss given default is described in details. Also, reviewing several important studies in the field, the estimation methods used in these studies, and the results of using different statistical methods in modeling loss given default have been presented.

Credit risk is the most important risk that banks are facing. Two main variables used for modeling this risk and determining the expected loss from lending are "Probability of Default" and "Loss Given Default." Given the importance of the loss-given-default (LGD) in various applications of credit risk management and credit rating, this study presents a method using the structural model approach to estimate this variable for both secured and unsecured debt, focusing on debt structure and collateral liquidity. The proposed approach has been applied to estimate the LGD for some selected firms active in the Iranian capital market.

To estimate the "Expected LGD" and "Downturn LGD" for secured (with both liquid and less liquid collateral) and unsecured debts, a structural model and Monte Carlo simulation approach have been employed. In this structural model, the market value of the firm's total assets follows a Jump-Diffusion process, and each collateral, being among the firm's tangible assets, has a separate but dependent stochastic process relative to the firm's total assets. Additionally, a liquidity penalty is considered for less liquid collateral.Furthermore, in this study, different values are considered for the ratio of tangible assets to total assets in default and non-default conditions (operations). To estimate the LGD  for the debts of eleven selected eligible firms, after determining the parameters of the stochastic process for assets of each firm and collateral using data up to the end of the fiscal year 1396 (2017), the Loss Given Default for these firms' debts at the end of the fiscal year 1397 (2018) was estimated using the structural model and Monte Carlo simulation approach.In the Monte Carlo simulation, 500,000 paths for total assets and collaterals were simulated. For the paths where defaults were observed, the expected Loss Given Default values were  estimated, first at the debt level and then at the firm level. Additionally, to perform a sensitivity analysis, the mentioned variables were estimated under alternative debt structures for the same firms.

For firms with a debt structure consisting of only one secured debt, where the collateral is liquid and the debt is recovered solely from the collateral, the expected Loss Given Default values for secured debt are similar, ranging from 14% to 14.5%. If the type of collateral changes to the less liquid one, for the same firms, this value ranges from 30% to 33%. For the total LGD variable (where debt recovery comes from both collateral and other remaining assets of the firm), the average expected values for these two debt structures are 9% and 12%, respectively. For firms with a debt structure involving two secured debts, the expected LGD values, where recovery is solely from collateral, are similar to those of firms with only one secured debt with the same type of collateral. However, the average expected total LGD for secured debt with liquid collateral is 10%, and for less liquid collateral, it is 15.8%. Additionally, as the proportion of secured debts with liquid collateral relative to total debts decreases, the expected LGD at the firm level tends to increase on average. Moreover, in the downturn, the LGD for secured debt with liquid collateral is less influenced by the debt structure and is primarily affected by the dynamics of assets and collateral and the values of these two variables under critical conditions.

In this study, the LGD for debts was estimated using a structural model and through Monte Carlo simulation for the debts of eleven selected firms listed on the Tehran Stock Exchange. Considering two types of collateral with different liquidity and three common debt structures of companies, it was determined that the liquidity of collateral plays a significant role in reducing the expected LGD for secured loans. The role of debt structure, given the priority of secured debt payments, affects the amount of LGD for unsecured debt, as well as the total LGD for secured debts and the total LGD at the firm level.

The probability of default is one factor that determines the cost of capital due to its role in credit risk. Dividend as a sign of cash flow or as a sign of ownership of wealth is one of the factors affecting the probability of default. There are two theories of dividend signaling theory and agency theory regarding the effect of dividends on credit risk. The cash profit signaling theory expresses the management’s confidence in the company’s future cash flows and causes market participants to calculate the company’s assets as high and the company’s asset volatility as low, thus reducing information asymmetry, it causes the probability of default calculated by market decreases and there is a negative relationship between dividend and estimated default probability. Conversely, agency theory posits that cash dividends decrease the company’s assets and increase the debt ratio, and this increases the risk of debtholders and the acquisition of their wealth by shareholders, and the conflict of interests between shareholders and debtholders. Therefore, it causes a positive relationship between dividends and estimated default probability. This article aims to examine the relationship between dividends and the probability of default, exploring its alignment with both dividends signaling theory and agency theory.

In this article, Geske’s method, which is an extension of Merton’s method, is used to calculate the probability of default. Subsequently, an unbalanced nonlinear regression is applied to investigate the quadratic relationship between cash interest and the probability of default during the years 2001-2021. The statistical population comprises companies listed on the Tehran Stock Exchange and the Iran Farabourse, with the exclusion of financial companies, those with more than six months of consecutive trading suspension, and those that have experienced trading suspension for more than twenty percent of their market lifespan. Ultimately, 462 companies meet these criteria and are included in the study.

The findings suggest a quadratic U-shaped nonlinear relationship between dividends and the probability of default. Initially, as dividends increase, the probability of default decreases with a diminishing slope. However, beyond a certain threshold of dividend increase, the probability of default starts to rise with an increasing slope.

According to the theory of dividend signaling, as dividends increase up to a certain threshold, the company's future earnings outlook is positively evaluated. The market, in turn, assesses the company's assets at a higher value with lower asset volatility. This positive assessment, attributed to the reduction of information asymmetry, leads to a decrease in the market's estimated probability of default. Once the dividend surpasses this threshold, it becomes advantageous for shareholders. This is due to a reduction in the company's assets, an elevation in the debt ratio, an increased risk for debtholders, and the potential transfer of the company's assets, ultimately leading to the appropriation of wealth from debtholders by shareholders. Therefore, the probability of default increases, which is in accordance with the empirical findings of the quadratic U-shaped relationship between dividend and the probability of default.

The purpose of this research is to model Value-at-Risk (VaR) of portfolio with EVT-Pair-Copulas approach. In the financial literature, a significant amount of empirical studies have been done on the characteristics of financial assets returns and researchers have found a set of stylized facts about this subject. In this regard leptokurtic, left-skewed, weak autocorrelation, volatility clustering, and heteroscedasticity can be mentioned. Any estimation of risk without considering these characteristics or using unrealistic assumptions about financial assets returns increases the probability of failure in the risk management process. For this purpose, at first, the marginal distributions of returns are obtained using extreme value theory (EVT). Concerning characteristics of financial assets returns and also the primary filter to apply EVT, we use heteroscedasticity models for the marginal distributions of assets. Then the structure of the dependence between different stocks is estimated by using C-Vine, D-Vine, and R-Vine pair copula models. Afterward, the VaR of portfolio is estimated using the Monte Carlo simulation method. The final results show that the model with GARCH marginal distribution and R-Vine pair copula has been able to achieve the best performance among rival models at 95% confidence level.

Real estate investment are characterized by low liquidity and irreversible cost. Real Estate industry is one of the most important industry in occupation. Moreover, its production has the biggest weight in family portfolio.These are important characteristics of real estate markets. Real estate industry has cyclical trend. In recession, investor delay their investment. Traditional capital Budgeting models such as Net Present Value are base on fix assumption and condition. They ignore management flexibility. In this paper residential Projects are evaluated with real options (option to delay) by Black-Scholes and Binomial Lattice Model.These model values managerial flexibility. Experimental results show that project Evaluation with real options outperforms the traditional models such as NPV. This paper studies the optimal timing of investment in an irreversible project where the benefits from the project and the investment cost follow continuous- time stochastic processes. According to optimal investment timing proposed by MC Donlad and Siegel, time to start this Project is 9/5 years from now.

Portfolio insurance strategies are structural methods that provide a certain level of certainty by setting a floor value. In other words, using these strategies can achieve a predetermined minimum return. PI strategies, while maintaining the potential for capital growth in bull markets, provide downside protection in the bear market and at the end of the investment horizon provide a guaranteed minimum return. This study explains how to construct a portfolio and allocate assets by using these strategies, and also examines the performance of a constant proportion portfolio insurance (CPPI) strategy and value at risk based portfolio insurance (VBPI).

In order to evaluate the performance of constant proportion portfolio insurance strategy and value at risk based portfolio insurance, first the mathematical model of the Constrained Constant Proportion portfolio insurance is presented. In the Constrained case risk-free borrowing is not possible which makes the model more realistic. By using the Fourier transform of the characteristic function, the density function of returns has been extracted. By using the Density Function, the value at risk is calculated at the desired confidence levels, and finally, the mathematical model of the risk-based approach is presented. A variable-rate model is used to estimate the risk-taking movement of the asset, which is closer to reality. To estimate the dynamic of the risky asset regime-switching model has been used to make the model closer to reality.

The results show that both strategies have been successful in controlling risk, and this performance improves with increasing confidence level and frequency of portfolio rebalancing. Omega measure shows that the performance of the constant proportion portfolio insurance is better at low thresholds. Also, the dispersion of the simulated results for the final value of the portfolios showed that the constant proportion portfolio insurance works better in protecting the floor.

Portfolio insurance strategies can dramatically improve the controlling of downside risk relative to buy and hold strategy and the performance of CPPI strategy is better than VBPI according to the performance measures.

Venture Capitals (VCs) which have recently financed significant amounts of start-up companies, are divided in two categories: Independent Venture Capital (IVC) and Bank-affiliated Venture Capital (BVC). In order to study the effect of VC on bank performance, it is necessary to analyze the various financial and economic variables and their relation. Since the relation between these variables is extremely enormous and complex, it is not possible to use econometrics and classical financial models. Therefore, a system dynamic approach is used in this paper to analyze the problem. The problem is studied in two stages; first, the consequences of bank’s invest in VC industry is investigated and second, a comparison is made between the BVC and IVC. The results show that bank with investing in VC is benefited from both yield of VC projects and also presenting more loans. Finally, using the designed systematic model, the proper proportion, with which bank should invest in VC to optimize its profits, is calculated.

Systemic risk is the cause of many financial crises and has adverse effects on economic performance at the macro level. For effective policy-making of systemic risk management, it is necessary to measure and monitor systemic risk and to study the mechanism of its effect on macro-economy. This paper aims at investigating the relationship between banking sector systemic risk and the performance of macroeconomic indexes including Gross Domestic Production (GDP), GDP without oil, the components of GDP and the value added of the sectors.

One of the best systemic risk measures is SRISK index which is used in this article, and the relationship between the changes of macroeconomic indexes and the changes of SRISK is evaluated using autoregressive distributed lags model.

There is a significant negative relationship between the banking sector systemic risk of Iran and GDP (with and without oil) for horizon of 12 months. Value added of construction, financial sector and industry sector is influenced more than other sectors from the changes of systemic risk of banking system. Furthermore, all of the components of GDP are influenced by the changes of systemic risk but this influence is stronger and more durable for the fixed investment component.

In addition to the increase of the probability of financial crisis, the increasing of systemic risk has long-term adverse effects on macroeconomic performance and investments. In order to take a timely measure for decreasing the adverse effects of systemic risks, Policy-makers should monitor SRISK index continuously.

The evaluation of VC projects (companies) is very important because the present value of them defines the proportion of Entrepreneur’s profit from all future profit of that project (company). In this article, VC projects have been evaluated by using Real Options and Installment Option. In order to doing that, the lower and upper bounds based on “No-Arbitrage” condition are obtained for pricing installment option in both discrete and continuous time. These bounds have been used for pricing Venture Capital projects. With simulation of stock price by Monte Carlo, they have been compared with DTS bounds (the bounds obtained by other authors). Results reveal the bounds in the present study are more effective than DTS bounds. For more confidence, the Bounds have been compared with Monte Carlo simulation based on Least Square approach (we have changed that approach to be used in the evaluation of Installment Option); as expected, they have confirmed each other.