Asset Dynamics Research Articles

Application of power series approximation techniques to valuation of European style options

Fourier transforms provide versatile techniques for pricing financial derivative securities. In applying such techniques, a typical derivative valuation expression is often written as an inner product of the Fourier transform of payoff and the characteristic function of the underlying asset dynamics. Some modelling specifications imply that it might be challenging to find a closed-form expression for the characteristic function. In such situations, numerical approximations have to be employed. This paper utilises the power series approximation technique in finding explicit expressions of the characteristic function for the underlying stochastic variables. We analyse the convergence and accuracy of this technique in the context of valuing European style options written on underlying securities whose dynamics evolve under the influence of multiple Heston-type stochastic volatilities [Heston, S., A closed-form solution for options with Stochastic volatility with applications to Bond and currency options. Rev. Financ. Stud., 1993, 6, 327–343] and Cox–Ingersoll–Ross stochastic interest rates [Cox, J., Ingerson, J. and Ross, S., A theory of the term structure of interest rates. Econometrica, 1985, 53, 385–407]. This paper contributes to the existing literature four-fold by: (i) adapting the valuation technique to long-dated instruments; (ii) providing an adjustment to a series of points around which the power series expansion is performed; (iii) analysing the performance of different strategies for hedging European call options; (iv) applying the power series approach to the valuation of guaranteed minimum accumulation benefit riders embedded in variable annuity contracts. Our results demonstrate a high computational efficiency of the power series approximation method for evaluation of derivative prices and hedge ratios.

Проблемна кредитна заборгованість банків України: сучасний стан та напрями її подолання

Introduction. The article is devoted to the study of problem about credit indebtedness of Ukrainian banks at the present stage and to identifying ways to overcome it. The article analyzes the loan portfolio of Ukrainian banks during 2014-2020. For the last five years, the banking system of Ukraine has been developing in the conditions of military conflict and permanent political and economic crisis. After the occupation of the Autonomous Republic of Crimea and certain regions of Donetsk and Luhansk, domestic commercial banks lost part of their assets that remained in the occupied territories. These events forced the National Bank of Ukraine to take measures to stabilize the credit system, which led to the withdrawal of a large number of insolvent banks from the market. Purpose. The purpose of the study is to analyze the current state of credit debt problem of Ukrainian banks and to identify ways to neutralize it. Results. Based on statistical data, the dynamics of individual assets of Ukrainian banks, characterized by the discount rate as the main deterrent to lending, certain factors influencing the emergence of problem loans in a banking institution. Statistical data on the volume of lending to banking institutions by business entities and individuals in Ukraine are presented and analyzed. Based on the analysis, the main factors of increasing creditworthiness are investigated. Based on world experience, we offer ways to overcome the problematic team of domestic banks in the rear stabilization of the credit system. Conclusions. The conducted research confirmed the theoretical expediency and practical significance of the analysis of the current state of credit indebtedness problem of Ukrainian banks, which allows to determine the ways of its neutralization. The assessment of some indicators of banks’ activity revealed a number of factors that negatively affect the work with problem loans, namely: reduction in the number of banks (in particular, banks with foreign capital), reduction in lending, which is directly related to rising interest rates on loans, real incomes, the devaluation of the national currency and more. Each bank must develop a set of measures applicable to a particular category of problem loans, work out algorithms for the interaction of units in the event of certain signs, options for behavior depending on the degree of effectiveness of the measures applied. Implementation of the proposed banks in practice measures to reduce bad debts will be the subject of our further study.

ASSESSMENT OF THE BORROWER'S CREDIT CAPACITY OF THE COMMERCIAL BANK: DIRECTIONS FOR IMPROVING THE QUALITY OF INFORMATION AND ANALYTICAL SUPPORT

The article is devoted to the study of theoretical and methodological bases and the development of practical recommendations for assessing the creditworthiness of a borrower of a commercial bank. The subject of the study is a set of theoretical, methodological and practical aspects to improve the quality of information and analytical support for assessing the creditworthiness of commercial bank borrowers. The purpose of the article is to develop theoretical and methodological provisions and substantiate practical recommendations for assessing the creditworthiness of the borrower. Objectives: to analyze the actual indicators of development of the banking system of Ukraine, including the scale of credit operations of commercial banks; to study and systematize the conceptual apparatus for assessing the creditworthiness of borrowers; on the basis of regulatory legal regulation to establish an algorithm for determining the value of the default factor of the borrower-legal entity; to develop measures to improve methodological approaches to assessing the creditworthiness of commercial bank borrowers. During the research the following methods were used: abstract-logical analysis, theoretical generalization, system and statistical analysis, graphical method. According to the results of the study, the dynamics of assets and loans of domestic banks for the period 2015-2020 was analyzed. and credit operations of domestic banks for the period 2017-2020. Theoretical and methodological approaches to assessing the creditworthiness of borrowers are summarized. Measures have been developed to form a scientifically sound methodological approach to assessing the creditworthiness of commercial bank borrowers. Conclusions: proposed measures to improve the methodological support for assessing the creditworthiness of commercial banks, to improve the quality of credit operations, minimize the likelihood of risks and threats, and thus contribute to the stability of development and a high level of financial and economic security of commercial banks.

The tasks of the analytical support of management and their implementation

The article is devoted to the actual and less studied problem of realization of the management decision-making analytical support tasks. It is grounded that full or partial uncertainty of the environment in which the enterprise operates determines the clearly structured regulations formation that maximize the information support volume and quality. It is noted that the analytical support task at tactical and strategic management levels is different. On the basis of application of scientific research common scholarly and special methods, the coordination of analytical support tasks of their realization decision-making and consequences in activity-based management was carried out. The comparison of the effective and efficient enterprise management essence has been carried out. It is determined that effective management is the integration of functional and infrastructural components to achieve the long-term enterprise goals. The comparative analysis of traditional tasks of effective management economic analysis and analytical support was carried out. It has been substantiated that the analytical support tasks must necessarily be coordinated with the format of the management solution support system and the management type. A strong correlation between effective management and accounting and analytical support has been established. The influence of tactical and strategic decisions information support by the level of materiality on the reasons of low-quality management has been identified. The model of managerial decisions acceptance and realization in the activity-based management system is reviewed and supplemented. It is offered to allocate two groups of management performance assessment indices-indicators. The first indices-indicators group includes indices of dynamics of assets, capital, liabilities, incomes, expenses, financial results, cash flows. The second group includes indices characterizing the decision-making system as a whole.

FORECASTING THE BEHAVIOR OF EXCHANGE FUTURES MARKET OF AGRICULTURAL PRODUCTS

Introduction. This article presents the analysis of the methodology for forecasting the behavior of the market based on the analysis of the market for financial contracts, giving the opportunity to see the basic idea of the forecast methodology of the market in the process of calculating the forecast values of the market behavior prognosis. The purpose of the article is to study the risks and forecasts for the behavior of the exchange futures market for agricultural products. Results. It is evident that the methodology for forecasting the behavior of the market based on analyzing the standard of futures contracts for wheat has been gradually receiving new information and until the end of the period reflects the main trends. The behavior of a particular point is also analyzed, but when the horizontal trend of the coordinate of a particular point is the same, when moving to the input trend, the coordinates of a particular point are seen from a particular point and the trend towards a particular coordinate is shown in line with the horizontal trend, and the difference between the coordinates and the real values of the price is positive. Carrying out a test of the other methods for forecasting economic indicators with the help of the advancement of the additional Brown model and the A-Y-model, implemented in the package of engineering projects of MatLаb, helps define the contract price. That is, when forecasting the dynamics of the markets of futures contracts, as a rule, the dynamics of the forecasting methods will change dramatically. Further, the urgency of the problem of investment and forecasting of market tends is not only due to the interests of private or corporate investors. Adequate information about the development of the market is necessary for securing the needs of the state administration bodies. Conclusions. The comparison of different methods of forecasting economic indicators with the proposed approach was made. It is highlighted that a Brown model and a standard neural network, implemented in the MatLab engineering calculation package specifically for forecasting asset dynamics, were chosen for this study. Keywords: futures, futures market, agricultural products, forecasting, risks, exchange, stock market.

Factors of the Russian ruble exchange rate dynamics in the 2000s and 2010s

The article discusses the key factors of the ruble exchange rate dynamics, analyzes the features of Russian currency market in the context of inflation targeting and the application of the budget rule. The basic theoretical approaches to modeling the dynamics of real and nominal exchange rates are presented, including behavioral models of the exchange rate, the monetary model of the exchange rate, and the hypothesis of uncovered interest parity. The most important factors of long-term and short-term dynamics of the exchange rate are revealed. The results of an econometric evaluation of the models of the real and nominal ruble exchange rates using dynamic least squares method (DOLS) are presented. It is shown that the key factors shaping the dynamics of the nominal ruble exchange rate are the terms of trade, the interest rate spread, the VIX volatility index, and the operations of the Russian Ministry of Finance under the budget rule. The long-term trajectory of the real exchange rate is formed by the terms of trade conditions, the Balassa—Samuelson effect, the dynamics of net foreign assets of the private sector.

The surprising robustness of dynamic Mean-Variance portfolio optimization to model misspecification errors

In single-period portfolio optimization settings, Mean-Variance (MV) optimization can result in notoriously unstable asset allocations due to small changes in the underlying asset parameters. This has resulted in the widespread questioning of whether and how MV optimization should be implemented in practice, and has also resulted in a number of alternatives being proposed to the MV objective for asset allocation purposes. In contrast, in dynamic or multi-period MV portfolio optimization settings, preliminary numerical results show that MV investment outcomes can be remarkably robust to model misspecification errors, which arise when the investor derives an optimal investment strategy based on some chosen model for the underlying asset dynamics (the investor model), but implements this strategy in a market driven by potentially completely different dynamics (the true model). In this paper, we systematically investigate the causes of this surprising robustness of dynamic MV portfolio optimization to model misspecification errors under both the pre-commitment MV (PCMV) and time-consistent MV (TCMV) approaches. We identify particular combinations of parameters that play a key role in explaining the observed model misspecification errors. We investigate the impact of the chosen dynamic MV approach, underlying model formulation, portfolio rebalancing frequency and the application of multiple realistic investment constraints on the robustness of investment outcomes, as well as the implications for model calibration.

Pricing vulnerable options in a hybrid credit risk model driven by Heston–Nandi GARCH processes

This paper proposes a hybrid credit risk model, in closed form, to price vulnerable options with stochastic volatility. The distinctive features of the model are threefold. First, both the underlying and the option issuer’s assets follow the Heston–Nandi GARCH model with their conditional variance being readily estimated and implemented solely on the basis of the observable prices in the market. Second, the model incorporates both idiosyncratic and systematic risks into the asset dynamics of the underlying and the option issuer, as well as the intensity process. Finally, the explicit pricing formula of vulnerable options enables us to undertake the comparative statistics analysis.

Fundamental analysis: the essence and necessity of application in portfolio investment (on the example of the Russian companies)

Fundamental analysis is the interpretation, assessment and forecast of analytical indicators at the macro- and micro-levels and expectations of market participants which can directly or indirectly affect the price dynamics of financial assets. To develop a mathematical apparatus for solving the problem of classifying sets, it is necessary to consider the formal solution of the problem. This statement immediately shows the main issue - the lack of solutions for constructing classifiers for the problem of classifying sets. The solution to the problem of investment analysis is expressed in the search for the overall best structure for all objects specified as sets available in the database. The main purpose of using the additional investment Toolkit is to try to reconcile the results of comparative analysis by applying NPV and IRR Methods, more precisely, to link the latter to the former, since this approach gives priority to the net reported income of the project. The economic value of this research method lies in the ability to predict the ratio of NPV and IRR in the future with high accuracy, based on the data entered into the model.

Trading-flow assisted estimation of the jump activity index

Existing estimators for the jump activity index only made use of the price dynamics of assets. In this study, we incorporate trading information and propose a trading-ow-adjusted (TA) estimator for the jump activity index for pure-jump Ito semimartingales observed at high frequencies. We derive the central limit theorem of the estimator and perform simulation studies that justify the theory. The new estimator is shown to be more efficient in terms of the convergence rate as compared with the existing estimators, which use only the price information under some realistic conditions. Empirical analysis shows estimates with lower standard errors than those that do not incorporate the trading information.

Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models

Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with jumps. The method combines continuous-time Markov chain approximation, with Fourier pricing techniques. In particular, our method encompasses Heston, Hull-White, Stein-Stein, 3/2 model as well as recently proposed Jacobi, $$\alpha $$ -Hypergeometric, and 4/2 models, for virtually any type of jump amplitude distribution in the return process. This framework thus provides a ‘unified’ approach to pricing Asian options in stochastic jump diffusion models and is readily extended to alternative exotic contracts. We also derive a characteristic function recursion by generalizing the Carverhill-Clewlow factorization which enables the application of transform methods in general. Numerical results are provided to illustrate the effectiveness of the method. Various extensions of this method have since been developed, including the pricing of barrier, American, and realized variance derivatives.

Black-Scholes Theory and Diffusion Processes on the Cotangent Bundle of the Affine Group.

The Black-Scholes partial differential equation (PDE) from mathematical finance has been analysed extensively and it is well known that the equation can be reduced to a heat equation on Euclidean space by a logarithmic transformation of variables. However, an alternative interpretation is proposed in this paper by reframing the PDE as evolving on a Lie group. This equation can be transformed into a diffusion process and solved using mean and covariance propagation techniques developed previously in the context of solving Fokker–Planck equations on Lie groups. An extension of the Black-Scholes theory with coupled asset dynamics produces a diffusion equation on the affine group, which is not a unimodular group. In this paper, we show that the cotangent bundle of a Lie group endowed with a semidirect product group operation, constructed in this paper for the case of groups with trivial centers, is always unimodular and considering PDEs as diffusion processes on the unimodular cotangent bundle group allows a direct application of previously developed mean and covariance propagation techniques, thereby offering an alternative means of solution of the PDEs. Ultimately these results, provided here in the context of PDEs in mathematical finance may be applied to PDEs arising in a variety of different fields and inform new methods of solution.

Efficient Asian Option Pricing Under Regime Switching Jump Diffusions and Stochastic Volatility Models

Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with jumps. The method combines Continuous-Time Markov Chain (CTMC) approximation, with Fourier pricing techniques. In particular, our method encompasses Heston, Hull-White, Stein-Stein, 3/2 model as well as recently proposed Jacobi, alpha-Hypergeometric, and 4/2 models, for virtually any type of jump amplitude distribution in the return process. This framework thus provides a unified approach to pricing Asian options in stochastic jump diffusion models and is readily extended to alternative exotic contracts. We also derive a characteristic function recursion by generalizing the Carverhill-Clewlow factorization which enables the application of transform methods in general. Numerical results are provided to illustrate the effectiveness of the method. Various extensions of this method have since been developed, including the pricing of barrier, American, and realized variance derivatives.

On solutions of a partial integro-differential equation in Bessel potential spaces with applications in option pricing models

In this paper we focus on qualitative properties of solutions to a nonlocal nonlinear partial integro-differential equation (PIDE). Using the theory of abstract semilinear parabolic equations we prove existence and uniqueness of a solution in the scale of Bessel potential spaces. Our aim is to generalize known existence results for a wide class of Levy measures including with a strong singular kernel. As an application we consider a class of PIDEs arising in the financial mathematics. The classical linear Black–Scholes model relies on several restrictive assumptions such as liquidity and completeness of the market. Relaxing the complete market hypothesis and assuming a Levy stochastic process dynamics for the underlying stock price process we obtain a model for pricing options by means of a PIDE. We investigate a model for pricing call and put options on underlying assets following a Levy stochastic process with jumps. We prove existence and uniqueness of solutions to the penalized PIDE representing approximation of the linear complementarity problem arising in pricing American style of options under Levy stochastic processes. We also present numerical results and comparison of option prices for various Levy stochastic processes modelling underlying asset dynamics.

A new remote-sensing-based indicator for integrating quantity and quality attributes to assess the dynamics of ecosystem assets

Ecological benefits provided by ecosystem assets play an important role in improving human wellbeing. However, there are few feasible methods to combine data on the quantity and quality of ecosystem assets to describe their state and trend. Here, we developed a new remote-sensing-based indicator by synthesizing ecosystem asset quantity and quality data for effective assessment at a regional or national scale. The new indicator includes a typological ecosystem asset index (TEAI) (e.g., forest ecosystem asset index) and an integrated ecosystem asset index (IEAI). The TEAI and IEAI can be used to assess the state and trend of a specific ecosystem or set of regional ecosystems, respectively. We applied the new indicator in the context of ecological protection policy in the Three-Rivers Source Region (TRSR), a region known as the ‘Chinese water tower’. From 2000 to 2015, the IEAI increased by 4.02% due to an increase in the ecosystem asset area (0.2%) and the ecosystem asset quality (0.66% and 0.02% increases in excellent and good level ecosystem assets, respectively). The implementation of ecological protection and ecological restoration programs was the main direct driver of regional ecological asset improvement. Our results suggest the new indicator is feasible for quickly and accurately evaluating the state and trend of ecosystem assets and can be used to guide ecosystem management at a large regional scale.

Methods of simulation mathematical modeling of the Russian derivatives market in modern times

Introduction. The paper is devoted to simulation modeling. Basic methods of the simulation mathematical modeling in the derivatives market are described. A group of realistic nonGaussian Levy processes that generalize the classical BlackScholes model is considered. The work objective is to study the most efficient methods of market forecasting, as well as the software implementation of the simulation mathematical modeling technique of the Russian derivatives market based on the Levy model. This research is relevant due to the demand for applications that simulate the dynamics of financial assets and evaluate options in realistic models of the derivatives market, allowing for jumps.Materials and Methods. Basic methods for forecasting the derivatives market, methods for determining the volatility rate at a known option price, are considered. The most effective types of Levy processes for the simulation mathematical modeling of the Russian derivatives market at the present stage are highlighted. The possibilities of the Java language for the implementation of mathematical methods are considered.Research Results. A program is developed in the Java programming language that implements the Levy mathematical model, which includes Gaussian and generalized Poisson processes. The program for calculating the mathematical method is created in the free integrated application development environment NetBeans IDE to work with any operating system.Discussion and Conclusions. The result of the simulation mathematical modeling analysis has shown that the most efficient methods in the derivatives market are those based on realistic non-Gaussian Levy processes. The software implementation of such mathematical methods can be used for educational purposes. The developed application has demonstrated high quality and speed of calculations using software resources.

Say anything you want about me if you spell my name right: the effect of Internet searches on financial market

In this paper, we focus on the influence of attention from investors on the dynamics of different financial assets. Investor attention is measured by the number of Google searches for three types of assets: stocks, gold and cryptocurrencies. We analyse the daily price of: the Standard & Poor’s 500 (S&P 500), the Russell 2000 Index (RUT), Bitcoin and the gold spot price in USD. The study covers a period of 5 years: 2013–2018. According to the results, the prices of different assets react differently to changes in the level of investor attention (and vice versa), and this relationship changes over time. Bitcoin seems to be the most sensitive to the changes in investor attention and changes in its dynamics appear to influence investor attention the most. Changes in the volatility and trade volume of stocks occur simultaneously with changes in investor interest. However, during periods of increased stock volatility, we can observe increased investor interest in gold over any other asset. The price of gold itself has proven itself to be most immune to changes in investor attention.

Ukrainian insurance market: current state and development prospects

The paper is devoted to the investigation of the current state and trends of the insurance market in Ukraine. A number of indicators characterizing the state of insurance market development, such as: the number of insurance companies engaged in risky types of insurance and life insurance; volume and dynamics of gross insurance bonuses and insurance payments; dynamics of the number of concluded agreements on voluntary and compulsory types of insurance, as well as reinsurance agreements; volume and dynamics of assets and insurance reserves of domestic insurance companies are analyzed in this scientific paper. Comparative analysis of the above mentioned indicators with similar indicators of foreign countries is carried out. It is defined that the insurance market of Ukraine lags far behind the countries of Europe, the USA, China, Japan and other developed countries. The reason for such low development is the difficult economic situation in the country caused by such factors as the change of power in 2015, the occupation of part of the territory by the Russian Federation, which shattered the previously unstable economy. Although the economic situation in the country has stabilized in recent years, this is not enough for the insurance market to reach the level of developed economies. The investigation results are presented in the form of tables and graphical interpretations. The factors of positive and negative influence on the development of domestic insurance market are determined and characterized. The main factor influencing the insurance market and ensuring its stability is the control of measures increasing the level of the population insurance culture and the reliability of insurance companies. Such measures will increase the demand for insurance services, insurers will be interested in doing their best and these factors will result in financial market stabilization. This effect will be achieved if the state and insurance companies act in coordinated manner, i.e. if the state provides the insurance market with regulatory framework with unobtrusive supervision, and insurers perform their work honestly and conscientiously. A number of recommendations for the development of domestic insurance companies and the market in general are developed. The main measures are to attract capital not only from European countries, making the insurance market more attractive, but to develop the health insurance, as medicine is quite expensive and the income is low, as well as to introduce the new insurance products due to the development of all industries.

INTANGIBLE ASSETS AND ADDED VALUE OF INDUSTRIAL COMPANIES

Investments in intangible assets are an important factor for improving performance of industrial companies, including increase in their added value. In a time of economic transformation, when national strategy is oriented towards creating a value-added economy in Bulgaria, every sectoral and corporate research in this field is relevant and significant. This report analyzes the dynamics of intangible assets and their structural share in non-current assets of industrial companies over the period 2007–2018. It also examines level and dynamics of added value created by these companies and relationship between her and intangible assets. On this basis, there are opportunities to improve the investment strategy of industrial companies.

Equilibrium investment and risk control for an insurer with non-Markovian regime-switching and no-shorting constraints

In this paper, we study the time-consistent equilibrium investment and risk control policies for an insurer under the mean-variance criterion. The dynamics of liability and assets are given by non-Markovian regime-switching models driven by a Brownian motion and a continuous time finite-state Markov chain. It is assumed that the insurer has a time-varying preference of risk depending dynamically on current wealth, and is not allowed to short sell the risky assets. With the aid of backward stochastic differential equations and bounded mean oscillation martingales, we obtain feedback representations of the open-loop equilibrium strategies. Finally, the result is also applied to solve an example of the Markovian regime-switching model.