Search results for: real options

Authors: I. Inthanongsone, C. Drebenstedt, J. C. Bongaerts, P. Sontamino

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The major concern in evaluating the value of mining projects related to the deficiency of the traditional discounted cash flow (DCF) method. This method does not take uncertainties into account and, hence it does not allow for an economic assessment of managerial flexibility and operational adaptability, which are increasingly determining long-term corporate success. Such an assessment can be performed with the real options valuation (ROV) approach, since it allows for a comparative evaluation of unforeseen uncertainties in a project life cycle. This paper presents an economic evaluation model for open pit mining projects based on real options valuation approach. Uncertainties in the model are caused by metal prices and cost uncertainties and the system dynamics (SD) modeling method is used to structure and solve the real options model. The model is applied to a case study. It can be shown that that managerial flexibility reacting to uncertainties may create additional value to a mining project in comparison to the outcomes of a DCF method. One important insight for management dealing with uncertainty is seen in choosing the optimal time to exercise strategic options.

Keywords: DCF methods, ROV approach, system dynamics modeling methods, uncertainty

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Authors: Luke Miller

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This paper develops an options pricing methodology to value strategic pricing strategies in the services sector. More specifically, this study provides a unifying taxonomy of current service sector pricing practices, frames these pricing decisions as strategic real options, demonstrates accepted option valuation techniques to assess service sector pricing decisions, and suggests future research areas where pricing decisions and real options overlap. Enhancing revenue in the service sector requires proactive decision making in a world of uncertainty. In an effort to strategically price service products, revenue enhancement necessitates a careful study of the service costs, customer base, competition, legalities, and shared economies with the market. Pricing decisions involve the quality of inputs, manpower, and best practices to maintain superior service. These decisions further hinge on identifying relevant pricing strategies and understanding how these strategies impact a firm’s value. A relatively new area of research applies option pricing theory to investments in real assets and is commonly known as real options. The real options approach is based on the premise that many corporate decisions to invest or divest in assets are simply an option wherein the firm has the right to make an investment without any obligation to act. The decision maker, therefore, has more flexibility and the value of this operating flexibility should be taken into consideration. The real options framework has already been applied to numerous areas including manufacturing, inventory, natural resources, research and development, strategic decisions, technology, and stock valuation. Additionally, numerous surveys have identified a growing need for the real options decision framework within all areas of corporate decision-making. Despite the wide applicability of real options, no study has been carried out linking service sector pricing decisions and real options. This is surprising given the service sector comprises 80% of the US employment and Gross Domestic Product (GDP). Identifying real options as a practical tool to value different service sector pricing strategies is believed to have a significant impact on firm decisions. This paper identifies and discusses four distinct pricing strategies available to the service sector from an options’ perspective: (1) Cost-based profit margin, (2) Increased customer base, (3) Platform pricing, and (4) Buffet pricing. Within each strategy lie several pricing tactics available to the service firm. These tactics can be viewed as options the decision maker has to best manage a strategic position in the market. To demonstrate the effectiveness of including flexibility in the pricing decision, a series of pricing strategies were developed and valued using a real options binomial lattice structure. The options pricing approach discussed in this study allows service firms to directly incorporate market-driven perspectives into the decision process and thus synchronizing service operations with organizational economic goals.

Keywords: option pricing theory, real options, service sector, valuation

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Authors: B. F. Nteumagne, E. Pindza, E. Mare

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We apply Lie symmetries analysis to price and hedge options in the fractional Brownian framework. The reputation of Lie groups is well spread in the area of Mathematical sciences and lately, in Finance. In the presence of transactions costs and under fractional Brownian motions, analytical solutions become difficult to obtain. Lie symmetries analysis allows us to simplify the problem and obtain new analytical solution. In this paper, we investigate the use of symmetries to reduce the partial differential equation obtained and obtain the analytical solution. We then proposed a hedging procedure and calibration technique for these types of options, and test the model on real market data. We show the robustness of our methodology by its application to the pricing of digital options.

Keywords: fractional brownian model, symmetry, transaction cost, option pricing

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Authors: Miroslav Čulík, Petr Gurný

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This paper is aimed at the financial assessment of the hard coal mining in a given region by real option methodology application. Hard coal mining in this mine makes net loss for the owner during the last years due to the long-term unfavourable mining conditions and significant drop in the coal prices during the last years. Management is going to shut down the operation and abandon the project to reduce the loss of the company. The goal is to assess whether the shutting down the operation is the only and correct solution of the problem. Due to the uncertainty in the future hard coal price evolution, the production might be again restarted if the price raises enough to cover the cost of the production. For the assessment, real option methodology is applied, which captures two important aspect of the financial decision-making: risk and flexibility. The paper is structured as follows: first, current state is described and problem is analysed. Next, methodology of real options is described. At last, project is evaluated by applying real option methodology. The results are commented and recommendations are provided.

Keywords: real option, investment, option to abandon, option to shut down and restart, risk, flexibility

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Authors: Cameron Truong, Mikhail Bhatia, Yangyang Chen, Viet Nga Cao

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Using a sample of U.S. firms between 1996 and 2011, this paper documents a positive association between options trading volume and future stock price crash risk. This relation is evidently more pronounced among firms with higher information asymmetry, business uncertainty, and short-sale constraints. In a dichotomous cross-sectional setting, we also document that firms with options trading have higher future crash risk than firms without options trading. We further show in a difference-in-difference analysis that firms experience an increase in crash risk immediately after the listing of options. The results suggest that options traders are able of identifying bad news hoarding by management and choose to trade in a liquid options market in anticipation of future crashes.

Keywords: bad news hoarding, cross-sectional setting, options trading, stock price crash

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Authors: Marasovic Branka, Aljinovic Zdravka, Poklepovic Tea

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Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?

Keywords: Bjerksund and Stensland approximations, computational analysis, finance, options pricing, numerical methods

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Authors: Svetlana Pushkar

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Eco-indicator 99 (EI99) considers fundamental life cycle assessment (LCA) uncertainties via egalitarian/egalitarian (e/e), hierarchist/hierarchist (h/h), individualist/individualist (i/i), individualist/average (i/a), egalitarian/average (e/a), and hierarchist/average (h/a) methodological options. The objective of this study is to provide a reliable two-stage nested mixed balanced Analysis of Variance (ANOVA) test as a supplemental test to EI99 to address the problematic combination of similarly and not similarly produced materials usually found in building technologies. The robustness of the test was determined from both the “EI99 (all options)” stage (including e/e, i/i, h/h, e/a, i/a, and h/a - all methodological options) and the “EI99 (perspectives)” stage (including e/e, i/i, and h/h methodological options of EI99 - the methodological options with their particular weighting set or e/a, i/a, and h/a methodological options of EI99 - the methodological options with the average weighting set) of evaluating building technologies.

Keywords: building technologies, LCA uncertainty, Eco-indicator 99, two-stage nested mixed ANOVA test

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Authors: Niranjan Devkota , Ram Kumar Phuya, Durga Lal Shreshta

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This paper estimates cost and benefit of adoption of climate change adaptation options available to the rural rice farmers of Nepal. Adoption of adaptation strategies, intensity of use of adaptation options, identification of labor and non-labor cost and finally per unit cost and benefit analysis of climate change adaptation were made. Multi-stage sampling technique was used to source respondents for the study and used structured questionnaire techniques to collect data from 773 households from seven districts; 3 from Terai and 4 from Hilly region of Nepal. The result revealed that there are 13 major adaptation options rice farmers practice in order to protect themselves from climatic risk. Among the given adaptation options, the first three popular adaptation options practiced by rice farmers are (i) increasing use of chemical fertilizer (60.93%) (ii) use of climate smart verities (49.29%) and (iii) change in nursery date (32.08%). Adaptation cost is obvious, based on that, the first three costly adaptation options are the alternative irrigation practice which incurred average cost of US $69.95 (US$ 1 = 102.84 Nepalese Rupees) followed by a denser plantation of local seeds ($ 20.69) and using climate smart varieties ($ 18.06). 88% farmers practiced more than one adaptation strategies on the same farm with the aim of reducing the effect of extreme climatic conditions. Total cost and revenue revealed that per unit total cost ranges from $28.34 to $32.79 whereas per unit total revenue ranges $33.4 to $49.02. Surprisingly, it is observed that farmers who do not adopt any adaptation options are able to receive highest income from per unit production. As Net Present Value (NPV) is positive and Benefit Cost Ration (BCR) is greater than one for every adaptation options that indicates the available adaptation options are profitable to the rice farmers.

Keywords: climate change, adaptation options, cost benefit analysis, rural rice farmers, Nepal

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Authors: Norm Josephy, Lucy Kimball, Victoria Steblovskaya

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Hedging of a portfolio of European options under proportional transaction costs is considered. Our discrete time financial market model extends the binomial market model with transaction costs to the case where the underlying stock price ratios are distributed over a bounded interval rather than over a two-point set. An optimal hedging strategy is chosen from a set of admissible non-self-financing hedging strategies. Our approach to optimal hedging of a portfolio of options is based on theoretical foundation that includes determination of a no-arbitrage option price interval as well as on properties of the non-self-financing strategies and their residuals. A computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies is developed. Applicability of our approach is demonstrated using both simulated data and real market data.

Keywords: extended binomial model, non-self-financing hedging, optimization, proportional transaction costs

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Authors: Mohammad Saber Rohi, Saghar Heidari

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In this paper, we studied the pricing problem of American options under a regime-switching model with the possibility of a non-optimal exercise policy (early or late exercise time) which is called an irrational strategy. For this, we consider a Markovmodulated model for the dynamic of the underlying asset as an alternative model to the classical Balck-Scholes-Merton model (BSM) and an intensity-based model for the irrational strategy, to provide more realistic results for American option prices under the irrational behavior in real financial markets. Applying a partial differential equation (PDE) approach, the pricing problem of American options under regime-switching models can be formulated as coupled PDEs. To solve the resulting systems of PDEs in this model, we apply a finite element method as the numerical solving procedure to the resulting variational inequality. Under some appropriate assumptions, we establish the stability of the method and compare its accuracy to some recent works to illustrate the suitability of the proposed model and the accuracy of the applied numerical method for the pricing problem of American options under the regime-switching model with irrational behaviors.

Keywords: irrational exercise strategy, rationality parameter, regime-switching model, American option, finite element method, variational inequality

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Authors: Guillaume Leduc

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In this paper, we describe a broad setting under which the error of the approximation can be quantified, controlled, and for which convergence occurs at a speed of n⁻¹ for European and American options. We describe how knowledge of the error allows for arbitrarily fast acceleration of the convergence.

Keywords: random walk approximation, European and American options, rate of convergence, option pricing

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Authors: Chantouch Wannathanom

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Research The study of elders’ needs in Bangkok metropolis for the options of health tourism. The objective is to study of elders’ needs in Bangkok Metropolis for the options of health tourism. The research her collected data using a questionnaire. The samples used in this research is elderly people living in the Dusit area. Of 400 people found the majority were female than male. Accounted for18 percent aged between 50-55 years, mostly undergraduate degree. Moreover, most seniors do not have underlying disease. The study found that 1. Elders’ needs in Bangkok Metropolis for the options of health tourism; 2. Tourism activity patterns that fit elderly was divided into 5 categories, including massage, massage, and herbal sauna. Practicing meditation and ascetic. The results showed that selection of elderly tourist activities by choosing healthy eating are the first. The hypothesis testing period: Elders’ needs in Bangkok Metropolis for the options of health tourism is different. The level of statistical significance .05 level.

Keywords: needs, elder, health tourism, Bangkok

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Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

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Concurrent planning of the resource constraint project scheduling and material ordering problems have received significant attention within the last decades. Hence, the issue has been investigated here with the aim to minimize total project costs. Furthermore, the presented model considers different discount options in order to approach the real world conditions. The incorporated alternatives consist of all-unit and incremental discount strategies. On the other hand, a modified version of the genetic algorithm is applied in order to solve the model for larger sizes, in particular. Finally, the applicability and efficiency of the given model is tested by different numerical instances.

Keywords: genetic algorithm, material ordering, project management, project scheduling

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Authors: Mimi Hafizah Abdullah, Hanani Farhah Harun, Nik Ruzni Nik Idris

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With the implied volatility as an important factor in financial decision-making, in particular in option pricing valuation, and also the given fact that the pricing biases of Leland option pricing models and the implied volatility structure for the options are related, this study considers examining the implied adjusted volatility smile patterns and term structures in the S&P/ASX 200 index options using the different Leland option pricing models. The examination of the implied adjusted volatility smiles and term structures in the Australian index options market covers the global financial crisis in the mid-2007. The implied adjusted volatility was found to escalate approximately triple the rate prior the crisis.

Keywords: implied adjusted volatility, financial crisis, Leland option pricing models, Australian index options

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Authors: Philemon Rakoto

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This paper tests the improvement of financial reporting quality when firms award stock options to their executives. The originality of this study is that we introduce the moderating effect of business ethics in the model. The sample is made up of 116 Canadian high-technology firms with available data for the fiscal year ending in 2012. We define the quality of financial reporting as the value relevance of accounting information as developed by Ohlson. Our results show that executive stock option award alone does not improve the quality of financial reporting. Rather, the quality improves when a firm awards stock options to its executives and investors perceive that the level of business ethics in that firm is high.

Keywords: business ethics, Canada, high-tech firms, stock options, value relevance

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Authors: Mohsen Akhlaghi, Tahereh Ebrahimi

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Considering the increasing demand for water and limited resources, there is a possibility of a water crisis in the not-so-distant future. Therefore, to prevent this crisis, other options for drinking water supply should be examined. In this regard, the application of multi-criteria decision-making methods in various aspects of water resource management and planning has always been of great interest to researchers. In this report, six options for supplying drinking water to Tehran City were considered. Then, experts' opinions were collected through matrices and questionnaires, and using the TOPSIS method, which is one of the types of multi-criteria decision-making methods, they were calculated and analyzed. In the TOPSIS method, the options were ranked by calculating their proximity to the ideal (Ci). The closer the numerical value of Ci is to one, the more desirable the option is. Based on this, the option with the optimization pattern of water consumption, with Ci = 0.9787, is the best option among the proposed options for supplying drinking water to Tehran City. The other options, in order of priority, are rainwater harvesting, wastewater reuse, increasing current water supply sources, desalination and its transfer, and transferring water from freshwater sources between basins. In conclusion, the findings of this study highlight the importance of exploring alternative drinking water supply options and utilizing multi-criteria decision-making approaches to address the potential water crisis.

Keywords: multi-criteria decision, sustainable development, topsis, water supply

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Authors: Mojtaba Hakimi-Moghaddam

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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions

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Authors: John Kong Shan Ho

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In June 2022, the Law Commission of England and Wales published an options paper to examine how the law on corporate criminal liability can be reformed under the English system. The paper merely details options for reform and does not seek to make recommendations. However, the paper has ruled out the “respondeat superior” approach of the US and “corporate culture” approach of Australia as reform options. On balance, the preferred reform option of the Law Commission is the “senior officer” approach as currently adopted in Canada. This article is written against such background and argues that due to similarities between the English and Canadian systems, the latter’s approach is more ideal to be adopted by the former as a model for reform in this area.

Keywords: corporate criminal liability, identification principle, directing mind and will, England, Canada

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Authors: Suresh Reddi, Mathew Leslie, Vishnu S. Das

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Sustainable design is a prominent concept across all sectors of engineering and its importance is widely recognized within the Arabian Gulf region. Despite that sustainable or soft engineering options are not widely deployed in coastal engineering projects and a preference for utilizing ‘hard engineering’ solutions remain. The concept of soft engineering lies in “working together” with the nature to manage the coastline. This approach allows hard engineering options, such as breakwaters or sea walls, to be minimized or even eliminated altogether. Hard structures provide a firm barrier to wave energy or flooding, but in doing so they often have a significant impact on the natural processes of the coastline. This may affect the area locally or impact on neighboring zones. In addition, they often have a negative environmental impact and may create a sense of disconnect between the marine environment and local users. Soft engineering options, seek to protect the coastline by working in harmony with the natural process of sediment transport/budget. They often consider new habitat creation and creating usable spaces that will increase the sense of connection with nature. Often soft engineering options, where appropriately deployed can provide a low-maintenance, aesthetically valued, natural line of coastal protection. This paper deals with an overview of the following: The widely accepted soft engineering practices across the world; How this approach has been considered by Ramboll in some recent projects in Middle East and Asia; Challenges and barriers to use in using soft engineering options in the region; Way forward towards more widespread adoption.

Keywords: coastline, hard engineering, low maintenance, soft engineering options

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Authors: Thomas Gerstner, Bastian von Harrach, Daniel Roth

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The Monte Carlo pathwise sensitivities approach is well established for smooth payoff functions. In this work, we present a new Monte Carlo algorithm that is able to calculate the pathwise sensitivities for discontinuous payoff functions. Our main tool is the one-step survival idea of Glasserman and Staum. Although this technique yields to new terms per observation, while differentiating, the algorithm is still efficient. As an application, we use the results for a two-dimensional calibration of a Coco-Bond, which we model with different types of discretely monitored barrier options.

Keywords: Monte Carlo, discretely monitored barrier options, pathwise sensitivities, Coco-Bond

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Authors: Kanya L. Khatri, Ashfaque A. Memon, Rod J. Smith, Shamas Bilal

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The viability and sustainability of crop production is currently threatened by increasing water scarcity. Water scarcity problems can be addressed through improved water productivity and the options usually presumed in this context are efficient water use and conversion of surface irrigation to pressurized systems. By replacing furrow irrigation with drip or centre pivot systems, the water efficiency can be improved by up to 30 to 45%. However, the installation and application of pumps and pipes, and the associated fuels needed for these alternatives increase energy consumption and cause significant greenhouse gas emissions. Hence, a balance between the improvement in water use and the potential increase in energy consumption is required keeping in view adverse impact of increased carbon emissions on the environment. When surface water is used, pressurized systems increase energy consumption substantially, by between 65% to 75%, and produce greenhouse gas emissions around 1.75 times higher than that of gravity based irrigation. With gravity based surface irrigation methods the energy consumption is assumed to be negligible. This study has shown that a novel real-time infiltration model REIP has enabled implementation of real-time optimization and control of surface irrigation and surface irrigation with real-time optimization has potential to bring significant improvements in irrigation performance along with substantial water savings of 2.92 ML/ha which is almost equivalent to that given by pressurized systems. Thus real-time optimization and control offers a modern, environment friendly and water efficient system with close to zero increase in energy consumption and minimal greenhouse gas emissions.

Keywords: pressurised irrigation, carbon emissions, real-time, environmentally-friendly, REIP

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Authors: A. Chateauneuf, M. Mostoufi, D. Vyncke

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Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting, such as estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, by using the comonotonic approximation as a control variate. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options when the logreturns follow a Black-Scholes model or a variance gamma model.

Keywords: control variate Monte Carlo, comonotonicity, option pricing, scientific computing

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Authors: Linda Kauškale, Ineta Geipele

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Due to the rapidly changing external environment, portfolio management strategies became closely interconnected with real estate industry development and macroeconomic development tendencies. The aim of the research is to analyze sustainable real estate market development influencing factors, with particular focus on its economic and management aspects that influences real estate investment decisions as well. Scientific literature and article analysis, data analysis, expert evaluation, and other quantitative and qualitative research methods were used in the research. Developed real estate market sustainability model and index analysis approach can be applied by investors and real estate companies in real estate asset management and can help in risk minimization activities in international entrepreneurship. Future research directions have been identified in the research as well.

Keywords: indexes, investment decisions, real estate market, sustainability

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Authors: Jiahau Guo, Yihe Zhang

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This paper proposes solutions for pricing options on stocks paying discrete dividends in markets with daily price limits. We first extend the intraday density function of Guo and Chang (2020) to a multi-day one and use the framework of Haug et al. (2003) to value European options on stocks paying discrete dividends. Next, we adopt the fast Fourier transform (FFT) to derive accurate and efficient formulae for American options and further employ the three-point Richardson extrapolation to accelerate the computation. Finally, the accuracy of our proposed methods is verified by simulations.

Keywords: daily price limit, discrete dividend, early exercise, fast Fourier transform, multi-day density function, Richardson extrapolation

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Authors: Rong-Tsorng Wang

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In this paper, we derive a pricing formula for catastrophe equity put options (or CatEPut) with non-homogeneous loss and approximated compound distributions. We assume that the loss claims arrival process is a nonhomogeneous Poisson process (NHPP) representing the clustering occurrences of loss claims, the size of loss claims is a sequence of independent and identically distributed random variables, and the accumulated loss distribution forms a compound distribution and is approximated by a heavy-tailed distribution. A numerical example is given to calibrate parameters, and we discuss how the value of CatEPut is affected by the changes of parameters in the pricing model we provided.

Keywords: catastrophe equity put options, compound distributions, nonhomogeneous Poisson process, pricing model

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Authors: Natalia M. Acevedo, Luis M. Jimenez, Erick Lambis

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Imperfections in the capital market are used to argue the relevance of the corporate risk management function. With corporate hedge, the value of the company is increased by reducing the volatility of the expected cash flow and making it possible to face a lower bankruptcy costs and financial difficulties, without sacrificing tax advantages for debt financing. With the propose to avoid exchange rate troubles over cash flows of Colombian exporting firms, this dissertation uses financial options, over exchange rate between Peso and Dollar, for realizing a financial hedge. In this study, a strategy of hedge is designed for an exporting company in Colombia with the objective of preventing fluctuations because, if the exchange rate down, the number of Colombian pesos that obtains the company by exports, is less than agreed. The exchange rate of Colombia is measured by the TRM (Representative Market Rate), representing the number of Colombian pesos for an American dollar. First, the TMR is modelled through the Geometric Brownian Motion, with this, the project price is simulated using Montecarlo simulations and finding the mean of TRM for three, six and twelve months. For financial hedging, currency options were used. The 6-month projection was covered with financial options on European-type currency with a strike price of $ 2,780.47 for each month; this value corresponds to the last value of the historical TRM. In the compensation of the options in each month, the price paid for the premium, calculated with the Black-Scholes method for currency options, was considered. Finally, with the modeling of prices and the Monte Carlo simulation, the effect of the exchange hedging with options on the exporting company was determined, this by means of the unit price estimate to which the dollars in the scenario without coverage were changed and scenario with coverage. After using the scenarios: is determinate that the TRM will have a bull trend and the exporting firm will be affected positively because they will get more pesos for each dollar. The results show that the financial options manage to reduce the exchange risk. The expected value with coverage is approximate to the expected value without coverage, but the 5% percentile with coverage is greater than without coverage. The foregoing indicates that in the worst scenarios the exporting companies will obtain better prices for the sale of the currencies if they cover.

Keywords: currency hedging, futures, geometric Brownian motion, options

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Authors: Mojtaba Hakimi-Moghaddam

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Positive realness as the most important property of driving point impedance of passive electrical networks appears in the control systems stability theory in 1960’s. There are three important subsets of positive real (PR) systems are introduced by researchers, that is, loos-less positive real (LLPR) systems, weakly strictly positive real (WSPR) systems and strictly positive real (SPR) systems. In this paper, definitions, properties, lemmas, and theorems related to family of positive real systems are summarized. Properties in both frequency domain and state space representation of system are explained. Also, several illustrative examples are presented.

Keywords: real rational matrix transfer functions, positive realness property, strictly positive realness property, Hermitian form asymptotic property, pole-zero properties

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Authors: Parminder Kaur Heer, Alexei Lapkin

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Due to global challenges of increased competition and demand for more sustainable products/processes, there is a rising pressure on the industry to develop innovative processes. Through Process Intensification (PI) the existing and new processes may be able to attain higher efficiency. However, very few PI options are generally considered. This is because processes are typically analysed at a unit operation level, thus limiting the search space for potential process options. PI performed at more detailed levels of a process can increase the size of the search space. The different levels at which PI can be achieved is unit operations, functional and phenomena level. Physical/chemical phenomena form the lowest level of aggregation and thus, are expected to give the highest impact because all the intensification options can be described by their enhancement. The objective of the current work is thus, generation of numerous process alternatives based on phenomena, and development of their corresponding computer aided models. The methodology comprises: a) automated generation of process options, and b) automated generation of process models. The process under investigation is disintegrated into functions viz. reaction, separation etc., and these functions are further broken down into the phenomena required to perform them. E.g., separation may be performed via vapour-liquid or liquid-liquid equilibrium. A list of phenomena for the process is formed and new phenomena, which can overcome the difficulties/drawbacks of the current process or can enhance the effectiveness of the process, are added to the list. For instance, catalyst separation issue can be handled by using solid catalysts; the corresponding phenomena are identified and added. The phenomena are then combined to generate all possible combinations. However, not all combinations make sense and, hence, screening is carried out to discard the combinations that are meaningless. For example, phase change phenomena need the co-presence of the energy transfer phenomena. Feasible combinations of phenomena are then assigned to the functions they execute. A combination may accomplish a single or multiple functions, i.e. it might perform reaction or reaction with separation. The combinations are then allotted to the functions needed for the process. This creates a series of options for carrying out each function. Combination of these options for different functions in the process leads to the generation of superstructure of process options. These process options, which are formed by a list of phenomena for each function, are passed to the model generation algorithm in the form of binaries (1, 0). The algorithm gathers the active phenomena and couples them to generate the model. A series of models is generated for the functions, which are combined to get the process model. The most promising process options are then chosen subjected to a performance criterion, for example purity of product, or via a multi-objective Pareto optimisation. The methodology was applied to a two-step process and the best route was determined based on the higher product yield. The current methodology can identify, produce and evaluate process intensification options from which the optimal process can be determined. It can be applied to any chemical/biochemical process because of its generic nature.

Keywords: Phenomena, Process intensification, Process models , Process options

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Authors: Salah Alrabeei, Mohammad Yousuf

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The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, , L-stable methods, pricing European options, Jump–diffusion model

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Authors: Saghar Heidari

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In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

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