Option Model Research Articles

Дослідження відносних деформацій міжуламкового регенерату в моделях різних варіантів остеосинтезу кісток гомілки з переломами в середній третині у дітей з недосконалим остогенезом та незавершеним ростом

Introduction. Osteogenesis imperfecta is a genetic pathology that leads to a violation of the processes of formation of collagen fibers, formation of bone matrix and its mineralization and, as a result, to the formation of bone tissue with low strength properties. The most promising means of stabilizing bone fragments under this condition are intramedullary fixators of various designs. Aim. To investigate the relative deformations of the interfragmentary regenerate under the influence of various types of loads in models of the tibia with fractures of both bones in the middle third and their osteosynthesis using intramedullary rods of various designs in children with osteogenesis imperfecta and incomplete growth. Materials and methods. Mathematical modeling of options for osteosynthesis of tibia bones with a fracture in the middle third in children with osteogenesis imperfecta was performed. Two variants for tibial osteosynthesis were modelled: a rod without rotational stability; rod with rotational stability. Osteosynthesis of the fibula was not modelled in all variants. The stress-strain state of the model under the influence of vertical compressive, bending and torsional loads, as well as the magnitude of the relative deformations of the interstitial regenerate, were studied. The results. A “growing” intramedullary shear with rotational stability provides essential advantages in the case of torsional loads. The presence of rotational stability makes it possible to ensure two times lower values of relative deformations of interfragmentary regenerates compared to osteosynthesis with a rotationally unstable rod. Under compressive and bending loads, both rods showed almost identical results of relative deformations of bone regenerates. High rates of deformation of interfragmentary tibial regenerates are due to the lack of longitudinal axial stability of both rods, which is the basis for the possibility of increasing their length during the growth of the patient. Conclusions. The use of osteosynthesis with intramedullary rods, which increase during the treatment of tibial fractures in patients with osteogenesis imperfecta, does not ensure a sufficient level of stability for the fixation of bone fragments under compression and bending loads, which leads to the greatest deformations of bone regenerates. A rod with rotational stability provides advantages in resistance to torsional loads, which is determined by twice lower relative deformations of interfragmentary regenerates. No conflict of interests was declared by the authors.

Reward-Respecting Subtasks for Model-Based Reinforcement Learning (Abstract Reprint)

To achieve the ambitious goals of artificial intelligence, reinforcement learning must include planning with a model of the world that is abstract in state and time. Deep learning has made progress with state abstraction, but temporal abstraction has rarely been used, despite extensively developed theory based on the options framework. One reason for this is that the space of possible options is immense, and the methods previously proposed for option discovery do not take into account how the option models will be used in planning. Options are typically discovered by posing subsidiary tasks, such as reaching a bottleneck state or maximizing the cumulative sum of a sensory signal other than reward. Each subtask is solved to produce an option, and then a model of the option is learned and made available to the planning process. In most previous work, the subtasks ignore the reward on the original problem, whereas we propose subtasks that use the original reward plus a bonus based on a feature of the state at the time the option terminates. We show that option models obtained from such reward-respecting subtasks are much more likely to be useful in planning than eigenoptions, shortest path options based on bottleneck states, or reward-respecting options generated by the option-critic. Reward respecting subtasks strongly constrain the space of options and thereby also provide a partial solution to the problem of option discovery. Finally, we show how values, policies, options, and models can all be learned online and off-policy using standard algorithms and general value functions.

Optimum investment strategy for hydrogen-based steelmaking project coupled with multiple uncertainties

The large-scale application of hydrogen steelmaking technology is expected to substantially accelerate the decarbonization process of the iron and steel industry. However, hydrogen steelmaking projects are still in the experimental or demonstration stage, and scientific investment decision-making methods are urgently needed to support the large-scale development of the technology. When assessing the investment value, existing studies usually only consider the intrinsic project value under a specific pathway, while ignoring the option value under realistic multiple uncertainties in terms of technology, market, and policy, leading to an underestimation of the investment value. To address this issue, this study constructs a real options model to explore the optimal investment timing and revenue of the hydrogen steelmaking project, by taking into account multi-dimensional uncertainties stemming from price fluctuations in the steel market, the development of the carbon market, and technological advances. Additionally, the impacts of various subsidy policies on the investment strategy are also investigated. Least Squares Monte Carlo method is applied to overcome computational challenges posed by dynamic programming under multi-dimensional uncertainties. The results show that: (i) Investment is not recommended based on current crude steel price and hydrogen price. (ii) When the annual reduction rate of hydrogen price reaches 5%, the optimal investment timing would advance to 2036. (iii) On this basis, with the introduction of a 20% green hydrogen subsidy policy, the optimal investment timing would be further brought forward to 2033. The implementation of tax incentives would significantly increase the investment value. The investment value would surge from 170 million CNY to 262 million CNY as the tax rate decreases from 20% to zero. The findings could provide reasonable suggestions for investment decisions under realistic volatile environments, as well as scientific references for policy design, thus facilitating the large-scale and high-level development of hydrogen-based steelmaking technology.

Application of the Black–Scholes Financial Model to Support Adaptability as a Sustainability Strategy for Buildings: A Case Study of an Adaptable Campus Parking Garage

In many construction projects, a “green premium” must be paid to implement sustainable designs that reduce environmental costs. Design for Adaptability (DfA) is a sustainable design philosophy that facilitates incremental renewal and infrastructure adaptation, thereby delaying future demolition and reconstruction. This paper focuses on the potential economic benefits of DfA. Notably, the paper contributes to answering the following question: is the green premium paid for an adaptable design justified by the potential long-term economic benefits? A modified version of the Black–Scholes financial options model is developed and demonstrated to address this question. A hypothetical case study of a parking garage is explored. This case study compares traditional and adaptable three-level parking garages and their potential expansion to a five-level garage at a future time. The “real option value” (i.e., the economic benefit of having the option to expand in the future) is calculated and compared under various assumptions and input parameters. The selection of reasonable model parameters for a given situation and the limitations of the Black–Scholes approach for valuing adaptable buildings are discussed. The model was developed for institutional (i.e., government or university) owners who consider their buildings as a cost of doing business without a direct relationship to revenue. It is concluded from the case study that the option value from the adaptable features of the parking garage exceeds the green premium given certain conditions. The payoff is most sensitive to the green premium, construction costs, and the owner’s inflation value on future additional parking. The work contributes to an economic case for DfA as a sustainability strategy for buildings.

Study of the stress-strain state in models of various options for osteosynthesis of tibial bones with diaphyseal fractures in the middle third in children with osteogenesis imperfecta and incomplete growth Part 1. Compression

Background. Osteogenesis imperfecta is accompanied by multiple fractures of skeletal bones, the development of progressive deformations of the long bones of the limbs and, as a result, the inability to stand and walk. At present, the most promising means for stabilizing bone fragments are intramedullary fixators of various designs. Installation of internal fixators without the possibility of their lengthening during the skeletal growth leads to an increase in the frequency of repeated surgical interventions due to the need for their replacement. The purpose was to investigate the stress-strain state of the lower leg models under the influence of compressive load in conditions of fracture of both bones in the middle third and their osteosynthesis using intramedullary rods of various designs in children with osteogenesis imperfecta and incomplete growth. Materials and methods. A mathematical modeling of osteosynthesis of tibial bones with a fracture in the middle third in children with osteogenesis imperfecta was performed in two options: 1 — using a rod without rotational stability; 2 — a rod with rotational stability of the structure. During the research, the stress-strain state of the model was studied under the influence of vertical compressive load. Results. Under compressive loads, the use of a rod with rotational stability does not lead to any significant changes in the stress-strain state of the model compared to tibial osteosynthesis with a rotationally unstable rod. This can be explained by the fact that before resisting the loads acting along the longitudinal axis of the rods, both rods are unstable, so all loads are carried by the bone structures. This is a “fee” for the opportunity to “grow”. The presence of rotational stability of an intramedullary rod does not have a significant effect on the stress distribution in the models under compressive loading. But it should be noted that when using a rotationally stable rod, the stresses in the distal tibia are slightly reduced, and what is especially important, in the fracture zone too. Thus, a growing rod with a locked rotational movement creates more favorable conditions for the fusion of tibial fractures in the middle third, which is of great importance in the treatment of children with osteogenesis imperfecta. Conclusions. Under the influence of compressive loads, the presence of rotational stability of an intramedullary rod does not provide significant advantages from the point of view of stress distribution in the model of a tibial fracture in the middle third. However, due to the presence of a movable support at the distal end of the tibia, even with a vertical compressive load, a small torque can occur between the bone fragments, which should block the rod with a locked rotational movement. This is the cause for a decrease in the stress in the distal fragment of the tibia.

Sustainable investments in the face of social unrest and risk: A new perspective on corporate social responsibility

In recent years, corporate social responsibility (CSR) activities have become increasingly prevalent as corporate initiatives, owing to their influence on companies and their societal dimensions. To address the gap in the literature on the effect of CSR activities on firms and their value, this study develops a theoretical model of real options considering market uncertainty and analyzes the relationship between a firm’s investment in CSR activities and the risk to its assets. The analysis demonstrates the existence of an optimal level of investment in CSR activities and shows that at this level, the beta of the firm’s assets undergoes the most significant decrease. Furthermore, by examining the relationship between the monetization potential of investment and the beta of assets, this study demonstrates that CSR activities can effectively reduce asset risk. It evaluates a firm’s value and beta from the perspective of investment in CSR activities and the potential for investment success, demonstrating the utility of this investment. It also highlights that the effectiveness of external CSR activities in increasing a firm’s value is contingent on their recognition and visibility in situations of significant social unrest and provides a practical implication that companies should consider engaging in outward-facing CSR activities.

Real options analysis for regional investment decisions of household PV-ESS in China

This paper takes 30 provinces in China as the research subjects and constructs a real options model to explore the impact of carbon emissions trading market, energy storage subsidies, and their synergy on the optimal investment decision of household PV-ESS projects. The results show that a single factor has a catalytic effect on project investment, and both together have a better effect. And, project investment benefits are better in areas with abundant light resources and higher than average electricity prices. In addition, a sensitivity analysis is conducted on the initial investment cost, CO2 price, and energy storage subsidies. The results show that immediate investment in all provincial projects can be achieved when the initial investment cost is reduced by 50%, or the CO2 price is increased by about 33 times, indicating that the current environment is insufficient to attract investors. The results provide a reference framework for investment in household PV-ESS projects.

Strategic flexibility in healthcare: an exploration of real options

PurposeThis survey explores the application of real options theory to the field of health economics. The integration of options theory offers a valuable framework to address these challenges, providing insights into healthcare investments, policy analysis and patient care pathways.Design/methodology/approachThis research employs the real options theory, a financial concept, to delve into health economics challenges. Through a systematic approach, three distinct models rooted in this theory are crafted and analyzed. Firstly, the study examines the value of investing in emerging health technology, factoring in future advantages, associated costs and unpredictability. The second model is patient-centric, evaluating the choice between immediate treatment switch and waiting for more clarity, while also weighing the associated risks. Lastly, the research assesses pandemic-related government policies, emphasizing the importance of delaying decisions in the face of uncertainties, thereby promoting data-driven policymaking.FindingsThree different real options models are presented in this study to illustrate their applicability and value in aiding decision-makers. (1) The first evaluates investments in new technology, analyzing future benefits, discount rates and benefit volatility to determine investment value. (2) In the second model, a patient has the option of switching treatments now or waiting for more information before optimally switching treatments. However, waiting has its risks, such as disease progression. By modeling the potential benefits and risks of both options, and factoring in the time value, this model aids doctors and patients in making informed decisions based on a quantified assessment of potential outcomes. (3) The third model concerns pandemic policy: governments can end or prolong lockdowns. While awaiting more data on the virus might lead to economic and societal strain, the model emphasizes the economic value of deferring decisions under uncertainty.Practical implicationsThis research provides a quantified perspective on various decisions in healthcare, from investments in new technology to treatment choices for patients to government decisions regarding pandemics. By applying real options theory, stakeholders can make more evidence-driven decisions.Social implicationsDecisions about patient care pathways and pandemic policies have direct societal implications. For instance, choices regarding the prolongation or ending of lockdowns can lead to economic and societal strain.Originality/valueThe originality of this study lies in its application of real options theory, a concept from finance, to the realm of health economics, offering novel insights and analytical tools for decision-makers in the healthcare sector.

Pre-electoral coalition agreement from the Black–Scholes point of view

A political party can be considered as a company whose value depends on the voters support i.e. on the percentage of population supporting the party. Dynamics of the support is thus as a stochastic process with a deterministic growth rate perturbed by a white noise modeled through the Wiener process. This is in an analogy with the option modeling where the stock price behaves similarly as the voters’ support. While in the option theory we have the question of fair price of an option, the question that we ask here is what is a reasonable level of support that the coalition of a “major” party (safely above the election threshold) and a “minor” party (under or around the election threshold) should achieve in order for the “minor” party to get one more representative. We shall elaborate some of the conclusions in the case of recent elections in Montenegro (June, 2023) which are particularly interesting due to lots of political subjects entering the race.

Construction, Real Uncertainty, and Stock-Level Investment Anomalies

Abstract We show that the negative relation between real investments and future stock returns is primarily driven by the subsample of firms building additional capacity. We develop a real options model to rationalize that evidence based on the premise that firms need to learn how to best operate modern capacity vintages, inducing idiosyncratic uncertainty in that capacity’s production costs over the learning period. Conversely, the uncertainty lowers the expected return of firms with newly built capacity until it is resolved. Further evidence based on profit sensitivities to aggregate conditions; analyst forecast-error volatilities; and high- versus low-tech industry subsamples supports our uncertainty explanation.

Creation of 3D landscape in AutoCAD Civil 3D according to data from MapInfo

The article presents the technology of constructing a 3D model of landscape in AutoCAD Civil 3D based on data from Mapinfo. The source material is a raster cadastral map. The resulting 3D model of landscape and visualization options are presented in this work.

Carbon leakage perspective: Unveiling policy dilemmas in emission trading and carbon tariffs under insurer green finance

This study delves into the intricacies of the policy dilemma surrounding carbon emission trading and carbon tariffs, with a specific focus on the perspective of carbon leakage. Using a capped call option model, we assess the equity of a life insurer, emphasizing the importance of carbon leakage resulting from borrowing by carbon-intensive manufacturers. The findings reveal a nuanced scenario: while an increase in green loans positively impacts the guaranteed rate of the insurer, it simultaneously poses a challenge to the equity of carbon-leakage vulnerable manufacturers. Stringent regulatory caps on emissions act as a limiting factor on guaranteed rates for carbon-intensive borrowers. Additionally, higher Carbon Border Adjustment Mechanism tariff rates contribute to a decrease in the guaranteed rate, affecting both the fund-providing insurer and the borrowing manufacturer. This analysis underscores the intricate balance required in policymaking and decision-making, where an understanding of these complex relationships becomes pivotal. Striking the right balance between environmental sustainability and financial stability is essential to navigating the policy dilemma inherent in carbon emission trading and carbon tariffs.

A Hybrid Model for Equity Option with Heston and Forward Market Model

A Hybrid Model for Equity Option with Heston and Forward Market Model

ТВОРЧИЙ ШЛЯХ УКРАЇНСЬКОГО ІСТОРИКА: ДО ЮВІЛЕЮ ПРОФЕСОРА ВОЛОДИМИРА КУЧЕРА

The article highlights the life path of Volodymyr Ivanovych Kucher, doctor of historical sciences, professor, chief researcher of the science sector of the Institute of History of Agrarian Science, Education and Technology of the National Scientific Agricultural Library of the National Academy of Sciences of the National Academy of Sciences in connection with the celebration of his 85th anniversary. The directions of the scientist’s research searches at various stages of scientific growth are revealed, among which the problems of the Second World War and Ukraine’s participation in it stand out, as such, which remains a through-and-through topic of fundamental research throughout his life. Interest in the new paradigm of ethno-national development, modeling of the optimal options for the ethno-politics of our state became no less productive; the question of the unity of Ukrainian lands, national liberation struggles. The significant contribution of the scientist to the creation of a source-based database for the study of the history of the development of agricultural research in Ukraine was noted.

On fundamental solution of the Cauchy problem for ultra-parabolic equations in the Asian options models

Paper studies ultra-parabolic equations with three groups of spatial variables appearing in Asian options problems. The class of these equations which satisfy some conditions was denoted by EB22. This class is a generalization of the well-known class of degenerate parabolic Kolmogorov type equations E22. So called L-type fundamental solutions have been constructed for the equations from the class EB22 previously, and some their properties have been established as well. The main feature of the research was the establishing of an one-to-one correspondence between the classes EB22 and E22. The Cauchy problem classic fundamental solutions for the equations from the class EB22 are considered. Special H\"older conditions with respect to spatial variables are applied to the coefficients of the equations.

Black-Scholes Model and Binomial Model Tests on Nvidia Stock Option Contracts

In order to invest, investors can purchase a number of shares. The characteristics of stocks are high risk/high return and low risk/low return. Stock price volatility is a measurement of how quickly and in a short period of time stock prices can rise or fall (fluctuate). With the advent of derivative instruments, specifically options, risk can be reduced in several ways. A contract known as an option grants its owner the right, but not the duty, to sell or acquire a specific quantity of the underlying asset at a specified price at a specific point in the future. Methods for calculating option prices in derivative instruments is the Binomial option model and the Black Scholes option model. The aim of this research to determine the accuracy of the Black Scholes compared with the Binomial in predicting call option shares of Nvidia Coorporation (NVDA) on the due date of 1 month, 2 months, and 3 months, using data price daily and call option which at 17 sample from January 2022 to May 2023. To determine the accuracy use price absolute error comparisson between the Black Scholes and the Binomial was conducted. In result the Black Scholes model is more accurate than the Binomial.

Assessment of the reasons for the loss of stability of the retaining wall and the choice of slope stabilization options, taking into account the use of retaining walls of different rigidity

An assessment of the reasons for the loss of stability of the sliding slope and the manifestation of significant movements of the existing retaining walls is presented, as well as the selection of measures to stabilize the slope by installing one of the variants of retaining walls of different rigidity is performed.
 To assess the stability of the slope and select the effective parameters of the retaining walls, a numerical simulation of the stress-strain state (SSS) of the elements "soil massif of the slope - retaining walls" was performed. Modeling was carried out by the method of finite elements using the "Plaxis" software complex in a non-linear setting, taking into account changes in the parameters of structures and soils at different stages of modeling.
 An assessment of the real movements of the retaining walls and the reasons for the loss of slope stability at the initial stage was carried out using geodetic monitoring.
 A characteristic engineering-geological section in the zone of the greatest deformations of the existing anti-slide structures was chosen for modeling the calculation scheme.
 Numerical calculations of the retaining walls, which were carried out using the finite element method, involve taking into account the technological sequence of the construction of the retaining walls and modeling the step-by-step development of the pit. Modeling was performed in several stages:
 1) Formation of soil SSS in the current natural state;
 2) Assessment of the stability of the slope before the start of construction, in the presence of an old massive retaining wall made of limestone blocks.
 3) Assessment of the stability of the slope in the version of the original design solution with a retaining wall made of short bored piles with a diameter of 820 mm and taking into account the development of the pit to the design mark.
 4) Modeling of SSS elements "soil array of the slope - retaining walls" with different options of the new retaining wall in order to choose an effective option that will ensure the possibility of developing the pit to the design marks and stabilizing the slope.
 Based on the results of numerical modeling of slope stabilization options with retaining walls of different designs and rigidity, the consumption of materials for each of the options was determined and the most effective option was selected.
 Studies have shown that depending on the change in the spatial rigidity of the retaining walls by introducing additional elements (buttresses, struts) it is possible to obtain an optimal solution and, in the future, to effectively design a complex of anti-landslide structures.

European Option Pricing under Sub-Fractional Brownian Motion Regime in Discrete Time

In this paper, the approximate stationarity of the second-order moment increments of the sub-fractional Brownian motion is given. Based on this, the pricing model for European options under the sub-fractional Brownian regime in discrete time is established. Pricing formulas for European options are given under the delta and mixed hedging strategies, respectively. Furthermore, European call option pricing under delta hedging is shown to be larger than under mixed hedging. The hedging error ratio of mixed hedging is shown to be smaller than that of delta hedging via numerical experiments.

Pricing and Optimization Model of European Options

Financial market forecasts are gradually gaining the attention of investors. The options market is an integral and important part. Commonly used analysis methods include traditional BS formula and CRR model. This article obtained the transaction data of SP&500 from February 2013 to February 2018, used the data of the first 4 years to train the model, and finally explored the actual price and predicted value of the European call option. To forecast the stock price, a hidden Markov model (HMM) is first applied. And on this basis, improve the parameter estimation in the traditional method BS-CRR, and compare each model with the actual value of the option. Compared with the traditional model, to some extent, the Hidden Markov Model can predict the state of the stock market., get rid of the limitations of the BS model assumptions, predict the direction of the price trend, and verify the feasibility of its application in the financial field.

Corporate sustainability, investment, and capital structure

AbstractThis study develops a real options model in which a firm invests in either a sustainable project or an unsustainable project. The sustainable project requires a high investment cost and yields cash flows perpetually, whereas the unsustainable project requires a low investment cost and yields cash flows until a random maturity. The random termination of cash flows reflects the project’s environmental, social, and governance (ESG) risk. In the model, the optimal investment choice and timing are analytically derived, and the effects of key parameters on the choice are also examined. Higher ESG risk, growth rate, and volatility, and lower discount rate encourage sustainable investing mainly through their impacts on the net present value and timing option value. The less sustainable firm chooses higher leverage because it cares less about the disadvantages of debt. Therefore, access to debt financing and a higher corporate tax rate (tax shield) discourage sustainable investing.