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Considering the growing global energy demand for continuous economic advancement, the issue of energy supply has become one of the most important topics of the twenty-first century. Today’s world supplies its energy demands in various ways, and fossil fuels are one of the key resources for energy supply. Due to their high efficiency and low production costs, fossil fuels have become one of the main energy supply resources since the beginning of the twentieth century. Two aspects of this field cause concern. First, fossil fuels are considered to be non-renewable resources, and predictions regarding their amount and consumption rate indicate that they will be depleted in the next 50 years. Second, converting these resources to electrical energy for consumption in industry and general applications produces carbon dioxide and global warming materials. The objective of this study is to find a suitable tool for politicians to further manipulate the choice of investors in this field toward renewable resources to produce electricity. In this regard, this study uses the real options theory and the dynamic programming model based on the Bellman equation. Finally, a combination of the Bellman equation and the binomial tree algorithm is used in the Monte Carlo simulation to analyze the effect of government policies and their impact on investor's behavior. The findings indicate that reducing the life span of fossil fuel power plants in favor of renewable power plants is the least expensive method.

In the following, we consider a market model where a non-risky asset (called bond) and a risky asset (called stock) are available. The bond price is denoted by B, while the stock price is denoted by S.

Chapter 8 focuses on the valuation of options along with their applications to arbitrage and hedging. After a general introduction to derivatives markets and hedging, put-call parity is explored, with its application to collars as a hedging technique. One, two, and n-time period binomial pricing models are derived from the binomial hedge ratio. The Black-Scholes model is discussed along with its "Greeks." Formation of delta and gamma neutral portfolios is explained. The Black-Scholes model is extended to FX options, which are applied to the management of exchange exposure. The Black-Scholes model is derived in the chapter appendix.

The global shipping market has been depressed and turbulent since 2008. Shipping companies have had to be more cautious with their investments, so as to buck the trend and get through this difficult period. Traditional net present value methods cannot help enterprises make effective investment decisions. Therefore, we employ real options theory—including expansion options, contraction options, deferral options, and abandonment options—to simulate various types of operational adjustment strategies used by investors in the process of ship investment and operations. Triangular fuzzy numbers and the generalized autoregressive conditional heteroscedasticity model are also introduced to describe the uncertainty and volatility of the shipping market. Subsequently, a fuzzy real options binomial tree pricing model is developed to assess the project value of ship investments. Based on the calculations and analysis of an actual ship investment case, the fuzzy real options method is shown to be more suitable for ship investment analysis, fitting more closely the actual market and operating situation.

Due to the long life, most mining projects face the risk of the parameters such as mineral price, grade, and cost. Uncertainty can lead to unfavorable results of the decisions made by managers and mining investors. Therefore, this paper aims to determine the Sari Gunay gold mine’s production planning, considering the certainty and uncertainty over the mineral price. Finally, the proposed planning will lead to the allocation of fixed or variable production rates throughout the mine life. These findings were assessed by Taylor and Zwiagin methods with 22 different scenarios in all conditions, including (a) price certainty and uncertainty such as daily price, 3- and 5-year average, Monte Carlo simulation, and binomial tree; (b) decreasing, increasing, and fixed production rates; and (c) mine life conditions. The scenarios evaluated under the price certainty conditions (scenarios 1 to 12) have lower NPV values than those under the price uncertainty conditions. This is because the price is fixed throughout the mine life. Due to historical price data and high fluctuations of estimated prices, this method’s NPV values fluctuate more than other scenarios evaluated by the Monte Carlo simulation. The binomial tree method scenarios have the lowest NPV value’s fluctuation because the fluctuation of the estimated prices is controlled, and the highest NPV values are related to this method. Out of the 22 scenarios, scenario 17 has the highest NPV value ($512,642,774). According to this scenario, the mine plan is determined, and the annual production rate is reduced to 3,241,977 tons in the first year and 270,165 tons in the last year with the Taylor life of 12 years.

This paper examines the performance of nonlinear short‐term forecasts of noncausal processes from closed‐form functional predictive density estimators. The processes considered have mixed causal–noncausal MAR(1, 1) dynamics and non‐Gaussian distributions with either finite or infinite variance. The quality of point forecasts is affected by spikes and bubbles in the trajectories of these processes, which also characterize many financial and economic time series. This is due to deformations of estimated predictive densities from multimodality during explosive episodes. We show that two‐step‐ahead predictive densities of future trajectories based on the MAR(1, 1) Cauchy process can be used as a new graphical tool for early detection of bubble outsets and bursts. The method is applied to the Bitcoin/US dollar exchange rates and commodity futures.

We present some formulations of the Cox-Ross-Rubinstein and Black-Scholes formulas for European options obtained through a suitable change of measure, which corresponds to a change of numèraire for the underlying price process. Among other consequences, a closed formula for the price of an European call option at each node of the multi-period binomial tree is achieved, too. Some of the results contained herein, though comparable with analogous ones appearing elsewhere in the financial literature, provide however a supplementary widening and deepening in view of useful applications in the more challenging framework of incomplete markets. This last issue, having the present paper as a preparatory material, will be treated extensively in a forthcoming paper.

In this article, we present the American option pricing procedure based on the binomial tree from an imprecise statistical aspect. Nonparametric Predictive Inference (NPI) is implemented to infer imprecise probabilities of underlying asset movements, reflecting uncertainty while learning from data, which is superior to the constant risk-neutral probability. In a recent article, we applied the NPI method to the European option pricing procedure that gives good results when the investor has non-perfect information. We now investigate the NPI method for American option pricing, of which imprecise probabilities are considered and updated for every one-time-step path. Different from the classic models, this method is shown that it may be optimal to early exercise an American non-dividend call option because our method considers all information that occurs in the future steps. We also study the performance of the NPI pricing method for American options via simulations in two different scenarios compared to the Cox, Ross and Rubinstein binomial tree model (CRR), first where the CRR assumptions are right, and second where the CRR model uses wrong assumptions. Through the performance study, we conclude that the investor using the NPI method tends to achieve good results in the second scenario.

In this paper, we combine the maximum entropy principle with binomial tree to construct a non-recombining entropy binomial tree pricing model under the volatility that is a function of time, and gi...

Option price prediction has been an important issue in the finance literature within recent years. Affected by numerous factors, option price forecasting remains a challenging problem. In this study, a novel hybrid model for forecasting option price consisting of parametric and non-parametric methods is presented. This method is composed of three stages. First, the conventional option pricing methods such as Binomial Tree, Monte Carlo, and Finite Difference are used to primarily calculate the option prices. Next, the author employs an Adaptive Neuro-Fuzzy Inference System (ANFIS) in which the parameters are trained with particle swarm optimization to minimize the prediction errors associated with parametric methods. To select the best input data for the ANFIS structure, which has high mutual information associated with the future option price, the proposed method uses an entropy approach. Experimental examples with data from the Australian options market demonstrate the effectivity of the proposed hybrid model in enhancing the prediction accuracy compared to another method.

With the development of mathematical applications for stock and energy markets, the subject of financial mathematics has attracted more attention from mathematicians in recent years. The main topics of my work have focused on the stock and energy markets, in particular, the electricity market. The first part of my thesis introduces stochastic modeling and derivatives pricing with pure and jump-diffusion models for energy markets, the second part develops a method to value an exotic option on stock markets and the third part demonstrates my financial toolbox for financial applications. Due to the lack of the analytic evaluation formulas for options in most applications, various numerical approaches have been applied in this thesis such as the binomial tree approach, and finite differences for solving partial differential equations.

The binomial tree consists of a single vertex. The binomial tree is an ordered tree defined recursively. The binomial tree consists of two binomial trees that are linked together: the root of one is the leftmost child of the root of the other. The popular Graceful Tree Conjecture states that every tree is graceful. In this paper, we show that binomial trees is graceful for every .

THE AIMS OF THE PAPER This study attempts to explore the links between venture capital (VC) investments and the real option approach (ROA) with analyzing the characteristic features of the venture capital investments and their process. The real options can be examined as a way of thinking and evaluation method and the study’s aim is to show that real option approach can provide an answer to the valuation challenges of venture capital investments. METHODOLOGY The choice of the appropriate valuation method requires consideration of its conditions of application, which, in the case of real option theory, result from the examination of uncertainty, flexibility and irreversibility. The venture capital investments are characterized by a high degree of uncertainty and risk, which can also be traced back to the provision of financing to innovative, early-stage companies. Real option theory also provides venture capital investors with professional experience through their active role in decision-making. The study evaluates a Hungarian start-up company venture capital investment with the help of a traditional discounted cash flow method and two real option valuation models: Black – Scholes model and binomial pricing model. Then a sensitivity analysis is prepared to analyze the value driver effect on option value and a volatility analysis to verify the importance of high-degree of uncertainty in real option valuation. MOST IMPORTANT RESULTS The paper concludes that the option-based valuation methods are more suitable for evaluating venture capital investments than other approaches such as the discounted cash flow methods, and the embedded flexibility can be determined by the real option approach. The binomial pricing model points out the advantages of staging investments with the higher real (call) option value. Besides the real option valuation, the sensitivity analysis shows a positive effect of the present value of the underlying assets, the time to maturity, the risk-free interest rate and volatility on the call option value. The analysis of the volatility emphasizes the importance of the degree of uncertainty in real option valuation. RECOMMENDATIONS The real option approach ensures proper evaluation of venture capital investment, avoiding the undervaluation and taking advantage of staging and timing investments in practice. Acknowledgment: Supported by the UNKP-19-3 New National Excellence Program of the Ministry for Innovation and Technology.

Ongoing digitalization of production accelerates trends like mass customization, ever shorter lead times, and shrinking product life cycles. Thereby, industrial companies face increasingly volatile demand that complicates an appropriate production capacity planning. On the other hand, the comprehensive digitalization of production environments favors, amongst others, the dynamic integration of flexible external on-demand production capacity provided by specialized external capacity providers (ECPs). To enable the usage of on-demand production capacity, industrial companies may require significant upfront investments (e.g., for inter-organizational information systems, planning and organizational processes, employee training). The objective of this paper is to develop a model that evaluates such enabling upfront investments from the perspective of a manufacturing company. To consider flexibility of action, we apply real options analysis in a discrete-time binomial tree model and weigh these so-called expansion options to related cash outflows. In addition, we evaluate our model by means of a simulation and sensitivity analyses and derive insights for both researchers and practitioners. The insights gained by our model present a profound economic basis for investment decisions on upfront investments in flexible on-demand production capacity.

El presente trabajo pretende aplicar la teoría de opciones reales en un proyecto de construcción de una pequeña central hidroeléctrica en Colombia. El cálculo del valor presente neto y de la tasa interna de retorno indica que el proyecto es viable; sin embargo, estas metodologías desconocen la opción de expansión existente en dicho proyecto. El artículo presenta el cálculo de esta opción basándose en la metodología de árboles binomiales, en los que la volatilidad se obtiene a través de un modelo EGARCH elaborado con base en los retornos diarios de los precios de la energía. Se concluye que la opción real hace viable el proyecto, a la vez que desarrolla herramientas que ayudan a trabajar este tipo de casos en las valoraciones de proyectos pertenecientes al sector energía.

Energy performance contracting (EPC) was developed and had ever been believed as an effective energy-saving method. Despite that a variety of schemes, Guaranteed Saving, Shared Saving, and First-Out schemes, are created to be applied in various conditions, it has not been widely adopted as expected, due to the complexity of its profit allocation, high uncertainty and investment-assessing deficiency. In order to promote the wide applications of EPC projects, Real option analysis (ROA) is applied in this paper with the attempt of seeking the optimal scheme, which could be feasible and profitable for both stakeholders. ROA is studied to be an effective tool capable of considering the uncertainty and the managerial flexibility, and of assessing the investment value. A ROA-enabled methodology is proposed and expected to (1) identify feasible options for both the energy service company and the owner, (2) evaluate the investment value using the binomial tree pricing model, (3) develop new metrics for the optimal EPC scheme, and finally (4) single out the optimal scheme that is feasible and attractive for both sides. A real EPC project is studied to test the effectiveness and applicability of the proposed approach. The Shared Saving scheme is identified as the optimal scheme for the EPC project, striking a more ideal profit difference between participants than the other two schemes. This demonstrates the capability and effectiveness of the proposed approach in optimizing the scheme into a new balance. The sensitivity of the sharing proportion on the optimal EPC scheme is discussed, and it is found that the sharing proportion of realized energy cost savings by the energy service company is positively correlated with the total investment value. The novelty of this research lies in (a) the incorporation of contractual flexibility by means of the real option into the EPC project for optimal design, and (b) new metrics for the selection of the optimal EPC scheme. The proposed model and suggestions based on the case study are supposed to help decision-makers optimize the scheme under different scenarios. A feasible and attractive EPC scheme can further prompt wide application of energy-saving projects, which in turn contributes to the improvement of energy-consuming efficiency and then to realize the environmental sustainability.

Investments in climate-change adaptation will have to be made while the extent of climate change is uncertain. However, some important sources of uncertainty will fall over time as more climate data become available. This paper investigates the effect on optimal investment decision-making of learning that reduces uncertainty. It develops a simple real options method to value options that are found in many climate-change adaptation contexts. This method modifies a binomial tree model frequently applied to climate-change adaptation problems, incorporating gradual learning using a Bayesian updating process driven by new observations of extreme events. It is used to investigate the timing, scale, or upgradable design of an adaptation project. Recognition that we might have more or different information in the future makes flexibility valuable. The amount of value added by flexibility and the ways in which flexibility should be exploited depend on how fast we learn about climate change. When learning will occur quickly, the value of the option to delay investment is high. When learning will occur slowly, the value of the option to build a small low-risk project instead of a large high-risk one is high. For intermediate cases, the option to build a small project that can be expanded in the future is high. The approach in this paper can support efficient decision-making on adaptation projects by anticipating that we gradually learn about climate change by the recurrence of extreme events.

This paper introduces a novel method for asset and option trading in a binomial scenario. This method uses nonparametric predictive inference (NPI), a statistical methodology within im- precise probability theory. Instead of inducing a single probability distribution from the existing observations, the imprecise method used here induces a set of probability distributions. Based on the induced imprecise probability, one could form a set of conservative trading strategies for assets and options. By integrating NPI imprecise probability and expectation with the classical nancial binomial tree model, two rational decision routes for asset trading and for European option trading are suggested. The performances of these trading routes are investigated by com- puter simulations. The simulation results indicate that the NPI based trading routes presented in this paper have good predictive properties.

How much to spend on an option contract is the main problem at the task of pricing options. This become more complex when it comes to projecting the future possible price of the option. This is attainable if one knows the probabilities of prices either increasing, decreasing or remaining the same. Every investor wishes to make profit on whatever amount they put in the stock exchange and thus the need for a good formula that give a very good approximations to the market prices. This paper aims at introducing the concept of pricing options by using numerical methods. In particular, we focus on the pricing of a European put option which lead us to having American put option curve using Trinomial lattice model. In Trinomial method, the concept of a random walk is used in the simulation of the path followed by the underlying stock price. The explicit price of the European put option is known. Therefore at the end of the paper, the numerical prices obtained by the Black Scholes equation will be compared to the numerical prices obtained using Trinomial and Binomial methods.

Purpose The purpose of this paper is to develop a trading and pricing method of expansion option (EO) model to solve expansion problems of build-operate-transfer (BOT) freeway project. Design/methodology/approach This paper proposes an ex ante mechanism through trading the EO to avoid the transaction costs. By editing the paths generated from binomial option pricing model, this paper establishes an American real option binomial lattice model and evaluates the value of EO. Data are collected from Liaoning province in China and the model is practiced in the context of a BOT freeway in Liaoning province. Findings Supported by empirical evidence, this study finds out that there exists a minimum price at which the government can sell the EO and a maximum price that the private sector is willing to pay. When the minimum price is negative, the government should transfer the EO to the private sector free of charge to avoid the transaction costs. Otherwise, the government should sell the EO at a reasonable price to protect public interests. Practical implications The study can be used for the government to reducing the transaction costs. By using the trading EO model, the government can sell its share of the EO to the private sector to manage its resources efficiently. Originality/value This paper builds a trading EO model to solve expansion problems instead of renegotiations. In addition to reducing the transaction costs for the whole society, trading EO can also raise the respective payoffs of both public and private sectors. An EO trading framework and algorithm is further developed. It realized an American option model, making the owner can exercise the option whenever he wants. Thus, the whole model is adapted to best fit BOT highway practice.

This paper proposes three evaluation models for evaluating the value of strategic waiting of real estate development project. In Model 1, the ratio of land cost to total real estate sales in period...

Air pollution severely impacts various social and economic sectors, underscoring the importance of a financial air quality derivatives market. This article focuses on designing an Air quality index (AQI) options contract, employing financial derivatives to hedge against air pollution risks. Next, the AQI day values are used to establish an Ornstein-Uhlenbeck (O-U) mean recovery model, from October 28, 2013 to May 31, 2017, in Shijiazhuang. Accounting for variation of the sequence over time, we obtain significant seasonal fluctuations and variances in the AQI data, used in estimating the model parameters. Finally, under the risk-neutral principle, three types of ADI index options contracts, with different maturities, are simulated, with pricing derived through the binomial tree model. Results show: the O-U model time series can improve accuracy when forecasting AQI changes. The use of a new binomial tree model can reasonably price derivatives of air quality. The AQI based air pollution option product, described in this paper, can hedge operating risks for companies in industries that are seriously affected by air pollution.

In accordance with Solvency II, the commonly tightened government regulation on insurance cooperations, they have been obligated to take conservative investment strategies such as those ruling out the possibility of bankruptcy. With this in mind, in this article, we aim to continue our work (Wong et al., 2017a,b) . First, we study the solvability of mean-risk portfolio optimization problem with bankruptcy prohibition, in the complete market in which the investor aims to maximize the expected payoff and to minimize the deviation risk simultaneously, which is of great use in the insurance paradigm. Secondly, we also provide the original weak convergence result of the optimal terminal wealth of a sequence of approximate markets to that of the limiting market through their corresponding pricing kernels. As a result, we establish an effective numerical algorithm calibrating the optimal terminal wealth under Black–Scholes models by that of binomial tree models. The results of our numerical simulations indicate that the downside risk of the optimal payoff can be effectively reduced by imposing the bankruptcy prohibition.

In finance, option pricing is one of the main topics. A basic model for option pricing is the Binomial Tree Model, proposed by Cox, Ross, and Rubinstein in 1979 (CRR). This model assumes that the underlying asset price follows a binomial distribution with a constant upward probability, the so-called risk-neutral probability. In this paper, we propose a novel method based on the binomial tree. Rather than using the risk-neutral probability, we apply Nonparametric Predictive Inference (NPI) to infer imprecise probabilities of movements, reflecting more uncertainty while learning from data. To study its performance, we price the same European options utilizing both the NPI method and the CRR model and compare the results in two different scenarios, firstly where the CRR assumptions are right, and secondly where the CRR model assumptions deviate from the real market. It turns out that our NPI method, as expected, cannot perform better than the CRR in the first scenario, but can do better in the second scenario.

Numerical calculations imply that tax-loss harvesting is valuable to holders of taxable stock accounts. These calculations are based on the assumption that a capital loss on a stock portfolio can always be netted against ordinary income (up to a limit) or a capital gain on the same stock portfolio. We provide market-based evidence that a capital loss that is realized in the beginning of the year is substantially less valuable than a loss that is taken at the end of the year. A simple binomial tree model that captures the resolution of tax rate uncertainty closely mimics observed market prices. Allowing investors to postpone unused losses into the future does not alter the conclusion that realized losses are less valuable early in the year.

This paper explores option-implied information measures for optimal portfolio allocation. We introduce two state variables constructed from option prices. The first state variable is the risk-premium on the risky asset and the second variable is the market price of risk. We also explore a lognormal distribution, a mixture of lognormal distributions, and a binomial tree for constructing the implied risk-neutral density function. Using a combination of statistical and economic measures applied to a portfolio given by the 1-month US Treasury bill and the S&P 500 Index we show the good performance of option-implied information measures for optimal portfolio allocation.

A new method is designed for software pricing, which is enlightened from binomial tree option pricing model. Firstly, it is constructed about the software pricing model based on binomial tree. Secondly, computation method is shown later. Thirdly, the applicability of this computation method is demonstrated by an example. According to the calculation results, it is found out that the most two important variables are initial value of software and successful probability of every stage, which are of strong effects to the price of software. In addition, it is also concluded that value created in coding stage is usually smaller than value created in requirements stage and design stage.

Communication plays an important role in MPI applications, and reduce operations are heavily used part of MPI. In this paper, we propose a k-nomial tree topology and a hierarchy tree topology to optimize the Reduce operation in MPI. The k-nomial tree can effectively decrease the communication steps and is suitable for lots of processes. Compared with the binomial tree algorithm in small and medium size messages, the Reduce operation performed by the k-nomial tree can improve communication performance by 46%. Hierarchy trees can dynamically group processes at run time to take advantage of high bandwidth to communicate as much as possible within nodes. The test results show that compared with the binomial tree algorithm, the performance of the hierarchy tree algorithm is stable. For Reduce operation, we can get a 30% performance improvement.

In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.

The objective of this paper is to detect the arbitrage opportunity and to manage the bubbles in the Korean real estate market based on a binomial American option pricing model with heteroscedasticity. The limitation of previous research where the real options framework was first introduced is its macro-economic implication based on the utilization of the general housing indices. Therefore, in this paper, we extensively apply the model to different residential types and regions. The results suggest that the model can detect the realistic and reasonable trend of housing bubbles and the arbitrage opportunities for different times, residential types, and regions. We also simulate two scenarios to encourage the trades of real estate assets: promotion of early exercise, and the shortened Contract period. Performing arbitrage trading based on these two methods, we discover that both approaches effectively reduce the housing bubbles in all residential types and regions. Specifically, the promotion of early exercise reduces the housing bubble more effectively than the shortened Contract period. Hence, we advocate the utilization of the information obtained from the model to boost the transactions in the Korean real estate market in order to reduce the bubble-related risks and to support sustainable economic growth.

International audience; The function solution to the functional scheme derived from the Binomial tree financial model with local volatility converges to thesolution of a diffusion equation of type ht(t, x)+ x2σ2(t,x) hxx(t, x) = 0 as the number of discrete dates n → ∞. Contrarily to classical numerical methods, in particular finite difference methods, the principle is only based on a discretization in time. We establish the uniform convergence in time of the scheme and provide the rate of convergence when the payoff function is not necessarily smooth as in finance. We illustrate the convergence result and compare its performance to the finite difference and finite element methods by numerical examples.

The aerospace industry is a rich source of innovation and novel technologies. However, structural drivers, such as product complexity and stringent performance requirements, inhibit the uptake of new technologies and present challenges to portfolio management specific to technology-rich environments. Although project risk is often managed through staged funding processes associated with intermediate milestones, this process is typically decoupled from portfolio valuation. In this paper, we use a simple real options binomial tree model to value the National Aeronautics and Space Administration portfolio funded through the Small Business Innovation Research program, accounting quantitatively for the funding stages and future opportunities accompanying technology infusion. For the 2009 portfolio, the average net project investment is $166k, suggesting the important role that early-stage funding plays in launching innovation efforts. We study the staged architecture to offer insight to managers of commercial and public portfolios alike.

We develop a general framework for statically hedging European-style options with nonstandard terminal payoffs which can be applied to mixed static-dynamic and semi-static hedges for many path dependent exotic options. This framework provides a new model-free method of derivatives pricing that builds on recent advances in transform-based numerical approaches. The goal is achieved by separating the hedging and pricing problems to obtain model-free replicating strategies. Once prices have been obtained for a set of basis payoffs, the pricing and hedging of financial securities with arbitrary payoffs functions is accomplished by computing a set of "hedge coefficients" for that security. This method is particularly well suited for pricing baskets of options simultaneously, and is robust to discontinuities of payoffs. In addition, the method enables a systematic comparison of the value of a payoff (or portfolio) across a set of competing model specifications with implications for security design.

Power transmission expansion planning (TEP) is a process affected by uncertainty that requires a long-term vision to anticipate requirements of interconnections among generators and load centers. Flexibility is an alternative to cope with uncertainty that increases social welfare. This article seeks for estimating the value of this flexibility and interpreting its meaning in the Colombian power system. In order to keep this focus clear, we implement a well-known methodology of Real Options (RO) in a simplified version of the Colombian power system. Accordingly, we introduce flexibility using a simple strategy of adding new transmission lines and make a simple comparison with a robust approach, as the one currently used in Colombia. Our results show that introducing this flexibility in the Colombian TEP increases social welfare in around $35 million, which represents an upper bound for the additional investment costs incurred to provide this adapting ability to the power system. These results suggest the need for revising the current paradigm of robust approach to prepare future Colombian transmission plans.

In this paper, a new model is proposed for pricing a European option using the binomial tree method in conjunction with the Greek letters. In the proposed method, the covariance matrix of high and low stock prices was calculated in an uncertainty region. Applying robust option pricing model, an ‘interval’ of prices (instead of ‘spot’ prices) for an option was obtained. Greek letters were incorporated into a robust option model to ameliorate the accuracy of the interval price. It was found out that the interval prices obtained by the present model were flexible with increased accuracy compared with those obtained by the robust option using the binomial tree model. It is also indicated that the advantage of the present model over existing models is more tangible in the event of ‘out of the money’ call option. Furthermore, the accuracy improvement was found to be less noticeable when the maximum costs were equal to each other.

The abandonment option of an operating oil project refers to the right to shut down or transfer the project. As a kind of American real option, it minimizes the impact of bad operating conditions, thus increases the initial project value. Meanwhile, as a put option, it maximizes the management flexibility in unfavorable environment, especially in the current low oil prices. This article uses the trinomial tree, rather than the binomial tree widely practiced in finance, to value the option. Its lattice structure shows flexibility and intelligibility, and improves computational efficiency and accuracy. In this article, the abandonment option value incorporates uncertainties of oil price, exchange rate, political environment and taxation policy. The risk-neutral based decisions are relatively objective for oil companies. The case study indicates that the relative relationship between the abandonment option value and the project scrap value or selling price is the key to the decision-making results. A novel conclusion from the risk-neutral prospective is that, the project is more likely to be sold at higher risk scenario or with higher profit requirement. Moreover, export duty and mineral extraction tax have a greater impact on the abandonment timing than corporate income tax. This decision-making model can be introduced with modifications to other investments with increasing risk of falling asset price.

In many projects the problem of selecting the start time of a non-critical activity arises. Usually it is possible to use the "as soon as possible" or "as late as possible" rules. In some situations, however, the result of such a decision depends on external factors such as exchange rate. This leads to an approach in which the problem of scheduling non-critical activities is solved using an expanded Cox-Ross-Rubinstein (CRR) binomial tree method. In the paper a bi-criteria problem of determining the start time of a non-critical activity is considered. We assume that the early start and the late start of the activity have been identified using Critical Path Method, but the project manager is free to select the time when the activity will actually be started. This decision cannot, however, be changed later, as it is associated with the allocation of key resources. Two main criteria are considered: cost and risk. While cost depends on exchange rate, risk increases with the delay of the start of the activity. The problem can be described as a dynamic process. We propose a new interactive technique for solving such a bi-criteria decision making problem under risk. The procedure uses trade-offs to identify a candidate solution. The CRR binomial method is applied to evaluate the cost of the activity.

We construct a discrete-time option valuation model capable of taking into consideration multiple exercises and stochastic interests rates under a generalized Brennan–Rubinstein framework, and further apply the Geske and Johnson (1984) method for the valuation of American options. For implementation, we use only the once- and twice-exercisable option values to approximate American option values. Our numerical results show that the effects of stochastic interest rates are very large, particularly for out-of-the-money American put options with a high-risk underlying asset price. For options with a high-risk return on asset as the underlying assets, the effects of stochastic interest rates are negligible, even for options with long-term maturity. Finally, the sign of correlation between asset prices and bond prices plays an important role in determining whether the values of American put options under stochastic interest rates are larger or smaller than those under constant interest rates.

The binomial-tree model is a numerical method widely used in finance with a computational complexity which is quadratic with respect to the solution accuracy. The existing research has employed reconfigurable computing to provide faster solutions compared with general-purpose processors, but they require low-level manual design by a hardware engineer, and can only solve American options. This paper presents a formal mathematical framework that captures a large class of binomial-tree problems, and provides a systolic data-movement template that maps the framework into digital hardware. This paper also presents a fully automated design flow, which takes C-level user descriptions of binomial trees, with custom data types and tree operations, and automatically generates fully pipelined reconfigurable hardware solutions in field-programmable gate array (FPGA) bit-stream files. On a Xilinx Virtex-7 xc7vx980t FPGA at a 100-MHz clock frequency, we require 54-μs latency to solve three 876-step 32-bit fixed-point American option binomial trees, with a pricing rate of 114k trees/s. From the same device and in comparison to the existing solutions with equivalent FPGA technology, we always achieve better throughput. This ranges from 1.4× throughput compared with a hand-tuned register-transfer level systolic design, to 9.1× and 5.6× improvement with respect to scalar and vector architectures, respectively.

In this paper, we combine the traditional binomial tree and trinomial tree to construct a new alternative tree pricing model, where the local volatility is a deterministic function of time. We then prove the convergence rates of the alternative tree method. The proposed model can price a wide range of derivatives efficiently and accurately. In addition, we research the optimization approach for the calibration of local volatility. The calibration problem can be transformed into a nonlinear unconstrained optimization problem by exterior penalty method. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S & P 500 index. Numerical results confirm the excellent performance of the alternative tree pricing model.

The aim of this paper is pricing the vulnerable options in a vague world. Due to the vulnerability of financial markets and the economy environment in the real world, investors cannot always have precise information about firm value and default recovery rate in vulnerable option pricing. Therefore, following the framework of Klein in 1996, a fuzzy binomial tree pricing model is derived by modelling the firm value and default recovery rate as fuzzy numbers. The numerical results show that the precise information assumption about the firm value and recovery rate in Klein model may lead to underestimate the credit risk on the values of vulnerable options. This study aims to provide insights for future research on defaultable options pricing under imprecise market information.

Contiguous allocation of parallel jobs in multicomputers usually suffers from the degrading effects of fragmentation, because it requires that the allocated processors be contiguous and have the same topology as that of the multicomputer's interconnection network. Fragmentation can be avoided by adopting non-contiguous allocation. However, non-contiguous allocation can increase the distances among processors allocated to a job, which can increase the interference among messages of different jobs and increases message contention and delays. This paper suggests a new non-contiguous processor allocation strategy, referred to as Minimum Interference Paging (MIP), for the 2D mesh network. MIP attempts to reduce the distances among processors allocated using a paging variant that chooses a set of processors with the lowest distance between the first and last allocated processors, where the distance is the number of processors between the first allocated node and last allocated node. Using software simulation, we compared the performance of MIP against that of several well-known non-contiguous allocation strategies: paging (0), Multiple Buddy System (MBS) and Adaptive Non-contiguous Allocation (ANCA). The comparative evaluation was conducted using First-Come-First-Served (FCFS) job scheduling, wormhole routing and six communication patterns. These are the one-to-all, all-to-all, Near Neighbour, Ring, Divide and Conquer Binomial Tree (DQBT), and Random communication patterns. The results show that MIP exhibits superior performance in terms of average turnaround time of jobs.

Recombinant binomial trees are binary trees where each non-leaf node has two child nodes, but adjacent parents share a common child node. Such trees arise in finance when pricing an option. For example, valuation of a European option can be carried out by evaluating the expected value of asset payoffs with respect to random paths in the tree. In many variants of the option valuation problem, a closed form solution cannot be obtained and computational methods are needed. The cost to exactly compute expected values over random paths grows exponentially in the depth of the tree, rendering a serial computation of one branch at a time impractical. We propose a parallelization method that transforms the calculation of the expected value into an "embarrassingly parallel" problem by mapping the branches of the binomial tree to the processes in a multiprocessor computing environment. We also propose a parallel Monte Carlo method which takes advantage of the mapping to achieve a reduced variance over the basic Monte Carlo estimator. Performance results from R and Julia implementations of the parallelization method on a distributed computing cluster indicate that both the implementations are scalable, but Julia is significantly faster than a similarly written R code. A simulation study is carried out to verify the convergence and the variance reduction behavior in the proposed Monte Carlo method., Comment: 19 pages and 5 figures (png/jpeg files)

Purpose Option pricing is an integral part of modern financial risk management. The well-known Black and Scholes (1973) formula is commonly used for this purpose. The purpose of this paper is to extend their work to a situation in which the unconditional volatility of the original asset is increasing during a certain period of time. Design/methodology/approach The authors consider a market suffering from a financial crisis. The authors provide the solution for the equation of the underlying asset price as well as finding the hedging strategy. In addition, a closed formula of the pricing problem is proved for a particular case. Furthermore, the underlying price sensitivities are derived. Findings The suggested formulas are expected to make the valuation of options and the underlying hedging strategies during a financial crisis more precise. A numerical application is provided for determining the premium for a call and a put European option along with the underlying price sensitivities for each option. Originality/value An alternative option pricing model is introduced that performs better than existing ones, especially during a financial crisis.