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The Suez Canal Area Development Project's Investment Opportunity: A The Suez Canal Area Development Project's Investment Opportunity: A Real Options Approach ∗ Boping Tiana, Mahmoud A. Eissaa;b,y Guangqiang Tenga, Qi Liangc aDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, China bDepartment of Mathematics, Faculty of Science, Menoufia University, Menoufia 32511, Egypt cDepartment of Business Administration, Sun Yat-sen University, Guangzhou, China Abstract. The importance of the Suez Canal in world trade shows through its strategic role such that providing a gateway between Eastern and Western world. Nearly 10% of all world trade pass through the Canal. But Suez Canal revenues are still small relative to its importance and unique position. So, the Egyptian government launched two inter-related major projects to transform the Suez Canal region into an international logistics, maritime and industrial hub which will offer enhanced opportunities for investment across all economic sectors including: ports and logistics, maritime services, industry, ICT, renewable energy (RE) and other areas of opportunity. Egypt has a gap on the power supply in the last three years. The government is putting a strategy plane to reach 20% of the total electricity generated from RE by 2020 Vs 9.1% in 2013 to address this energy deficit. But, one of the challenges facing the Egyptian strategy plane is how to attract RE investments?, though the RE investment are irreversible and uncertain such that the RE investment are long-term, costly and depend on a feed-in tariff system. In this paper, we discuss a real option framework for use in RE investment and apply this framework on RE investment opportunity under the Suez canal area development Project (SCADP) in the light of steps taken by the Egyptian Government to support investment in this sector. A real option framework is modeled to optimizing the time of launching the project to maximizing the utility to assess the value, and assess the value of deferred option and abandonment option. At any stage in the project, the model can inform a strategic options to defer or abandon project. Numerical methods form one of the important tools of options valuation and especially in cases where there is no closed form analytic formula. Here, we construct new two numerical methods, the first one is drifting split- step Theta Milstein (DSSθM) methods and the second one is modified split-step Theta Milstein (MSSθM) methods for solving It^ostochastic differential equations (SDEs). We examine commonly used methods DSSθM and MSSθM with another two methods, finite difference methods (FDM) and Monte Carlo (MC) method in options valuation for investments with uncertainty. A new split- step methods are integrated with concepts of Black-Scholes option pricing theory and economic principles of cost, value, risk and flexibility. Finally, we discuss the deferred and abandonment options for the project, 140 MW integrated solar combined cycle power plant in Kuraymat. Keywords. Stochastic differential equation, Real option, Renewables energy, Egypt, Suez Canal . 1 Introduction In recent years many efficient numerical methods are constructed for solving different types of stochastic differential equations (SDEs) with different properties (see [12, 15, 19, 41]). Split- step Theta (SSθ) methods have attracted a lot of attention due to its advantage in flexibility ∗This research was partly financed by NSFC grant 71350005 and State Natural Sciences Foundation Monumental Projects 13&ZD166. yE-mail:[email protected] (Corresponding Author). 1 and stability. The split-step backward Euler (SSBE) method has been given [13, 26]. In order to improve the numerical properties based on the work of Higham et al. [13], many numerical methods depend on split-step methods and Milstein method have been introduced in [9, 11, 40, 43, 54]. In this paper, we derive the drifting split-step Theta Milstein (DSSθM) methods and modified split- step Theta Milstein (MSSθM) methods for use on SDEs. Numerical methods are needed for real option valuation in cases where analytic solutions are either unavailable or not easily compatible. In the area of options valuation the subject of numerical methods is very broad. There are many different types of numerical methods can be applied to real option valuation, approximation of partial differential equations (PDE) and approximation of stochastic process for underlying asset are available. There are several candidates models for the stochastic evolution of the underlying asset [25]. An overview of two of numerical methods available in the context of Black-Scholes-Merton [18, 45]. Brennan et al. [31] considered finite difference methods (FDM) which are governed by solving the underlying PDE. Monte Carlo (MC) approach is introduced by Boyle [38] give simulation of stochastic process. The comparative study of FDM and MC method for pricing European option was considered by [10]. In addition to basic usage of the methods, the methods are typically tailored to fit into a specific problem at hand (see [1, 34, 44]). In this study, we present the applicability of the two families of methods DSSθM and MSSθM that can be used to approximate a stochastic process arising from real options analysis for underlying asset and comparing with another two numerical methods FDM and MC method in assessment the uncertainty investment. In international trade, the Suez Canal has a strategic role such that providing a gateway between Asia and Europe. Nearly 10% of all world trade and 20% of world containers pass through the Canal. Its annual revenues do not exceed $ US 5 billion dollars [17]. So, The Egyptian Government launched two inter-related major projects to transform the Suez Canal region into an international logistics, maritime and industrial hub by exploiting the economic potential of the unique position of the Suez Canal. The government expects a world-class value-added services hub which will offer enhanced opportunities for investment across all economic sectors including ports and logistics, maritime services, industry, ICT, renewable energy (RE) and other areas of opportunity. There are many research studies demonstrate the economic value of the Suez Canal and discussed future vision and current projects for the Suez Canal area (see [5, 14, 20, 30, 32, 49]). Recently, The Egyptian government has faced increasing difficulties in satisfying growing elec- tricity demand. Final consumption is dominated by the residential and industrial sectors, with respective shares of 42.3 , and 31.4 percent [22]. The installed capacity 1 has been slow to grow and has increasing peak load (i.e., peak demand) 2 Iman and Nadine discussed the energy security in Egypt [21]. Egypt plans to expand its capacity of electricity generation from RE. Renewables in Egypt are mainly hydro power, wind and solar energy. Renewables share of electricity generation is 9 % only [16]. Recently, Egypt has adopted an ambitious plan to reach 20% of the total electricity generated from RE by 2020. The Egyptian government develops policies to encourage local and international investors to invest in projects to produce electricity from RE sources. In September 2014, Egypt issued the feed-in tariffs for electricity projects produced from solar and wind sources (see [35, 46, 51]). So, in this work we introduce investment opportunities in the RE sector in the light of the Suez Canal projects and policies are taken by the Egyptian Government to encourage investment in this sector. The renewable energy is uncertain investment such that it is long-term, costly and depend on a feed-in tariff system. A. Dixit et al. [2] addressed the subject of investment under uncertainty. Here, we follow the real options approach (ROA) to address the real option valuation (ROV) of an investment in a RE and the optimal time to invest under a number of different payments settings 1 Installed capacity is the maximum electric output a generator can produce under specific conditions. 2Peak electricity load is defined as the maximum electrical power that a system can supply for a sustained period above its average supply level, so as to meet peak demand. Such peak demand is dictated by the highest point of customer consumption of electricity at a given point in time (e.g., one hour), and is affected by seasonal factors (e.g., excessively hot or cold weather). 2 [23, 24]. Fernandes et al. [7] present a review of the current state of the art in the application of ROA to investments in non-renewable and renewable energy sources. Valuation of wind energy projects are introduced by L. M. Abadie et al. [28]. The approach of Solar and wind energy production as a ROA are discussed in [3, 27]. Our work introduce, a real option framework for use in RE investment. The real option framework consider the volatility in RE price during the project lifetime and the development lag between launch the project and start the production. Also, The real option framework differs of a previous work since, the new numerical methods DSSθM and MSSθM methods are integrated with option theory and the four economic elements cost, value, risk and flexibility to value a real option. The paper is organized as follows. In section 2, we derive the DSSθM and MSSθM methods. The projects to development the Suez Canal area are presented. The investment opportunity in sector RE in Egypt under the Suez canal projects and Egyptian government policies is discussed in section 3. In Section 4, we present a real option frame work. Numerical applications for the solar thermal in Egypt is discussed in section 5. 2 The Split-step Theta Milstein methods We consider the It^oSDEs of the form dy(t) = f(y(t))dt + g(y(t))dW (t); t 2 [t0;T ]; y(t0) = y0; (2.1) where f(y(t)) is the drift coefficient, g(y(t)) is the diffusion coefficients. Wiener process W (t) is defined on a given probability space (Ω; F;P ) with a filtration fFtgt≥0 which satisfies the usual conditions, whose increment ∆W (t) = W (t + ∆t) − W (t) is a Gaussian random variable N(0; ∆t).
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