• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1411-1425
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• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• Korean Journal of Construction Engineering and Management
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• v.22 no.6
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• pp.87-95
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• 2021

This study analyzed economic feasibility using the real options theory of the eco-environment area project in Saemangeum. I defined the main factors affecting project sales during the 30 years operation period. The real option-based analysis is proposed through the managerial flexibility by estimating the volatility of project sales using scenarios analysis method. The number of visitors, admission fee, leisure program fee, and O&M costs required for economic analysis of eco-environment park were analyzed by reviewing cases of similar eco-environment parks in Korea. The option value is calculated by assuming that the developers have an option right that can be abandoned. B/C is less than 1 and NPV is negative, so it is impossible to proceed with the project using the traditional economic analysis. The project value difference between NPV (-46.6 billion Won) and option value (28.1 billion Won) increased by 74.7 billion Won. Through this study, decision-makers of public institutions and private developers who plan eco-environment area projects will be able to use the real option technique proposed in this study.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.1
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• pp.75-89
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• 2018

This paper presents the numerical valuation of the arithmetic Asian option by using the operator-splitting method (OSM). Since there is no closed-form solution for the arithmetic Asian option, finding a good numerical algorithm to value the arithmetic Asian option is important. In this paper, we focus on a two-dimensional PDE. The OSM is famous for dealing with plural-dimensional PDE using finite difference discretization. We provide a detailed numerical algorithm and compare results with MCS method to show the performance of the method.

• The Korean Journal of Financial Management
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• v.1 no.1
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• pp.133-149
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• 1985

The theory of option pricing has undergone rapid advances in recent years. Simultaneously, organized option markets have developed in the United States and Europe. The closed form solution for pricing options has only recently been developed, but its potential for application to problems in finance is tremendous. Almost all financial assets are really contingent claims. Especially, Black and Scholes(1973) suggest that the equity in a levered firm can be thought of as a call option. When shareholders issue bonds, it is equivalent to selling the assets of the firm to the bond holders in return for cash (the proceeds of the bond issues) and a call option. This paper takes the insight provided by Black and Scholes and shows how it may be applied to many of the traditional issues in corporate finance such as dividend policy, acquisitions and divestitures and capital structure. In this paper a combined capital asset pricing model (CAPM) and option pricing model (OPM) is considered and then applied to the derivation of equity value and its systematic risk. Essentially, this paper is an attempt to gain a clearer focus theoretically on the question of corporate stock risk and how the OPM adds to its understanding.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• Proceedings of the Korea Technology Innovation Society Conference
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• 2002.05b
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• pp.181-198
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• 2002

This article describes a methodology for evaluating huge aerospace R&D investments using the real options pricing method. Option pricing has been proposed as a useful approach for modeling investment in R&D. Two important features of R&D investments are that an R&D project takes time to complete and that the outcome of R&D investments is highly uncertain. This makes the analysis of R&D investments difficult. Traditional tools for project evaluation, like IRR or the NPV, are inadequate for coping with the high uncertainty. Hence, In this article I propose a log-transformed binomal lattice method, and it will show that option pricing might be an adequate framework for evaluating such types of aerospace investments.

• Journal of the Korean Solar Energy Society
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• v.30 no.4
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• pp.49-54
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• 2010

Most energy using in building part is mainly consumed for heating and cooling to meet occupancy's comfort temperature. Generally, heating energy consumption show high value than cooling energy in Korea because of high temperature difference in winter season as compared with summer in apartment building. The efforts to develope mechanical performance have been studied to reduce energy consumption in building energy field until now. However, the energy consumption in building is impacted by not only system performance but also PMV particularly at temperature and Clo value. This means that energy consumption can be changed by occupancy's comfort setting temperature in apartment building. This study investigated the passibility of overheating in apartment building by occupant' slow Clo and its setting temperature from preceding research and then the heating energy consumption by setting temperature was calculated with ESP-r. The effects of heating energy and $CO_2$ reduction are also evaluated quantitatively with Clo value. The results showed that keeping ISO-7730 standards can reduce heating energy up to 21% in compared with option 2; also, wearing underclothes with ISO-7730 standard can considerably reduce heating energy consumption up to 50%. As compared with option 2, the reduction of $CO_2$ emission for option 3 showed 0.63TCO2 of kerosene, 0.49TCO2 of LNG and 1.09TCO2 of electricity. The option 4 can be reduced by 1.48TCO2 of kerosene, 1.16TCO2 of LNG and 2.57TCO2 of electricity respectively.

• Journal of Navigation and Port Research
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• v.33 no.7
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• pp.469-476
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• 2009

Recent collapse of shipping market right after unprecedent surge clearly demonstrates that shipping industry is extremely risky. Due to the volatile movements of the freight rates, investors tend to ask higher rate of return; higher required return reduces the total net present value of the investment project. For several decades, the Discounted Cash Flow(DCF hereafter) analysis has been the most frequently used valuation technique. However, the main problem of the DCF analysis is its assumption that the discount rate would stay the same during the project life. In other words, it usually does not address the decisions that managers have after a project has been accepted. The purpose of this study is investigate a new valuation method of investment: the Real Option Analysis(ROA hereafter) on ship investment. By replacing the existing valuation methods with the new one, the research will present a new perspective on investment with uncertainty. While uncertainty increases risk of investment and consequently discounts the value of it in the traditional feasibility analysis, in the ROA, a new valuation method which will be addressed in the research, uncertainty means some additional value of flexibility so that the tool can help investors produce more accurate decisions. Contrary to the DCF analysis, the ROA takes managerial flexibilities into account. In reality, capital budgeting and project management is typically dynamic, rather than static in nature. The ROA finds and assesses the values of managerial flexibilities or real options in the investments. The main structures of the research will be as follows: (1) overview of the ship investment project, (2) evaluation of the project by the Net Present Value analysis, (3) evaluation of the same project by the Real Option Analysis, (4) comparision of the two techniques.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.4 no.3
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• pp.289-295
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• 2003

In this paper, the option valuation of venture business was calculated by utilizing growth option model, chosen from real option valuation method. The evaluation of venture business was estimated by adding option value to the terminal value discounted from cashflow method. As the result of the empirical analysis, ROV model applied in the Study is more reliable Han the DCF model concerning the pricing of venture business. Unlike the previous study of Schartz & Moon which only analyzed one venture business, this study estimated and analyzed the rational pricing of venture business with comparative methods using various parameters of sampling 99 domestic venture businesses.

• Korean Management Science Review
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• v.31 no.1
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• pp.17-26
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• 2014

This study presents a new real estate value analysis model considering the changes in the population structure. We propose a new model that takes advantage of the binomial option model one of the techniques of real options and considers the changes in the population structure. The real estate market price data of Seoul city from year 2001 to 2012 were extracted and the correlation analysis between real estate prices and changes in the population structure was performed. The result shows that they have positive correlation with one year time lag. The coefficient between the real estate prices and demographic changes was estimated using the OLS analysis and included in the traditional binomial option model to calculate the value of the property. It is assumed for the future price prediction that real estate invested in Seoul in January, 2013 will be sold within five years. Analysis result shows that the values of real estate in September of 2013 were predicted as 583.5 million won in the new model and as 582.4 million won in the traditional model. This reflects that the new model considering the change of population change gives better realistic performance than the traditional one.