• 대한수학회보
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• 제53권5호
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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).

• 한국건설관리학회논문집
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• 제22권6호
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• pp.87-95
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• 2021

본 연구는 새만금에 조성되는 환경생태용지사업의 실물옵션기법을 사용하여 경제성분석을 하였다. 30년 동안 운영하는 동안 수익에 영향을 주는 주요 요소들을 정의하였다. 수익의 변동성을 시나리오 분석방법으로 계산하여, 경영적 유연성을 적용할 수 있는 옵션 기반 분석방법을 제시하였다. 환경생태공원 경제성분석에 필요한 이용객수, 입장요금, 체험프로그램요금, 유지관리비용 등은 국내 유사한 환경생태공원의 사례를 분석하였다. 운영 중 포기할 수 있는 옵션권리를 가지는 것으로 가정하여 옵션가치를 계산하였다. B/C는 1미만의 값이 나오고, NPV는 음수로 나와 전통적인 경제성분석방법으로는 사업을 진행할 수가 없으나, 실물옵션분석으로 평가하면 사업의 가치가 상승하여 수익성을 확보할 수 있다. NPV(-466억원)과 옵션가치(281억원)의 가격차이 747억원의 가치상승이 발생하였다. 본 연구를 통해서 환경생태용지사업을 계획하려는 공공기관 및 민간사업자의 투자담당자는 본 연구에서 제시된 실물옵션기법을 활용하여 상황에 적절한 옵션을 선택하여 경제성분석을 할 수 있도록 도움을 줄 수 있을 것이다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권1호
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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.

• 재무관리연구
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• 제1권1호
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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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• 제18권1호
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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.

• 한국기술혁신학회:학술대회논문집
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• 한국기술혁신학회 2002년도 춘계학술대회
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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.

• 한국태양에너지학회 논문집
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• 제30권4호
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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.

• 한국항해항만학회지
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• 제33권7호
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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.

• 한국산학기술학회논문지
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• 제4권3호
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• pp.289-295
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• 2003

본 논문은 벤처기업을 합리적으로 평가할 수 있는 평가모형과 방법을 제시할 목적으로 코스닥 등록기업 중 무작위 추출에 의해 선정된 99개 벤처기업을 분석표본으로 삼았으며 기업별 시장주가로 2000년 1월부터 2001년12월까지의 최고, 최저, 평균주가를 추출하였다. 본 논문에서는 벤처기업가치평가 모형으로 실물옵션 평가모형 중 성장옵션모형을 이용하여 각 기업의 현재가격, 행사가격, 변동성, 행사기간, 무위험이자율의 5개 변수로 벤처기업의 옵션가치를 산출하고 여기에 잔존가치를 현금흐름 할인 법으로 할인 산출하여 그 값을 합하여 기업 가치를 평가하였고 또한 현금흐름 할인 법(DCF)을 이용하여 기업 가치를 평가하였다. 여기에 사용된 각종 파라미터 값은 우리나라 벤처기업과 산업의 자료를 중심으로 추출하여 본 모형에 적용, 기업의 가치를 실증적으로 평가하였다.

• 경영과학
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• 제31권1호
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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.